Answers
Answer:
[tex]0< b\leq 14.5[/tex]
Step-by-step explanation:
Let's set up our equation. We know that rectangles have two pairs of equal sides. We are also given that one pair of those sides is 1 unit longer than the other pair. Finally, we are told that the perimeter is at most 60 meters. 'At most' tells me to set up an inequality.
I'm going to set up two equations to solve this problem. First, let [tex]a[/tex] be the longer side and [tex]b[/tex] be the shorter side.
[tex]2a+2b\leq 60[/tex]
Next, because the sides are consecutive integers and [tex]b[/tex] is shorter, we can say that [tex]a-b=1[/tex].
We now have a system of equations. I will solve using substitution.
[tex]a-b=1\\a=b+1[/tex]
Substitute [tex]a[/tex] into the first equation.
[tex]2(b+1)+2b\leq 60[/tex]
Solve algebraically.
[tex]2b+2+2b\leq 60\\4b+2\leq 60\\4b\leq 58\\b\leq 14.5[/tex]
So, [tex]b[/tex] could be any integer between 0 (since distance cannot be negative) and 14.5, also written as [tex]0<b\leq 14.5[/tex].
I hope this helped!
Related Questions
x/2 + 7 = 12 what color
Answers
Answer:
Red
Step-by-step explanation:
it is 10
I really need help,Please help:))))))
Answers
Please Help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!1111
Answers
x+12=38
If we all draw a triangle using the same three side lengths, will we all draw exactly the same triangle?
Answers
I JUST WANT POINTS /\ /\
_
comple the similarity statement for 2 triangles shown
HELP ASAP
Answers
£330 is divided between Henry, Gavin & Jim so that Henry gets twice as much as Gavin, and Gavin gets three times as much as Jim. How much does Gavin get?
Answers
Answer: Gavin gets $99
Step-by-step explanation:
Step 1
LET amount gotten by Jim be =x
amount gotten by Gavin be = 3x
amount gotten by Henry be = 2 x 3x = 6x
Such that the total amount shared by the three of them can be expressed as
x+ 3x + 6x = 330
Step 2
x+ 3x + 6x = 330
10x= 330
x= 330/10
x = 33
Jim gets $33
Gavin gets 3x= 3x 33= $99
Henry gets 6x= 6x 33= $198
Can someone plz help me the info is in the photo I'm begging you and I need the equation to show my work.
Answers
Answer:
$65.02
Step-by-step explanation:
15% of 85 = 12.75
sale price = 85-12.75 = 72.25
10% of 72.25 = 7.225 = 7.23
final cost = 72.25 - 7.23 = 65.02
PLEASE HELP
4 1/3 - 2 1/4
Answers
Answer:
4 1/3 - 2 1/4 = 25/12 or 2 1/12
Step-by-step explanation:
Frank is buying birthday candles for his grandmother's birthday cake. Her age, in years, will determine how many boxes of candles Frank will need to
buy. Which is the dependent quantity?
O b= how many boxes of candles Frank will buy
O a = Grandmother's age in years
Answers
Answer:
I believe A because the grandmothers age affects how many boxs of candles Frank will buy. Hope this helps
Step-by-step explanation:
What is the equation of the line that passes through the point (6,14) and is parallel to the line with the following equation? y= -4/3x - 1
Answers
Answer:
Which of the following is the equation of a line parallel to the line given by ... Parallel lines have the same slope and different y-intercepts. ... Thus the only one that fits the description is:.
What is the slope (-2,0) and (1,-4)
Answers
Answer:
-4/3
Step-by-step explanation:
y2-y1
--------
x2-x1
Explanation: you would first substitute in the values of x and y into the equation to find the slope, you then would simplify the numerator by multiplying -1 and -2 over 0-(-4) and subtract 2 from -1 and after this you would simplify the denominator by multiplying -1 by 4 and after you get your result you subtract 4 from 0 and you would then divide your 2 negative values results in a positive value which is m=3/4
HELP QUICK!! WILL GIVE BRAINILIST
Find the value of x in the triangle shown below.
Answers
Answer:
58
Step-by-step explanation:
Since two of the sides are both 6.2, we know that this is an isosceles triangle. Thus, the two angles opposite of x are both equal (61 degrees).
The angles inside of a triangle always add up to 180, so now we have
180 = 61 + 61 + x
Solving for x, we get x = 180 - (61 + 61) = 180 - 122 = 58
Janice used 1/3 yard of ribbon to tie a package and 1/6 yard of ribbon to tie a bow. How many yards of ribbon did Janice use? Is it 9/18? Which is 1/2? Sorry I really can't help her. I can help Sean with algebra no problem
Answers
Answer:
1/2 yard of ribbon
Step-by-step explanation:
Janice used 1/3 yard of ribbon to tie a package and 1/6 yard of ribbon to tie a bow. How many yards of ribbon did Janice use?
The number of yards that Janice used is calculated as:
1/3 yard + 1/6 yard
Lowest Common Denominator = 6
2 + 1/6
= 3/6
= 1/2 yard of ribbon
Janice used 1/2 yard of ribbon
In BCD, H is the centroid. If DE=51 find HE.
Answers
Answer:
[tex]HE=17[/tex] units.
Step-by-step explanation:
In a triangle, centroid is the intersecting point of the medians.
Centroid divides each of the medians in ratio [tex]2:1[/tex]
So,
[tex]\frac{DH}{HE}=\frac{2}{1} \\\\\frac{DH}{HE}+1=\frac{2}{1}+1\\\\ \frac{DH+HE}{HE} =3\\\\\frac{DE}{HE}=3[/tex]
Put [tex]DE=51[/tex] units
[tex]\frac{51}{HE}=3\\\\HE=\frac{51}{3}[/tex]
[tex]HE=17[/tex] units.
The lengths of two sides of a triangle are given.
Find the range of possible lengths for the third side. 17 cm and 12 cm
Answers
Answer:
Range = 5 - 29
Step-by-step explanation:
a + b > c
a+c > b
c+b > a
so
17+ 12 > c ,,,,,,,,,,,,,,,,,,,,,,,,,,,, so it should be lesser than 17+12 which is 29
17 +c > 12 ,,,,,,,,,,,,,,,,,,,,,,,,, and it should be greater than 17- 12 = 5
c+12 > 17 ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, same here, it should be greater than 17- 12 = 5
So the range is ,
17 + 12
to
17-12
whcih is - (5 to 29)
I hope I am right!!!
Please help me. what is 10x10+4
Answers
104
Step-by-step explanation:
EUJDJFKFKDEISHXHJRD
Answer:
104
10 × 10 = 100
100 + 4 = 104
Therefor, the answer is 104.
Find mZA. The diagram is not to scale.
96°
118°
159
104°
Answers
Answer:
A=73
Step-by-step explanation:
sum of interior angles is (n-2)*180
5 sides, so (5-2)*180 = 3x180=540
sum of current interior angles (118+96+115+104)=433
subtract 540-433=107
This is NOT "A", this is your final interior measurement.
To get "A", take 180-107=73
A=73 degrees
Which of the following equations, where t represents time in days, and represents length in centimeters,
could be descriptions of the growth of a bamboo plant?
Choose all answers that apply:
A
L=1.1t
B
L = 2.5t
C
L = 7.1t
D
L = 9.3t
Answers
C.L=3.6t
D.L=7.1t
E.L=9.3t
(I am really not sure of this)
A ski slope is 320 yards long with a vertical drop of 100 yards. Find the
angle of elevation of the ski run. Round to the nearest degree.
Answers
Answer:
18°
Step-by-step explanation:
A ski slope is 320 yards long with a vertical drop of 100 yards. Find the
angle of elevation of the ski run. Round to the nearest degree.
The formula for angle of elevation is given as:
sin θ =Opposite/ Hypotenuse
Opposite = Vertical drop = 100 yards
Hypotenuse = Ski slope = 320 yards.
Angle of elevation =
sin θ = 100/320
sin θ = 0.3125
θ = arc sin(0.3125)
= 18.209956864°
Approximately = 18°
Solve for p
PLEASE ANSWER FAST
Answers
Answer:
p = 43
Step-by-step explanation:
p + 7 + 3p + 1 = 180
4p + 8 = 180
4p = 172
p = 43
Answer:
yo, i answered this yesterday, but the answer button wasn't available omg
p =43
Step-by-step explanation:
A projectile is thrown upward so that its distance above the ground after t seconds is h=-121t^2 +504t. After how many seconds does it reach it maximum height?
Answers
Answer:
2.08secs
Step-by-step explanation:
Given the equation modeled by the height as h=-121t^2 +504t
The velocity of the object at the max height is zero, hence;
v = dh/dt = 0
dh/dt = -2(121)t + 504
dh/dt = -242t + 504
0 = -242t + 504
242t = 504
t = 504/242
t = 2.08secs
Hence the projectile reaches its maximum height after 2.08secs
Item 3 The Hampton family used 17,158 kilowatts of electricity last year. They used about the same amount of electricity each week. About how many kilowatts of electricity did the Hampton family use each week? (There are 52 weeks in a year).
Answers
Please help :)
If it's correct I might give your brainliest
Answers
could you help me with this question plz
Answers
Answer:
In last year's survey, 10 people asked for a playwriting class.
Step-by-step explanation:
It supports the statement 'a playwriting class would be well attended' because it provides the proof that at least 10 people wanted a playwriting class to be hosted - this data shows a playwriting class would indeed be popular.
Simplify:
4n + 6 - (5n+3)
Answers
Answer:
-n+3
Step-by-step explanation:
Subtract the 5n and 3
Last week, the price of apples at a grocery store was $1.60 per pound. This week, apples at the same grocery store are on sale at a 10% discount. What is the total price of 4 1/2 pounds of apples this week at the grocery store?
Answers
Answer:
6.48 dollars total,
Step-by-step explanation:
First, you would want to multiply the amount of money per pound, by the amount of pounds. 1.60 multiplied by 4 1/2 or 4.5, would equal to 7.2 dollars. In order to find 10% of 7.2, your would need to multiply 7.2 by 0.10, which would give you 0.72. Then you would subtract 7.2 by 0.72 to get 6.48. So your answer would be 6.48 dollars. Hoped this helped.
Kris has 3 daughters who all live in different cities across Georgia. She wants to live somewhere that is an equal distance from each of her daughters. She mapped out the 3 cities and drew a triangle connecting them. How can she find a point on the map that is an equal distance from all 3 cities?
construct the incenter
construct the orthocenter
estimate the best place
construct the circumcenter
Answers
===========================================================
Explanation:
Consider triangle ABC. The vertex points are at A,B,C. These represent the three cities in which the three different daughters live. Constructing the circumcenter will produce a circle such that all three points A,B,C are on that circle. Let's say that D is the center of that circle.
This means that AD, BD, CD are all radii of this same circle. Radii of the same circle are the same length, which is why point D is equally distant from A,B,C. If the mother lives at point D, then she will travel the same distance to visit any three of her daughters. See the note below.
To construct the circumcenter, we form perpendicular bisectors to segments AB, BC and AC. Technically you only need two of them. All three of these perpendicular bisectors intersect at point D.
-------------
Note: Keep in mind that roads aren't completely straight, so that means we'll have to factor in the curvature of each road. But to keep things simple, we assume each road is a straight line segment.
Pls help me no explain need ❤️❤️❤️
Answers
Answer:
[tex]\displaystyle m=2[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Reading a Cartesian planeCoordinates (x, y)Slope Formula: [tex]\displaystyle m=\frac{y_2-y_1}{x_2-x_1}[/tex]Step-by-step explanation:
Step 1: Define
Find points from graph.
Point (-5, 0)
Point (-9, -8)
Step 2: Find slope m
Simply plug in the 2 coordinates into the slope formula to find slope m
Substitute in points [Slope Formula]: [tex]\displaystyle m=\frac{-8-0}{-9+5}[/tex][Fraction] Subtract/Add: [tex]\displaystyle m=\frac{-8}{-4}[/tex][Fraction] Divide: [tex]\displaystyle m=2[/tex]helpppppp
kddbbbjkluuuu
Answers
How many questions are there?
Simplify the expression using the distributive property:
5 (2x – 3y + 4)
Answers
Apply the distributive property. 5 (2x) +5 (−3y) + 5 ⋅ 4
Multiply 2 by 5
10x + 5 ( − 3y ) + 5 ⋅ 4
Multiply −3 by 5 10x − 15y + 5 ⋅ 4
Multiply 5 by 4
Answer: 10x −15y + 20
Tip: The sign "⋅" means multiply