Answer:
Length is 5, width is 3.
Step-by-step explanation:
The formula for the perimeter of a rectangle is:
[tex]P=2l+2w[/tex]
Where P is the perimeter, l is the length, and w is the width.
With the original length and width, the perimeter is 16, thus:
[tex]16=2l+2w[/tex]
Now, if we double the length, the 2l will become 4l. Also, the perimeter will change to 26. Thus:
[tex]26=4l+2w[/tex]
Now, we have a system of equations. We can solve it using elimination. Multiply everything by -1 in the first equation:
[tex]16=2l+2w\\-16=-2l-2w[/tex]
Now, add the equations:
[tex]-16=-2l-2w\\26=4l+2w[/tex]
-16 plus 26 is 10. -2l plus 4l is 2l. The 2w cancel. Thus:
[tex]10=2l[/tex]
Divide both sides by 2:
[tex]l=5[/tex]
So, the original length was 5.
To find the original width, substitute 5 back into the first equation:
[tex]16=2(5)+2w[/tex]
Multiply:
[tex]16=10+2w[/tex]
Subtract 10 from both sides:
[tex]2w=6[/tex]
Divide both sides by 2:
[tex]w=3[/tex]
So, the original width was 3.
And we're done!
Checking:
Originally, our length was 5 and 3. This means that the perimeter is 2(5+3)=2(8)=16 which is correct.
After we double our length, our length will be 10. This means that the new perimeter is 2(10+3)=2(13)=26. So, our answers are correct!
Let's assume that length be L and width be B.
Perimeter of rectangle is given by,
Perimeter = 2( L + B)
So,
⇒ 16 cm = 2 ( L + B )
⇒ 8cm = L + B _______( Say equation 1)
Now, we are given that when length is doubled perimeter is 26.
So,
⇒ 26 cm = 2 ( 2 L + B )
⇒ 13 cm = 2 L + B
⇒ 13 cm = L + L + B
Now use equation-1
⇒13 cm = L + 8cm
⇒13 cm - 8 cm = L
⇒5 cm = L
Therefore length is 5cm.
Now substitute this value in equation 1
⇒L + B = 8 cm
⇒5cm + B = 8 cm
⇒B = 8 cm - 5 cm
⇒B = 3 cm
Therefore breadth is 3 cm.
4. Factor x2 - 4x – 32.
Answer:
(x - 8)(x + 4)
Step-by-step explanation:
We need to find something that multiplies to 32 and adds up to 4.
The 2 special numbers would be -8 and 4.
-8(4) = -32
-8 + 4 = -4
We then simply write out the factored form:
(x - 8)(x + 4)
Answer: (x+4)(x-8)
Step-by-step explanation:
x^2 - 4x -32 Find two numbers that their product is -32 and their sum is -4. The numbers -8 and 4 will work out because -8 times 4 is -32 and -8 plus 4 is -4.
Now rewrite the whole polynomial as
x^2 +4x -8x -32 Now group them
(x^2 +4x) (-8x -32) Now factor each side
x(x +4) -8(x +4) factor out x+4
(x+4)(x-8)
Please answer the question in the picture
Answer: Slope = -7/5
=========================================================
Explanation:
Pick any two rows you want. I'll select the first two rows.
Each row represents an (x,y) point
The first row means (-8,55) is one point and the second row means (2,41) is another point.
Use these two points in the slope formula to get
m = (y2 - y1)/(x2 - x1)
m = (41-55)/(2- (-8) )
m = (41-55)/(2 + 8)
m = -14/10
m = -7/5 is the slope
The negative slope means the line goes downhill as you move from left to right.
Specifically, every time it drops 7 units the line moves over to the right 5 units.
slope = rise/run = -7/5
rise = -7, negative rise means we go down 7 spaces
run = 5 means we move to the right 5 spaces
What is the median of the data shown heights of the members of me.smith class
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{72}}}}}[/tex]
Step-by-step explanation:
Given data : 68 , 69 , 71 , 71 , 71 , 73 , 74 , 75 , 75 , 78
N ( total number of observation ) = 10
Finding the position of median
[tex] \boxed{ \sf{median = { (\frac{n + 1}{2} )}^{th \: item} }}[/tex]
[tex] \dashrightarrow{ \sf{median = { (\frac{10 + 1}{2} )}^{th \: item}}} [/tex]
[tex] \dashrightarrow{ \sf{median = {( \frac{11}{2}) }^{th \: item}} }[/tex]
[tex] \dashrightarrow{ \sf{ median = {5.5}^{th \: item}}} [/tex]
[tex] \sf{ {5.5}^{th} }[/tex] item is the average of 5 th and 6 th items.
Now, Finding the median
[tex] \dashrightarrow{ \sf{median = \frac{ {5}^{th}item + {6}^{th} item}{2} }}[/tex]
[tex] \dashrightarrow{ \sf{ \frac{71 + 73}{2} }}[/tex]
[tex] \dashrightarrow{ \sf{ \frac{144}{2} }}[/tex]
[tex] \dashrightarrow{ \sf{72}}[/tex]
Hope I helped!
Best regards! :D
at 1pm there are 16 seagulls at 3pm there are 40 how many increased in 2 hours
Answer:
24
Step-by-step explanation:
40-16=24 ( brainlist? ) and your welcome!
The two figures below, a regular hexagon and a regular pentagon, have the same
perimeter. What is the length of a side of the pentagon?
Answer:
69
Step-by-step explanation:
Perimeter = sum of all sides of a regular polygon = the number of sides*length of a side
Length of a side of the given regular hexagon = 3x + 5
Perimeter of hexagon = 6(3x + 5) = 6(3x) + 6(5) = 18x + 30
Length of a side of the given regular pentagon = 4x - 1
Perimeter of pentagon = 5(4x - 1) = 5(4x) - 5(1) = 20x - 5
Since we are told that the perimeter of the regular hexagon is the same as that of the regular pentagon, therefore:
18x + 30 = 20x - 5
Solve for x.
Subtract 20x from both sides
18x + 30 - 20x = 20x - 5 - 20x
-2x + 30 = -5
Subtract 30 from both sides
-2x+ 30 - 30 = -5 - 30
-2x = -35
Divide both sides by -2
x = -35/-2
x = 17.5
Length of a side of pentagon = 4x - 1
Plug in the value of x
4(17.5) - 1 = 70 - 1 = 69
length of a side of the pentagon = 69
Can someone help please
Answer:
option a
Step-by-step explanation:
in figure 1: 4n+8 = 4×1=4+8=12
figure 2:4n+8 =4×2=8+8=16 and so on
This summer, Silvia has been selling lemonade for $9 per cup. If Silvia has sold 19 cups so far, how much money has she made?
Answer:
$171
Step-by-step explanation:
Price of lemonade = $9 per cup
Quantity sold = 19 cups of lemonade
Revenue = price of the product × quantity of the product sold
Silvia's total revenue = price × Quantity
= $9 × 19 cups
= $171
Silvia has made a total of $171 from selling 19 cups of lemonade at $9 each
Allen and Renaldo are gaining weight for basketball season. Allen weighs
178 pounds and is gaining three pounds per week. Renaldo weighs
203 pounds but is gaining two pounds per week.
Part A: In how many weeks will they both weigh the same amount?
Which graph shows all natural numbers less than three?
Answer:
A i think
Step-by-step explanation:
Answer:
Try b out
Step-by-step explanation:
if that isn’t working for you {because it didn’t work for me}try b because it says less the 3 b is the only one the is less then three
which equation could you use to solve for x in the proportion 4/5=9/x?
Answer:
Hope u liked it..............
Find g(F(4)).
g(f(4)) =
4
Answer:
Step-by-step explanation:
f(4)= 4 - 7 = -3
g(-3) = (-3)^2 = 9
Answer:
g(f(4)) = 9
Step-by-step explanation:
Which equation could be used to create the graph
we have 10 marbles. five are blue Five are red. we select three marbles. what are the odds (in percent) that all three chosen are red?
Answer:
12.5%
Step-by-step explanation:
Step 1:
We need to find out the percentage of picking a marble that is red. In total, there are 10 marbles, and there are 5 red. To find the probability of picking a red marble, you need to do:
# of red / total marbles.
There are 5 red marbles and 10 total marbles, so the probability of getting a red marble is 5/10, and you can simplify it to 1/2 (5/10 * 5/5).
Step 2:
Now we can start finding the probability of finding the probability of choosing three red marbles in a row. Since we need to find the probability of choosing red marbles three times, you can multiply 1/2 by itself 3 times (1/2 * 1/2 * 1/2).
1/2 * 1/2 * 1/2 = 1/8
Step 3:
Now we need to convert the fraction into a percentage. You can find the percentage by dividing 1 by 8. You should get 0.125, and you can multiply 0.125 by 100, and your final answer should be 12.5%.
round the prices to the nearest dollar. use the rounded prices to estimate the total bill. Crackers $1.28, Cheese $8.92, Jam $ 3.77, Butter $9.34.
Answer:
Crackers $1
Cheese $9
Jam $4
Butter $9
1+9+4+9
= $23
-6 < 3х + 15 <6
Pls help show all work
Answer:
-7<x<-3
Step-by-step explanation:
separate into two inequalities:
3x+15>-6
3x+15<6
solve inequalities:
3x>-21........3x<-9
x>-7.............x<-3
-7<x<-3
I really need help on this. >.
Answer:
∠ D = 48°
Step-by-step explanation:
Since AC ~ BC then Δ ABC is isosceles and the base angles are equal, thus
∠ B = ∠ C = 69°, then
∠ ACB = 180° - (69 + 69)° = 180° - 138° = 42° ( sum of angles in Δ )
∠ DCE = ∠ ACB = 42° ( vertical angles )
∠ D = 180° - (90 + 42)° = 180° - 132° = 48°
Which can be used to prove that lines are parallel? 1.Vertical Angle Theorem 2.Alternate Interior Angles Theorem 3.Converse of Corresponding Angles Postulate 4.Converse of Same-Side Interior Angles Theorem
Answer:
4. Converse of Corresponding Angles Postulate
Step-by-step explanation:
There are several theorems to prove line relationships in plane geometry.
The proof of parallel lines is done by
(3) Converse of Corresponding Angles Postulate(4) Converse of Same-Side Interior Angles TheoremTo prove that lines are parallel, we make use of the concept of line transversal.
The vertical angle theorem is based on two lines intersecting at a point
The alternate interior angle theorem is used to determine the congruence of angles in a transversal of parallel lines
The converse of corresponding angles postulate, and the converse of same-side interior angles theorem are used to determine if lines are parallel based on the angles on the transversal.
Hence, the true options are (3) and (4)
Read more about parallel lines at:
https://brainly.com/question/2973276
(9x+1/2)+(7x-9 1/12)
Step-by-step explanation:
Input Equation can be rewritten:
= (9*1/2)+(7*-91/12)
= (9/2)+(7*-91/12)
= (4.5)+(7*-91/12)
= 4.5+(7*-91/12)
= 4.5+(-637/12)
= 4.5+(-53.083333333333)
= 4.5+-53.083333333333
= 4.5-53.083333333333
= -48.583333333333
hope this helps!
Answer:
16x-103/12
Step-by-step explanation:
(9x+1/2)+(7x-9 1/12)
9x+1/2+(7x-109/12)
remove parenthesis
9x+1/2+&x-109/12
combine like terms and differences.
16x-103/12
The value of the expression - 3. () is (Do without a calculator and use "T" as your fraction bar.)
Answer:
-10/21
Step-by-step explanation:
A police officer monitored the speed (mph) of the cars in a particular traffic area.
Prepare a frequency distribution for this data using 7 classes.
36, 21, 27, 24, 54, 28 ,36, 43,
22, 29, 37, 40, 26, 25, 38, 23,
44, 30, 26, 39, 37, 40, 38, 36,
41, 45, 52, 42, 43, 42, 48, 50, 53
Answer:
03/23/2020
OverdueLPercents and Fractions--Assigned
Spelling 600
DueTypeTitleScoreStatus
04/13/2020
OverdueTUnit Test--Assigned
Step-by-step explanation:
03/23/2020
OverdueLPercents and Fractions--Assigned
Spelling 600
DueTypeTitleScoreStatus
04/13/2020
OverdueTUnit Test--Assigned
Answer:
20-25: 5
26-30: 5
31-35: 0
36-40: 10
41-45: 7
46-50: 2
51-55: 4
Step-by-step explanation:
The answer is
20-25: 5
26-30: 5
31-35: 0
36-40: 10
41-45: 7
46-50: 2
51-55: 4
because to solve this problem you must make seven intervals and sort the numbers into those seven intervals.
Help plz!! It is about 1.62 x 106 miles from Venus to the Earth. It
is about 5.4 x 107 from Earth to Mars. How far is it total
from Venus to Earth then Earth to Mars? Write your
answer in scientific notation.
Answer:
The nearest that Mars has ever been to the Earth is 56 million km or about 34.8 million miles. On the opposite end of the scale, Mars and Earth can be a whopping 401 million km (249 million miles) apart when they are in opposition and both are at aphelion. The average distance between the two is 225 million km (140 million miles).
Step-by-step explanation:
Answer: 81.398 million miles
Step-by-step explanation: Hope that helped you.
Write 6 1/6 as an improper fraction
Answer:
37/6
Step-by-step explanation:
The improper fraction is 37/6.
What is improper fraction?
An improper fraction is defined as a fraction whose numerator is greater than the denominator. Suppose, x/y is an improper fraction, such that x > y. It is therefore, the improper fraction is always greater than one.
Fractions have two parts, numerator and denominator. If ⅓ is a fraction, then 1 is the numerator, and 3 is the denominator. An improper fraction has a numerator greater than the denominator. For example, 3/2 is an improper fraction.
Given fraction is [tex]6\frac{1}{6}[/tex]
firstly we will multiply 6 by 6 and then we will add 1
(36+1)/6
= 37/6
Which is improper fraction.
To know more about improper fraction, visit:
https://brainly.com/question/21449807
#SPJ2
Which expression is equivalent to 8x + 14 + 9x - 5
Answer:
Step-by-step explanation:
17x + 9
4.06/x = 0.18/0.5 please could you answer
Answer:
x=203/18
Step-by-step explanation:
convert the decimal into a fraction
203/50/x = 9/50 / 1/2
simply the complex fraction:
203/50x = 9/25
cross multiply
450x = 5075
divide both sides by 450:
x= 203/18
Answer:
X=11.2778
Step-by-step explanation:
4.06/X=0.18/0.5
cross multiply
0.18×X=4.06×0.5
0.18X=2.03
divide both sides by 0.18
0.18X/0.18=2.03/0.18
it becomes
X=2.03/0.18
X is therefore 11.2778
Solve d + (-d)
A. -2d
B. 0
C. d
D. 2d
Answer:
B. 0
Step-by-step explanation:
=>d+(-d)
=>d-d
=>0
Answer:
The answer is B. 0
Step-by-step explanation:
If the problem is d + (-d), then the answer is 0. Suppose that d = 7. Then it would be 7 + (-7), which is 0. You can't get any other number from that equation unless you do d + d or d - d.
Hope this helps.
* pleasegive me brainliest, i only need four more *
There are 3 different highways from City W to
City X, 4 different highways from City X to
City Y, and 3 different highways from City Y
to City Z. How many different routes are there
for a trip from City W to City X to City Y to
City Z?
Answer:
6 x 4 you have 4 numbers and each can be put in 6 different ways. so it is 24 i think
Step-by-step explanation:
Answer:
36
Step-by-step explanation:
4*3*3
12*3
36
HELP ME PLZ !! First one who answer these right gets brainliest !
Answer:
3. z = 0
I could only find the answer for number 3. I'm sorry! I hope this helps anyway!
Answer:
It might be very wrong
3. 6z + 12 = 30z + 12
0 = 24z
z = 0
4. 3x +3 +1 +2x = 4x +4+ x
4 +5x = 5x +4
0 = 0
5. - 2b = - 2b +4+3-3
0 = 4
two thirds as many books b. Translate into algebraic expression plz
Answer:
Ez, 2/3x
Step-by-step explanation:
Since he wants two thirds as many as book b so,
2 over 3 multiplied by b
What is Absolute value
Answer:
Absolute value is the distance on a number line. In other words, a number with absolute value will always be positive.
Answer:
Absolute value means to remove any negative sign in front of a number, and to think of all numbers as positive or zero.
10. a? = 3,600
algebra solve each equation
Answer:
a=360
Step-by-step explanation:
3600 divided by 10 is 360