Answer:
The dimensions are 6 by 5 feet.
Length = 6 feet.
Width = 5 feet.
Step-by-step explanation:
Let the length = L
Let the width = W
Perimeter of a rectangle = 2L + 2W
Translating the word problem into an algebraic equation, we have;
L = 2W - 4 ........equation 1
22 = 2L + 2W .......equation 2
Substituting the value of "L" into equation 2, we have;
22 = 2(2W - 4) + 2W
22 = 4W - 8 + 2W
22 + 8 = 6W
30 = 6W
W = 30/6
Width, W = 5 feet.
To find the length, L
Substituting the value of "W" into equation 1, we have;
L = 2W - 4
L = 2(5) - 4
L = 10-4
Length, L =6 feet
Therefore, the dimensions of the garden are 6 by 5 feet.
Evaluate 3(x + 4) + 2x - x2 for x = 5.
O A. O
O B. -4
O C. -12
O D. 40
Answer:
[tex]12[/tex] is the answer
Step-by-step explanation:
Given
[tex]x = 5[/tex]
Required
Evaluate
[tex]3(x + 4) + 2x - x^2[/tex]
To answer this question, we simply substitute 5 for x in [tex]3(x + 4) + 2x - x^2[/tex]
[tex]3(x + 4) + 2x - x^2[/tex] becomes
[tex]3(5 + 4) + 2*5 - 5^2[/tex]
[tex]3(9) + 10 - 25[/tex]
Open all brackets
[tex]3*9 + 10 - 25[/tex]
[tex]27 + 10 - 25[/tex]
[tex]12[/tex]
Consider the integers x and y. When y is divided by x the remainder is 29. When y is divided by x/2, the remainder is 13. Determine x.
===============================================
Explanation:
When we divide y over x to get a remainder of 29, this means we are dividing over a value greater than 29. This means x > 29.
If we divided over a number 29 or less, then the remainder would be smaller than the divisor.
------------------------------------------
The variable x is some integer. When we divide y over (x/2) we get some other integer. This implies that x/2 itself is also an integer. That tells us that x is some even integer.
So far we know that x > 29 and x is some even number.
------------------------------------------
y divided by x leads to a remainder of 29. This means
y/x = q + 29/x
for some integer q, which is the quotient.
Multiply both sides by x
x*(y/x) = x*(q + 29/x)
y = qx + 29
We'll come back to this later.
------------------------------------------
Now divide y over (x/2) to get a remainder 13. We'll let n be the quotient this time
y/(x/2) = n + 13/(x/2)
which is equivalent to
y = n(x/2) + 13
We can multiply both sides by 2 further getting
2y = 2*( n(x/2) + 13 )
2y = nx + 26
Plug in y = qx+29 from earlier
2(qx+29) = nx + 26
2qx + 58 = nx + 26
Let's group the x terms to one side and everything else on the other side
2qx - nx = 26-58
2qx - nx = -32
-nx + 2qx = -32
nx - 2qx = 32
I multiplied both sides by -1 to turn that -32 into 32
Factoring x from the left side gives
nx - 2qx = 32
x(n - 2q) = 32
We have x as an integer, which is stated in the instructions.
In order to have x(n-2q) = 32 be true, this must mean n-2q is an integer.
We can say n-2q = 32/x, so 32/x is some integer because x is an integer.
------------------------------------------
In short, x and n-2q are both integers. In order for the two integers to multiply to 32, the factors must be smaller than 32 or equal to 32.
So [tex]x \le 32[/tex] and [tex]n-2q \le 32[/tex]
We don't need to worry about the second inequality since all we care about is x.
Recall that earlier we stated that x > 29 and x is even.
Combine this with [tex]x \le 32[/tex] and we form the compound inequality [tex]29 < x \le 32[/tex]
This basically says x is a value from the set {30, 32}
But x = 30 is not a factor of 32. There's no way to have x(n-2q) = 32 be a true equation if x = 30. We must rule x = 30 out.
The only thing left is x = 32. This is the final answer.
------------------------------------------
If x = 32 and y = 29, then we fit the requirements of the problem.
y/x = 29/32 = 0 remainder 29
y/(x/2) = 29/16 = 1 remainder 13
The solution has been confirmed.
Ben drives 405 mile on 15 gallons
Answer: 27 miles per gallon
Step-by-step explanation: 405/15=27
You deposit $500 into a savings account that increasing by 7% interest annually. Write the function that represents the balance after t years. Then what is the balance after 2 years.
Step-by-step explanation:
500 ×1.07^t <-- function (I think)
500 × 1 07^2 = $572.45 <-- balance after 2 years
Jorge bought 16 apples for $8.00.
Let x represent the number of apples purchased, and let y represent the total cost.
Graph the line that represents the proportional relationship.
i go to wiva
Answer:
x=16
y=8.00
8/16=0.5 (50 cents per apple)
y=0.5x+0
hii can someone help me with this question please
Move AC and BD so that their midpoints coincide. Then draw a polygon through A, B, C, and D to form quadrilateral ABCD. Measure and record the slope of each slide of quadrilateral ABCD
Answer:
look attachment below
Step-by-step explanation:
We find the midpoints of AC and BD and the corresponding coordinates for quadrilateral ABCD.
Midpoint of AC: ( (x₁ + x₃) / 2 , (y₁ + y₃) / 2 )
Midpoint of BD: ( (x₂ + x₄) / 2 , (y₂ + y₄) / 2 )
Then we can measure and record the slopes of each side.
Slope = (y₂ - y₁) / (x₂ - x₁)
Here,
To draw quadrilateral ABCD with the midpoints of AC and BD coinciding, we first need to find the midpoints of AC and BD.
The midpoint of a line segment is the average of the coordinates of its endpoints.
Given points A(x₁, y₁), B(x₂, y₂), C(x₃, y₃), and D(x₄, y₄), we can find the midpoints as follows:
Midpoint of AC: ( (x₁ + x₃) / 2 , (y₁ + y₃) / 2 )
Midpoint of BD: ( (x₂ + x₄) / 2 , (y₂ + y₄) / 2 )
Once we have the coordinates of the midpoints, we can connect them to form quadrilateral ABCD.
To measure the slope of each side of quadrilateral ABCD, we need to find the slope of each line segment formed by connecting points A, B, B, C, C, D, and D, A.
The slope of a line passing through two points (x₁, y₁) and (x₂, y₂) is given by:
Slope = (y₂ - y₁) / (x₂ - x₁)
Let's assume we find the midpoints of AC and BD and the corresponding coordinates for quadrilateral ABCD. Then we can measure and record the slopes of each side.
To learn more on slope click:
brainly.com/question/3605446
#SPJ4
The winning candidate in an election receives 0.52 of the votes. a. There are 1000 voters. How many votes does the winning candidate receive?
Answer:
520
Step-by-step explanation:
0.52 as a percent is 52%. 52% of 1000 is 520.
Instead of using the values {1,2,3,4,5,6}
on dice, suppose a pair of dice have the
following: {1,2,2,3,3,4} on one die and
{1,3,4,5,6,8} on the other. Find the
probability of rolling a sum of 7 with
these dice. Be sure to reduce.
?
]
Answer:
[tex]Probability(sum7)=\frac{4}{24}=\frac{1}{6}[/tex]
Step-by-step explanation:
The dice form pairs of outcomes, so if the dice has repeating sides then the set of outcomes will be pairs of elements from the set {1,2,3,4} and {1,3,4,5,6,8}. The number of possible two pair combinations is 4 times 6 which equals 24 possible pairs. Now we find which of these pairs would have values summing up to 7: [tex](1,6),(2,5),(3,4),(4,3)[/tex] So 4 outcomes out of a possible 24 outcomes have this qualityThat's [tex]Probability(sum7)=\frac{4}{24}=\frac{1}{6}[/tex]Answer:
1/6
Step-by-step explanation:
select the numbers that have 9 as a factor. Mark all that apply
A = 27
B = 36
c = 39
d = 48
E = 54
Answer:
A,B,E
Step-by-step explanation:
All are divisible by 9
Which describes the transformation shown below
A
B
C
D
Answer:
i think the answer is a to be honest
Step-by-step explanation:
In ΔABC, m∠CAB=60° and AD is angle bisector with D∈BC and AD = 8ft. Find the distances from D to the sides of the triangle.
( AD and BC have lines above them but i didn't know the symbol.)
Answer:
nope
Step-by-step explanation:
need help on this please
Samuel's lunch account begins with $50 and has $4 taken out each day.
Susie's lunch account begins with $36 and has $3 taken out each day.
Which inequality can be used to find x, how many days the balance in
Samuel's account will be less than the balance in Susie's account?
50 - 4x > 36 - 3x
50 + 4x > 36 + 3x
50 - 4x < 36. 3x
50+ 4x < 36. 3x
Answer:
C. 50 - 4x < 36 - 3x
Step-by-step explanation:
The teacher prepares a tour. Its cost is $246 for her and 5 people to take a day-long guided tour of the Eveglades. How much does the guided tour cost per person, the unit rate?
a
$246
b
$6
c
$24.60
d
$41
Answer:
its either C or D :)
(giving brainly if u helpp mee)
What is static electricity?
A) Build up of electrical charges on the surface of an object
B) Build up of light energy that causes electrical charges to move
C) The flow of electrical charges in a conductor
D) The movement of electrical charges through an insulator
Evacuate the following expression for z=197.
Answer:
138
Step-by-step explanation:
12+9sqrt 196=138
Anumeha mows lawns. She charges an initial fee and a constant fee for each hour of work.
F represents Anumcha's fee (in dollars) for working t hours.
F = 6 + 12t
How much does Anumeha charge for each hour of work?
Answer:
.50 dollars for each hour
Step-by-step explanation:
Answer:
The answer is $12 fir each hour
Step-by-step explanation:
The highest mountain in the world is Mt. Everest, whose peak is 29,029 feet above sea level. But the tallest mountain is Mauna Kea. The base of Mauna Kea is 19,669 feet below sea level, and its peak is 33,465 feet above its base. How much higher above sea level is Mt. Everest than Mauna Kea?
42825 or 9360
Step-by-step explanation:
So we know that Mt. Everest has a peak that is 29,029 feet above sea level.
To find how much Mauna Kea is above sea level then we would subtract the feet below sea level (19,669ft) from the overall height of the mountain (33,465ft). Like this:
33,465ft - 19669ft = 13,796 feet
Now that we know both mountains height above sea level, we can answer the question.
We will take Everest's height above sea level and subtract Mauna's height above sea level. Like this:
29,029ft - 13,796ft = 15,233
Therefore, Mt. Everest is 15,233 feet taller above sea level than Mauna Kea.
Hope this helps!
- Kay
In the triangle above the value of x = _____ degrees (nearest whole number)
Answer:
60 degree it is ez math it is 6 grade math
Answer:
200 or 160
Step-by-step explanation:
50=100 70=100 = 200
Most of the time it's 160 or 200, so try those 2
A. (2, -1)
B. (2, 1)
C. (-1, 2)
D. No solution
Which expression is equivalent to (r^-7)^6?
Jordan noticed it rained 1/4 of the days that he recorded the weather in Fulton County . In Boone County , Aubrey found that it rained 1/8 of the days she kept records . According to the records , which county had rain a greater fraction of the time ?
Answer: Jordan
Step-by-step explanation: Jordan's number is short 1/4 which means that it had more of a chance of rain than Aubrey.
If a = 2 and b = 4, then 27 - b 2 ÷ a + (11 - 5) is equal to _____. 23 11.5 29 25
Answer:
29
Step-by-step explanation:
Plug in your variables and follow the order of operations.
11-5 which equals 6.
4x2 which is 8
then divide the 8 by 2 which equals 4
then subtract 27 and 4 which equals 23
and finally add 23 and 6 which equals 29.
The area of a rectangular vegetable garden is 200 feet. The width is 10 feet. What is the length?
Answer:
The length is 20 ft. 10ft times 20ft = 200ft^2
Step-by-step explanation:
PLS MARK AS BRAINLIEST
Answer:
20
Explanation:
200 = 20 x 10
PLEASE HELP: Tangent, Sine, or Cosine? Please only answer if you know I genuinely need help. WILL GIVE BRAINLIEST IF CORRECT
Answer:
cosine
Step-by-step explanation:
cos 27=x/20
x=20 cos 27≈17.82
Solve the inequality
|7-2y|-8 ≥ -3
Answer:
y is less than or equal to 1 OR y is greater than or equal to 6
Step-by-step explanation:
What is 43x12+3-2=______
Answer:
517
Step-by-step explanation:
Answer:
517
Step-by-step explanation:
43×12+3-2 = 516+3-2
Do the multiplication/division before the addition/subtraction
516+3-2 = 519-2
Work from left to right
519-2 = 517
The medians of triangle XYZ intersect at Point P. If PY=12, what is VY?
Answer:
18
Step-by-step explanation:
PY = [tex]\frac{2}{3}[/tex] YV
[tex]\frac{2}{3}[/tex] YV = 12
VY = 18
Babe wants to find out how many groups of 4 are in 28. If she uses repeated subtraction what is her first step?
Answer:
28 - 4
Step-by-step explanation:
The points (-3,1), (-1,1) (0,-1) (-1,-3) (-3,-3) and (-4,-1) what polygon is this
MAY GOD BLESS YOU AND HELP YOU WITH ALL YOUR PROBLEMS..............................