Given:
A rectangle has a length of 8 and a width of 4.
Four equal rectangles are drawn within that rectangle, creating the longest lengths possible for the rectangles.
To find:
The sum of the perimeters of two of these equal rectangles.
Solution:
We have to draw 2 lines which are bisecting the length and width respectively, to divide a rectangle in 4 equal parts with longest lengths.
Half of length 8 = 4
Half of width 4 = 2
It means each rectangle have a length of 4 and a width of 2.
Perimeter of a rectangle is
[tex]Perimeter=2(length+width)[/tex]
[tex]Perimeter=2(4+2)[/tex]
[tex]Perimeter=2(6)[/tex]
[tex]Perimeter=12[/tex]
So, perimeter of each equal rectangle is 12 units.
Sum of the perimeters of two of these equal rectangles is
[tex]12+12=24[/tex]
Therefore, sum of the perimeters of two of these equal rectangles is 24.
help please I'm dumb
Answer:
I am too so sorry
Step-by-step explanation:
Answer:
3 and 3/4 yards
Step-by-step explanation:
she needs 10 and a half yards, if she already has 2 and a half and 4 and 1/4th, she would only need 3 and 3/4 yards left
i have 375 baseball cards in my collection . this is 5 times more than my brother has in his collection . how many do we have all together
Answer:
450
Step-by-step explanation:
A certain number of sixes and nines is added to give a sum of 126; if the number of sixes and nines is interchanged, the new sum is 114. How many of each were there originally?
Answer:
Original number of sixes = 6
Original number of nines = 10
Step-by-step explanation:
We are told in the question that:
A certain number of sixes and nines is added to give a sum of 126
Let us represent originally
the number of sixes = a
the number of nines = b
Hence:
6 × a + 9 × b = 126
6a + 9b = 126.....Equation 1
If the number of sixes and nines is interchanged, the new sum is 114.
For this second part, because it is interchanged,
Let us represent
the number of sixes = b
the number of nines = a
6 × b + 9 × a = 114
6b + 9a = 114.......Equation 2
9a + 6b = 114 .......Equation 2
6a + 9b = 126.....Equation 1
9a + 6b = 114 .......Equation 2
We solve using Elimination method
Multiply Equation 1 by the coefficient of a in Equation 2
Multiply Equation 2 by the coefficient of a in Equation 1
6a + 9b = 126.....Equation 1 × 9
9a + 6b = 114 .......Equation 2 × 6
54a + 81b = 1134 ........ Equation 3
54a + 36b = 684.........Equation 4
Subtract Equation 4 from Equation 3
= 45b = 450
divide both sides by b
45b/45 = 450/45
b = 10
Therefore, since the original the number of nines = b,
Original number of nines = 10
Also, to find the original number of sixes = a
We substitute 10 for b in Equation 1
6a + 9b = 126.....Equation 1
6a + 9 × 10 = 126
6a + 90 = 126
6a = 126 - 90
6a = 36
a = 36/6
a = 6
Therefore, the original number of sixes is 6
Are the following lines parallel, perpendicular, or neither: x=6 and x=12 Please show work or explain
Answer:
x=6 and x=12 are parallel.
Step-by-step explanation:
If you graph x=6 it will be a straight verticle line on the x-axis where 6 is, same with x=12 (put a vertical line on 12 for the x-axis). When you put these both on the same graph you see they are directly across from each other but will never touch. Therefore, they are parallel. If you are writing this on paper, simply draw a graph to show this.
Can Someone please help me with this math problem.
Answer:
[tex]\huge\boxed{x=9}[/tex]
Step-by-step explanation:
We know that ∠A and ∠B are the same exact length. Since one of the angles is given to us in an exact length, we can set the measures equal to each other.
[tex]4x + 9 = 45[/tex]
Let’s solve for x.
[tex]4x +9-9=45-9\\\\4x=36\\\\x=9[/tex]
Hope this helped!
Use linear approximation to approximate √25.3 as follows.
Let f(x)=√x. The equation of the tangent line to f(x) at x=25 can be written in the form y=mx+b. Compute m,b.
Using this, find the approximation for √25.3.
The idea is to use the tangent line to [tex]f(x)=\sqrt x[/tex] at [tex]x=25[/tex] in order to approximate [tex]f(25.3)=\sqrt{25.3}[/tex].
We have
[tex]f(x)=\sqrt x\implies f(25)=\sqrt{25}=5[/tex]
[tex]f'(x)=\dfrac1{2\sqrt x}\implies f'(25)=\dfrac1{10}[/tex]
so the linear approximation to [tex]f(x)[/tex] is
[tex]L(x)=f(5)+f'(5)(x-5)=5+\dfrac{x-5}{10}=\dfrac x{10}+\dfrac92[/tex]
Hence [tex]m=\frac1{10}[/tex] and [tex]b=\frac92[/tex].
Then
[tex]f(25.3)\approx L(25.3)=\dfrac{25.3}{10}+\dfrac92=\boxed{7.03}[/tex]
The function h (x) = StartFraction 2 (x + 3) Over x EndFraction is a result of the composition (g compose f) (x). If g (x) = StartFraction 2 over x EndFraction, what is f(x)?
Answer:
[tex]f(x) = \frac{2x}{2x + 3}[/tex]
Step-by-step explanation:
Given
[tex]h(x) = \frac{2x + 3}{x}[/tex]
[tex]g(x) = \frac{2}{x}[/tex]
[tex]g(f(x)) = h(x)[/tex]
Required
Find f(x)
[tex]g(x) = \frac{2}{x}[/tex]
Substitute x for f(x)
[tex]g(f(x)) = \frac{2}{f(x)}[/tex]
Recall that
[tex]g(f(x)) = h(x)[/tex]
This gives
[tex]\frac{2}{f(x)} = \frac{2x + 3}{x}[/tex]
Cross Multiply
[tex]f(x) * (2x + 3) = 2 * x[/tex]
[tex]f(x) * (2x + 3) = 2 x[/tex]
Make f(x) the subject of formula
[tex]f(x) = \frac{2x}{2x + 3}[/tex]
Answer:
x/x+3
Step-by-step explanation:
The second statement is the
of the first.
Foundations of Geometry
Answer:
C. contrapositive
Step-by-step explanation:
The contrapositive is formed by negating both statements and swapping them, as here.
medicare provides medical insurance for those
a. under age 55
b. over age 50
c. over age 65
d. under age 15
Answer:
c. over 65:))
Which mathematical term is undefined?
A. Line
B. Parallel Lines
C. Angle
D. Line Segment
Answer:
Line
Step-by-step explanation:
I got it right.
mark brainliest
please
DVDs are on sale for $29 each. Felipe writes the expression 2 x 29 to find the cost in dollars of buying 2
DVDs
How can you rewrite Felipe's expression using the Distributive Property?
Answer:
1(29 + 29)= a
Step-by-step explanation:
If the DVD costs 29$, and he buys 2, then you will just add them and multiply them by one.
I need help please
what is the length of the altitude of the equilateral triangle
Answer:
Altitude of Equilateral Triangle
Step-by-step explanation:
Classify the equilibrium solutions as asymptotically stable or unstable. Entry field with incorrect answer is unstable, is unstable, is unstable. is unstable, is asymptotically stable, is unstable. is asymptotically stable, is unstable, is asymptotically stable. is asymptotically stable, is asymptotically stable, is unstable. is unstable, is asymptotically stable, is asymptotically stable.
Answer:
asymptotically stable.
Step-by-step explanation:
Equilibrium solutions in which solutions that starts near and then moves away from equilibrium solutions are asymptotically unstable. Equilibrium solutions which solutions starts nears and then move towards the equilibrium are asymptotically stable.
4. A bakery can make 58 packages of cookies
in one hour. There are 24 cookies in each
package. Which is the best estimate of the
number of cookies the bakery makes in one
hour.
a. 12,000
b. 120
c. 1,200
Show work to support your answer.
Answer:
C
Step-by-step explanation:
58*24=1392, which is closest to 1200.
Or, you could round the numbers to the nearest tens place, which would give you 60*20, giving you the exact answer of 1200. I think this was the preferred way of solving it.
Given the function h (x) = 2x + 4, for which value of x does h (x) = 18?
The required value for which h(x) = 18 is given as x = 7.
What are functions?Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
Here,
The function h(x) = 2x + 4 - - - - (1)
Since h(x) =18
Substitute h(x) = 18 in equation 1,
18 = 2x + 4
Simplify
18 - 4 = 2x
x = 14 / 2
x = 7
Thus, the required value for which h(x) = 18 is given as x = 7.
Learn more about function here:
brainly.com/question/21145944
#SPJ2
The graph below shows the experimental probability of a runner finishing in first place (1), in second place (2), in third place (3), or not placing (4). Which of the following describes the probability distribution?
Answer:
im honestly not sure but to help out a little bit im sure its either negatively skewed or constant
Step-by-step explanation:
Answer:
It is C. Negatively skewed.
Step-by-step explanation:
If the bigger portion of the data is to the right, then the data is negatively skewed.
When do you know to use either the shell method or washer method and how do you know what to take it to respect to when it is rotating around, x=a, y=a, x=0, and y=0?
Step-by-step explanation:
Let's first consider a rotation about a vertical axis (x=0 or x=a).
Using washer method, the volume is:
∫ᵧ₁ᵞ² π (x₂² − x₁²) dy
∫ᵧ₁ᵞ² π ((x₂ − a)² − (x₁ − a)²) dy
Using shell method, the volume is:
∫ₓ₁ˣ² 2π x (y₂ − y₁) dx
∫ₓ₁ˣ² 2π (x − a) (y₂ − y₁) dx
First, notice that with washer method, the differential dy is parallel to the axis of rotation. With shell method, the differential dx is perpendicular to the axis of rotation.
Also, notice that the limits of integration must match the differential.
Choosing the best method will depend on the function.
If x² can be written in terms of y, and integrated, then washer method is the one to use.
If y can be written in terms of x, and integrated, then shell method is the one to use.
In other words, use washer method if x = f(y) is simple to integrate. Use shell method if y = f(x) is simple to integrate.
If instead we rotate about a horizontal axis (y=0 or y=a), the volume with washer method is:
∫ₓ₁ˣ² π (y₂² − y₁²) dx
∫ₓ₁ˣ² π ((y₂ − a)² − (y₁ − a)²) dx
Using shell method, the volume is:
∫ᵧ₁ᵞ² 2π y (x₂ − x₁) dy
∫ᵧ₁ᵞ² 2π (y − a) (x₂ − x₁) dy
We choose washer method when y² = f(x) is easy to integrate.
We choose shell method when x = f(y) is easy to integrate.
So here's the takeaway:
If the axis of rotation is x = 0 or x = a, and x² = f(y) is easy to integrate, use washer method.
If the axis of rotation is y = 0 or y = a, and y² = f(x) is easy to integrate, use washer method.
Otherwise, use shell method.
The mixed number 1 1/2 is between which two numbers? 2 and 3 and 1 3 and 4 1 and 2
Answer:1 and 1/2
Step-by-step explanation:
Answer:
1 and 1/2
Step-by-step explanation:
Given the translation rule (x, y) —— (x+7, y - 1), what is the pre-image
of D' (2,-3)?
A. D(-5, -2)
B. D(9,-4)
C. D(9,-2)
D. D(-5, -4)
Answer:
A
Step-by-step explanation:
it says pre-image so you want the value before you added 7 and subtracted 1.
5k-2k=12k what is the value of k
Step-by-step explanation:
12k=3k
12k-3k=0
9k=0
k=0/9
k=0
f(x) = 4x - 3
g(x) = 3x - 1
Find (fºg)(x)
Answer:
0.5 or -0.5
Step-by-step explanation:
4x - 3 = 3x - 1
-1 + 3 = 2
4x = 3x - 2
4 - 3 = 1
1x = -2 or positive 2
1x ÷ -2
-0.5 or 0.5
-----‐------------------------
4x-3 = 1
3x -1 = 0.5
f= 1
g= 0.5
1 x 0.5 = x
x= 0.5
Determine if the two triangles shown are similar. If so, write the similarity statement.
Solve for x in 3 = (1/44)x
Answer:
132
Step-by-step explanation:
3 = 1/44x
÷1/44. - 1/44
= 132. = x
Answer:
x = 132
Step-by-step explanation:
3 = (1/44)x
3/(1/44) = (1/44)x/(1/44)
132 = x
what is the answer
HELP QUICK WILL GIVE BRAINLIEST
Answer:
there should be no greather less than sign
Answer:
ok here's the graph for the system of equations, so you can look at it and find the points that are in the purple shaded area
hope this helps!
(also, this is from m4th way *the 4 is an a* which is a super helpful online calc)
16) The original price of a shirt is $18. The shirt is on sale for a 20% discount. What is the sale price of
the shirt?
The Environmental Protection Agency provided fuel-economy data on 1,134 traditional gasoline powered vehicles. These vehicles have mileage that's normally distributed with mean 22.2 miles per gallon, and standard deviation of 5.2 mpg. What percentage of vehicles have gas mileage above 25 mpg?
A. 70.5%
B. 89.5%
C. 50%
D. 29.5%
Answer:
A
Step-by-step explanation:
Which is an equation in point-slope form of the line that passes through the points
(-4, -1) and (5, 7)
what is the domain of this function
Answer:
it would be C i believe
Step-by-step explanation:
Answer:
C. {-1, 3, 5}
Step-by-step explanation:
The first oval is the domain and the second oval is the range.
