The area of a rectangular wall of a barn is 135 square feet. It's length is 6 feet longer than a width. Find the length and width of the wall of the barn
Answer: [tex]15\ ft,6\ ft[/tex]
Step-by-step explanation:
Given
The area of a rectangular wall of a barn is [tex]135\ ft^2[/tex]
Suppose the width of the wall is [tex]x[/tex]
So, the length of the wall is [tex]6+x[/tex]
Area can be written as the product of length and width
[tex]\Rightarrow (6+x)x=135\\\Rightarrow 6x+x^2=135\\\Rightarrow x^2+6x-135=0\\\Rightarrow x=\dfrac{-6\pm \sqrt{6^2-4(1)(-135)}}{2(1)}\\\\\Rightarrow x=\dfrac{-6\pm 24}{2}\\\\\Rightarrow x=-15,9[/tex]
neglecting the negative value, width of the wall is [tex]9\ ft[/tex]
So, the length of the wall is [tex]9+6=15\ ft[/tex]
Sides are added to a convex polygon so that the sum of its interior angle measures is increased by 540°. How many sides are added to the polygon. Explain your reasoning.
Use the Substitution method to solve the system of equations
3x+4y=10
y=x-1
Answer: 2
Step-by-step explanation:
3x+4y=10
3x+4(x-1)=10
3x+4x-4=10
7x-4=10
Add 4 to both sides
7x=14
x=2
Answer:(2,1)
Step-by-step explanation:ap3x beans
How many three digit numbers greater than 540 can be formed using the digits
0,2,4,5,6,8 ?
Answer:
Step-by-step explanation:
Write an equation of the line that passes through the point (4,5) and has a slope of -2.
Answer:
y = - 2x + 13
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Here m = - 2 , then
y = - 2x + c ← is the partial equation
To find c substitute (4, 5) into the partial equation
5 = - 8 + c ⇒ c = 5 + 8 = 13
y = - 2x + 13 ← equation of line
Answer:
Step-by-step explanation:
slope=-2
now using slope intercet formof equation of straight line,we get
y=mx+b
or, y=-2x + b
y + 2x =b
2x + y=b ...................... eq(i)
since the line passes through the point (4,5) it satisfies the equation (i)
y=5 and x=4 so,
equation is 2x +y =b
2*4 + 5=b
8+5=b
13=b
substituting the value of b in eq(i)
2x + y=b
2x + y=13
2x + y-13=0 is the required equation of the line.
Henry sees a train with 8 cars. Each car has 5 windows on the side that henry sees. Which number sentence can be used to find how many windows henry sees
Answer:
8 x 5 x 2
Step-by-step explanation:
total number of windows seen = total number of cars x total number of windows a car has
total number of windows a car has = number of windows a car has x total number of sides = 5 x 2
total number of windows seen = 8 x 5 x 2
Three friends go out for pizza. A slice costs $3.75 a soda costs $2.25. If they each get a soda and a total of 8 slices, how much did they spend altogether
Rina added 5/6 of a bag of soil to her garden,Her neigboir Jessa Added 1 1/8 bags of soil to her garden,How much more soil did jessa add than rina?
Which of the following rational functions is graphed below?
Answer:
"C" has to be the answer...
there is a vertical asymptote at -5
thus you need a denominator that is zero at -5
plug in -5 into the equations only "C" ends up with a zero in the denominator at that point
Step-by-step explanation:
(47.5+45.5+48.5+46.5+47+45+48+46+49)/9
:)
Answer:
47 and now I'm just typing so it lets me answer
Step-by-step explanation:
calculator
Avery invested $8,100 in an account paying an interest rate of 6 1 4 6 4 1 % compounded continuously. Khloe invested $8,100 in an account paying an interest rate of 5 5 8 5 8 5 % compounded monthly. To the nearest hundredth of a year, how much longer would it take for Khloe's money to double than for Avery's money to double
Answer:
1.26 years
Step-by-step explanation:
Which equations can pair with y = 3x – 2 to create a consistent and independent system? x = 3y – 2 y = –3x – 2 y = 3x + 2 6x – 2y = 4 3y – x = –2
Answer:
[tex](a)\ x = 3y - 2[/tex]
[tex](b)\ y = -3x - 2[/tex]
[tex](e)\ 3y - x = -2[/tex]
Step-by-step explanation:
Given
[tex]y =3x -2[/tex]
Required
Equations that can create consistent and independent systems
For a pair of equation to have consistent and independent systems, the equations must have different slopes.
An equation of the form [tex]y = mx + c[/tex] has m has its slope.
In [tex]y =3x -2[/tex]
[tex]m = 3[/tex] --- slope
Considering the options
[tex](a)\ x = 3y - 2[/tex]
Make y the subject
[tex]x = 3y - 2[/tex]
[tex]3y = x+2[/tex]
Divide by 3
[tex]y = \frac{1}{3}x+\frac{2}{3}[/tex]
The slope is:
[tex]m_1 = \frac{1}{3}[/tex]
Hence, (a) can make a consistent and independent system with [tex]y =3x -2[/tex]
[tex](b)\ y = -3x - 2[/tex]
The slope is:
[tex]m= -3[/tex]
Hence, (b) can make a consistent and independent system with [tex]y =3x -2[/tex]
[tex](c)\ y = 3x + 2[/tex]
The slope is:
[tex]m=3[/tex]
Hence, (c) cannot make a consistent and independent system with [tex]y =3x -2[/tex]
[tex](d)\ 6x - 2y = 4[/tex]
Make y the subject
[tex]2y = 6x -4[/tex]
Divide by 2
[tex]y = 3x -2[/tex]
The slope is
[tex]m =3[/tex]
Hence, (d) cannot make a consistent and independent system with [tex]y =3x -2[/tex]
[tex](e)\ 3y - x = -2[/tex]
Make y the subject
[tex]3y = x -2[/tex]
Divide by 3
[tex]y = \frac{1}{3}x -\frac{2}{3}[/tex]
The slope is:
[tex]m = \frac{1}{3}[/tex]
Hence, (e) can make a consistent and independent system with [tex]y =3x -2[/tex]
determine the equation of the circle graphed below.
( please help me )
Answer:
(x - 3)² + (y + 5)² = 10
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
Here (h, k) = (3, - 5 ) , then
(x - 3)² + (y - (- 5) )² = r² , that is
(x - 3)² + (y + 5)² = r²
r is the distance from the centre to a point on the line
Calculate r using the distance formula
r = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = (3, - 5) and (x₂, y₂ ) = (6, - 4)
r = [tex]\sqrt{(6-3)^2+(-4+5)^2}[/tex]
= [tex]\sqrt{3^2+1^2}[/tex]
= [tex]\sqrt{9+1}[/tex]
= [tex]\sqrt{10}[/tex] ⇒ r² = ([tex]\sqrt{10}[/tex] )² = 10
(x - 3)² + (y + 5)² = 10 ← equation of circle
a circular tabletop has a diameter of 2.1 m. what is its area
PLEASE HELP! NO SPAMMING! SHOW WORK!
The ratio of the dimensions of the model to the dimensions of the Great Pyramid is about 1 to 38. The surface area of the real pyramid is about how many times the surface area of the model.
Dimensions: a pyramid with a square base.
base sides: 6m
height: 4m
========================================================
Explanation:
Consider a square on paper that is 3 inches by 3 inches. It's area would be 3*3 = 9 square inches.
The ratio 1 to 38 means that 1 inch on paper corresponds to 38 inches in real life (assuming the "1 to 38" doesn't have any verbal units attached to it; if so, then refer to the note below). So a 3 by 3 square corresponds to a 114 by 114 square because 3*38 = 114.
The area of the second larger square is 114*114 = 12,996 square inches.
Now divide the two areas: (12,996)/(9) = 1444
It's probably not entirely obvious, but through a bit of playing around with various numbers, you should find that 38^2 = 1444. It's not a coincidence that this happens. The linear scale factor is 38 which means the area scale factor is 38^2 = 1444.
In short, the larger square in real life has area that is 1444 times that of its scaled down counterpart.
Or put another way:
large area = 1444*(small area)
------------------
Side note: This all assumes that the numbers in "1 to 38" are both the same unit. If we had a mixed ratio of units like "1 inch to 38 feet", then the answer would be different. You would need to convert from feet to inches, and then follow the steps above to get a different answer.
analee wants to buy a flute that costs $240 she has saved $20 each week for 3 weeks how many more weeks does analee need to save money if she continues to save $20 each week
Answer:
9
Step-by-step explanation:
240/20=12
That mean's takes 12 weeks in total.
But, 3 weeks was already done.
So, you do 12 -3.
Which equals 9.
So, the answer is 9.
Please give me brainiest!!!
∠aangle, a and \angle b∠bangle, b are complementary angles. \angle a∠aangle, a measures 55^\circ55 ∘ 55, degrees. What is the measure of \angle b∠bangle, b? \Large{^\circ} ∘
Answer:
35
Step-by-step explanation:
Cause they both add up to a right angle which is 90 degrees. so 90-55=35
∠angle, a and ∠angle, b are complementary angles. ∠ an ∠angle, a measures 5 5 ∘ 55 ∘ 55, degrees. so we can conclude that ∠b = 35.
What is the angle sum property?The angle sum property of a triangle states that the sum of the interior angles of a triangle is 180 degrees.
∠angle, a and ∠angle, b are complementary angles.
∠ an ∠angle, a measures 5 5 ∘ 55 ∘ 55, degrees.
we want to measure ∠ b
We know that the sum of Complementary angles is equal to 90 degrees.
so to find the measure of angle B we subtract the given angle from 90
∠ b + ∠ a = 90
∠ b + 55 = 90
∠ b = 90-55
∠ b =35
so we can conclude that ∠b = 35.
Learn more about the triangles;
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I know how do it but the fraction is confusing me please help will give branliest
Replace x and y in the equation with what they tell you x and y equal.
2(14) / 13 - 9(1/3)
Now simplify:
2 x 14 = 28
9 x 1/3 = 3
You now have:
28/13-3
Simplify again to het 28/10 this can be reduced to 14/5
HELP PLEASE HELP MEEEE PLEASEEE
Answer: a. x=4 b. x=17.5
Step-by-step explanation:
a. 5x/2+1=11
subtract 1 from both sides : 5x/2=10
multiply both sides by 2 : 5x=20
divide both sides by 4 : x=4
b. 2x/7-3=2
add 3 to both sides : 2x/7=5
multiply both sides by 7 : 2x=35
divide both sides by 2 : x=17.5
PLEASE HELPP
64, 16, 4, 1 converging or diverging
Answer:
The series 64, 16, 4, 1 is convergent.
Step-by-step explanation:
Let be [tex]\{x_{1}, x_{2},...,x_{n}\}[/tex] the set of values of the series. A series is convergent if and only if:
[tex]\frac{x_{i + 1}}{x_{i}} < 1, \, \forall\,i\in \mathbb{N}[/tex] (1)
If we know that [tex]x_{1} = 64[/tex], [tex]x_{2} = 16[/tex], [tex]x_{3} = 4[/tex] and [tex]x_{4} = 1[/tex], then the convergence ratio of each pair of consecutive values are, respectively:
[tex]\frac{x_{2}}{x_{1}} = \frac{1}{4}[/tex], [tex]\frac{x_{3}}{x_{2}} = \frac{1}{4}[/tex], [tex]\frac{x_{4}}{x_{3}} = \frac{1}{4}[/tex]
Hence, the series 64, 16, 4, 1 is convergent.
Help Please.
Classify the tringle below.
acute right
equilateral
isosceles right
isosceles scalene
Answer:
isosceles right
Step-by-step explanation:
It is an isosceles right angled triangle because according to the figure it's two sides are equal which means it is isosceles triangle and there is 90 degree symbol which denotes right angle.
An Isosceles Right Triangle is a right triangle that consists of two equal length legs. Since the two legs of the right triangle are equal in length, the corresponding angles would also be congruent. Thus, in an isosceles right triangle, two legs and the two acute angles are congruent.
Answer:
it is a right angled triangle
Step-by-step explanation:
it has a hypothenuse,opposite and adjacent
у X -7 -5 -5 -4 -3 -2 ברן 4 LO- To 2 -3 -6 -7 In this graph, the v-intercept of the line is 1. The equation of the line is v=
Answer:
The y intercepts is -2
y = 1x-2
Step-by-step explanation:
The y intercept is where it crosses the y axis
The y intercepts is -2
We need to determine the slope, by using to points on the line
(0,-2) and (2,0)
m = (y2-y1)/(x2-x1)
= (0 --2)/(2-0)
= (0+2)/(2-0)
= 2/2
= 1
The equation for the line is
y = mx+b where m is the slope and b is the y intercept
y = 1x-2
Find the zeros of the function.
Enter the solutions from least to greatest.
h(2) = -5x2 + 180
lesser x=
greater x =
Answer:
lesser x = -6
greater x = 6
Step-by-step explanation:
-5x² + 180 = 0
5x² = 180
x² = 36
x = ±6
Answer:
x = - 6, x = 6
Step-by-step explanation:
Given
h(x) = - 5x² + 180
To find the zeros let h(x) = 0 , that is
- 5x² + 180 = 0 ( subtract 180 from both sides )
- 5x² = - 180 ( divide both sides by - 5 )
x² = 36 ( take the square root of both sides )
x = ± [tex]\sqrt{36}[/tex] = ± 6 , then
lesser x = - 6
greater x = + 6
A 5 kg stone falls from height of 100m and penetrate 2m in a layer of sand. The force applied by ground is
Answer:
49N
Step-by-step explanation:
Below is the calculation for the force applied:
It is given that the mass of stone is 5 kg and it falls from the height of 100 meters. Therefore, a force can be determined by multiplying the mass will a constant value of "a".
Force = Mass x a
Force = 5 x 9.8
Force = 49 N
Since the action-reaction are equal and opposite so the each will apply the same force.
HI I NEED HELP ASAP I GIVE BRAINLEST IF YOU GET IT RIGHT
Solve for r.
Enter the solutions from least to greatest.
-2x2 – 9 = -107
lesser I =
greater x =
Step-by-step explanation:
[tex] - 2 {x}^{2} - 9 = - 107 \\ - {2x}^{2} = - 98 \\ {x}^{2} = 49 \\ x = \sqrt{49} \\ x = 7 \\ { \boxed{lesser : \: - 7}} \\ { \boxed{greater : \: + 7}}[/tex]
I need help with number 1 and 2
Answer:
1. 452.39
2. 615.75
Step-by-step explanation:
area of a circle = A=πr2
Can someone please help me with this question
Answer:
If x is the one vertically opposite to 40, then x will be 40, due to vertically opposite angles.
(b) Simplify 4q2 – 3q2
Hellllllppppppppppp
Plsssss
Answer:
q^2
Step-by-step explanation:
Answer:
q^2
Step-by-step explanation:
4q^2 – 3q^2
Factor out the q^2
q^2 ( 4-3)
q^2(1)
1q^2
q^2
Which is equal to 6-45?
Answer:
-39
Step-by-step explanation:
Please give me brainliest.
Answer:
-39
Step-by-step explanation:
6-45
A buyer owes a seller $45 and has gone to pay $6. The remaining dollars which the buyer must give the seller is $39.