The area of the new garden is found to be (x-3)(y+2) square units where x and y are the original dimensions.
What is the rectangle area formula?When calculating a rectangle's area, we multiply the length by the width of the rectangle.
What are examples of the area's practical applications?The area of the floors and walls must be measured before applying carpet or tiles on the floor, painting the walls, or installing cabinets in a space.
Given: A rectangular garden has x and y dimensions. The garden's width is increased by 2 feet while its length is decreased by 3 feet.
New length = x-3
New width = y+2
Area of new garden is given as:
=(length)(width)
= (x-3)(y+2)
Therefore, the area of the new garden is found to be (x-3)(y+2) square units where x and y are the original dimensions.
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An arithmetic sequence a starts 24, 20,... Explain how you would calculate the value
of the 20th term.
Answer:
Step-by-step explanation:
first you need to find the nth term
that would be -4n+28
then you just need to substitute 20 into the position of n
-4*20 = -80
-80+28=-52
How do i solve this one ? (Equilateral Angle ?)
a rancher has 200 feet of fencing with which to enclose two adjacent rectangular corrals (see figure). what dimensions should be used so that the enclosed area will be a maximum?
The dimension of each corral should be 25 feet in width and 33⅓ feet in length so that the enclosed area will be a maximum.
Adjacent rectengular corral has length and width with area formula as below.
A = L × W
Given:
The dimension of adjacent rectangular corrals are the same.Adjacent side = 200 feet.Because the dimension of adjacent rectangular corrals are the same, so:
W = 4x
L = 3y
3y + 4x = 200
[tex]y = \frac{200 - 4x}{3} [/tex]
There are two adjacent rectangular corrals, so:
A = 2×L×W
[tex]A = 2 \times \frac{200 - 4x}{3} \times \: x [/tex]
A = ⅓(400x–8x²)
We can differentiate to get the maximum area:
⅓×(400x–8x²) = 0
400–16x = 0
16x = 400
x = 25 feet
Substitute x value (width) to get y value (length):
y = (200–4(25)) ÷ 3
y = (200–100) ÷ 3
y = 100 ÷ 3
y = 33⅓ feet
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Graph the line that represents a proportional relationship between d and t with the property that an increase of 5 units in t corresponds to an increase of 8 units in d.
What is the unit rate of change of d with respect to t? (That is, a change of 1 unit in t will correspond to a change of how many units in d?)
The unit rate is
?
Graph the relationship.
The unit rate of change , d with respect to t is = 1.6 .
In the question,
it is given that , the relationship between d and t is proportional
also given that " increase of 5 units in t corresponds to increase of 8 units in d ".
which is represented as 5t = 8d
Divide both sides of the equation 5t = 8d by "5" ,
t = 8/5d
t = 1.6d
next we plot the graph of t = 1.6d
we see that the above equation is a proportional linear equation
and A proportional linear equation is represented as
t = md , Where m represents the unit rate .
So , after comparing , we get
m = 1.6
Therefore , The unit rate of change of d with respect to t is 1.6 .
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18. STREETS If Pine Street is parallel to Locust
Street, find the values of a and b. (Lesson 3-7)
Answer:
b=98 and a=82
Step-by-step explanation:
b and 98 are corrisponding angles which means that they are both 98
a+b=180 because it is a straight line
a+98=180 subtract 98 from both sides a d you get a=82
A carpenter needs to build a box to hold his wood screws. He has a sheet of wood that measures 18 inches by 12 inches. He then cuts equal squares from each corner. (a) Write an expression for the length, width, and height for the open box. (b) Write a function for the volume (use factored form).
The expressions for the length, width, and height are 18 - 2x, 12 - 2x, and x while the volume function is V = (12 - 2x)(18 - 2x)x
(a) How to determine the expression for the length, width, and heightFrom the question, we have the following parameters:
Dimension of sheet = 8 inches by 12 inches
Also from the question, we understand that:
He cuts equal squares from each corner.
The cut-out length from the sheet would represent the height of the box
Represent this cut-out length with x
So, we have
Height = x
The width and the length are then represented as
Width = Initial width - 2x
Length = Initial length - 2x
So, we have
Width = 12 - 2x
Length = 18 - 2x
(b) Write a function for the volumeThe volume of a box is the product of its dimensions
In this case, we have
Width = 12 - 2x
Length = 18 - 2x
Height = x
So, we have
Volume = Width * Length * Height
Substitute the known values in the above equation So, we have the following equation
V = (12 - 2x)(18 - 2x)x
So, the volume function is V = (12 - 2x)(18 - 2x)x
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Question 1(Multiple Choice Worth 2 points)
(Pythagorean Theorem MC)
One leg of a right triangle is 8 units long, and its hypotenuse is 14 units long. What is the length of the other leg? Round to the nearest whole number.
11 units
13 units
18 units
22 units
Question 2(Multiple Choice Worth 2 points)
(Interior and Exterior Angles LC)
Two angles in triangle PQR are congruent, ∠P and ∠Q; ∠R measures 34.15°. What is the measure of ∠P?
145.85°
57.45°
34.15°
72.925°
Question 3(Multiple Choice Worth 2 points)
(Pythagorean Theorem and the Coordinate Plane MC)
Determine the length of the line segment shown.
line segment from negative 3 comma 10 to 4 comma negative 1
13 units
12 units
7 units
3 units
Question 4(Multiple Choice Worth 2 points)
(Polygon Angle Sums MC)
A regular polygon has 25 sides. If one of its angles measures (6h − 15)°, what is the value of h?
h = 6.7
h = 16.7
h = 30.1
h = 33.8
Question 5(Multiple Choice Worth 2 points)
(Angle Relationships LC)
Angles A and B are supplementary. Determine the measure of angle A if the measure of angle B is 109.6°.
250.4°
63.2°
70.4°
19.6°
Question 6(Multiple Choice Worth 2 points)
(Angle Relationships MC)
Two angles are complementary to each other. One angle measures 26°, and the other angle measures (10x − 11)°. Determine the value of x.
2.6
5.6
7.5
24.5
Question 7(Multiple Choice Worth 2 points)
(Pythagorean Theorem and the Coordinate Plane MC)
Determine the distance between the points (−4, −5) and (8, 0).
13 units
12 units
8 units
29 units
Question 8(Multiple Choice Worth 2 points)
(Interior and Exterior Angles MC)
In triangle EFG, m∠E = 95.2° and m∠F = 43.7°. Determine the measure of the exterior angle to ∠G.
138.9°
84.8°
51.5°
41.1°
Question 9(Multiple Choice Worth 2 points)
(Angle Relationships MC)
The following angles are supplementary to each other.
m∠A = (3x + 21)° and m∠B = (6x − 21)°
Determine x.
10
20
36
60
Question 10(Multiple Choice Worth 2 points)
(Pythagorean Theorem LC)
Determine which set of side measurements could be used to form a right triangle.
square root of 19 comma square root of 35 comma 54
square root of 15 comma 6 comma square root of 51
5, 8, 30
5, 6, 7
Question 11(Multiple Choice Worth 2 points)
(Pythagorean Theorem LC)
Determine which set of side measurements could be used to form a triangle.
2, 6, 10
3, 18, 22
7, 13, 16
8, 7, 19
Question 12(Multiple Choice Worth 2 points)
(Interior and Exterior Angles MC)
For triangle XYZ, m∠X = (7g + 12)° and the exterior angle to ∠X measures (2g + 60)°. Find the measure of ∠X and its exterior angle.
Interior angle = 49°; exterior angle = 131°
Interior angle = 131°; exterior angle = 49°
Interior angle = 96°; exterior angle = 84°
Interior angle = 84°; exterior angle = 96°
Question 13(Multiple Choice Worth 2 points)
(Pythagorean Theorem MC)
In a video game, Shar has to build a pen shaped like a right triangle for her animals. If she needs 9 feet of fence for the shortest side and 15 feet of fence for the longest side, how many feet of fencing is needed for the entire animal pen?
12 feet
16 feet
36 feet
38 feet
Question 14(Multiple Choice Worth 2 points)
(Polygon Angle Sums LC)
Find the sum of the interior angles of a 12-sided polygon.
1,080°
1,800°
2,100°
2,160°
Question 15(Multiple Choice Worth 2 points)
(Pythagorean Theorem and the Coordinate Plane MC)
The locations of student desks are mapped using a coordinate plane where the origin represents the center of the classroom. Maria's desk is located at (1 −1), and Monique's desk is located at (−4, 5). If each unit represents 1 foot, what is the distance from Maria's desk to Monique's desk?
square root of 7 feet
square root of 14 feet
square root of 85 feet
square root of 61 feet
Answer:
Step-by-step explanation:
This problem is solved using the Pythagorean theorem (a2+b2=c2). In this formula a and b are the legs of the right triangle while c is the hypotenuse.
Using the labels of our triangle we have:
o2+a2=h2
\dpi{100} h^{2}=(10ft)^{2} +(17ft)^{2}
h2=100ft2+289ft2
h=389ft2−−−−−√
So with this information you can see that the correct answer is 19.7ft
Please helppp!
1 :What is the solution to the equation?
−4=x9
2 :Solve for t.
−32=4t
Responses
t=−8
t equals negative 8
A:T = -8
B:T = - 1/8
C:T= 28
D:T=36
3 : What is the solution to the equation?
x−18=−72
4 ;What is the solution to the equation?
−18=x−15
Enter your answer in the box.
5 :What is the solution to the equation?
−24x=−4
Enter your answer as a simplified
The value of the variables in the equation are as follows:
1. x = -4 / 9
2. t = -8
3. x = -54
4. x = -3
5. x = 1 / 6
How to solve an equation?Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign.
Let's find the solution of the equations. The solution of the equation is the value of the variable x. A variable is a number represented by a letter in an equation.
Therefore,
1.
-4 = 9x
divide both sides of the equation by 9
x = - 4 / 9
2.
−32=4t
divide both sides of the equation by 4
t = - 32 / 4
t = - 8
3.
x − 18 = −72
add 18 to both sides of the equation
x - 18 + 18 = -72 + 18
x = -54
4.
−18 = x − 15
add 15 to both sides of the equation
-18 + 15 = x - 15 + 15
-3 = x
x = -3
5.
−24x = −4
divide both sides of the equation by - 24
x = - 4 / -24
x = 1 / 6
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Desiree and Nicole spent a total of $23.75 on decorations for the school dance. They bought
fifteen rolls of streamers on sale at Party City for $0.75 a roll. The remainder of the money
was spent on ornaments costing $0.50 each. How many ornaments did they buy?
Ornaments:
Streamers:
Total:
What is the third term of the sequence 20 - n²
A sequence or series is the generalized form of the pattern thus the third term of the given sequence 20 - n² is 11.
What is a series?A sequence's series is the total number of terms in the sequence.
A series follows some pattern for example if you take data set of natural numbers then there will be a sequence of that data and something will be due to that we can form that series.
As per the given sequence, 20 - n²
The 20 - n² represents the nth term of the sequence.
Thus a(n) = 20 - n²
For the third term n = 3
a(3) = 20 - (3)²
a(3) = 20 - 9 = 11
Hence "A sequence or series is the generalized form of the pattern thus the third term of the given sequence 20 - n² is 11".
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please help me with this problem, i will give u brainliest. mLNM=…
Check the picture below.
Solve for x 5 x + 2 = 7 x − 4
Answer: x=3
Step-by-step explanation:
5x+2=7x-4
-5x +4 -5x +4
2x=6
divide both sides by 2
x=3
The geometric mean of a number and nine times the number is 30. What is the number?
sara has 20 sweets
12 liquorice sweets , 5 mint sweets and 3 humbugs.
sara takes two random sweets
work out probability that the two sweets will not be the same
If sara takes two random sweets. The probability that the two sweets will not be the same is :111/190.
How to find the probability?Probability of getting two of each sweet:
P( Liquorice) = (12/20)×(11/19)
P (Liquorice) =132/380
P (mints) =(5/20)×(4/19)
P (mints) =20/380
P (Humbugs) =(3/20)×(2/19)
P (Humbugs) =6/380
Probability that two sweets will be the same
P(same) =132/380+20/380+6/380
P(same) =158/380
Hence,
Probability that two sweets will not be the same
P(not same) = 1- (158/380)
P(not same) =380 -158 /380
P(not same) = 222 /380
P(not same) =111 /190
Therefore the probability is 111/190.
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In the translation T of the graph below, use the figure to describe the following transformation.
The translation T due to the transformation is (5,3)
How to describe the transformation using the figure?Translation can be defined as movement in a straight line
Given the rule: (x,y) → (x + 3, y + 1) as seen in the image. That means (x,y) translated to (x + 3, y + 1). This is what we use to solve this problem.
From the figure, the value of (x, y) can be read i.e. (x, y) = (2,2)
Thus the translation will be:
(x,y) → (x + 3, y + 1)
(2,2) → (2 + 3, 2 + 1) = (5, 3)
Therefore, the translation T of the transformation shown in the graph is (5, 3)
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help meeeeeeeeeeee pleaseeeeeeeeeee rn rnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeeeeee pleaseeeeeeeeeee rn rnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The width, labelled x in the figure is 162.5 meters
How to determine the width of the rectangle?From the question, we have the following parameters that can be used in our computation:
Length = 650 - 2x
Width = x
The area of a rectangle is the product of its dimensions
So, we have
Area = Length x Width
Substitute the known values in the above equation, so, we have the following representation
A = (650 - 2x) * x
Evaluate
A = 650x - 2x²
Differentiate and set to 0
650 - 4x = 0
So, we have
4x = 650
Divide by 4
x = 162.5
Hence, the width is 162.5 meters
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Meal Deal £5.00
A sandwich
A dessert
A drink
The following choice is available:
5 different sandwiches
4 different desserts
6 different drinks
a) How many different combinations are possible with the Meal Deal?
b) Two of the desserts are sugar-free.
Three of the drinks are sugar-free.
A Meal Deal combination is selected at random.
Work out the probability that both the dessert and the drink are sugar-free
Give your answer as a fraction.
what finding the range of possible values for the length of missing side of a triangle means
Answer:
range
Step-by-step explanation:
I got angle D but I am confused with others I need help ASAP tysm
Considering the figure the unknown angles are
a = 65b = 25c = 25How to determine the unknown anglesUsing the angle in a straight line are supplementary we have
60 + a + 55 = 180
a + 115 = 180
a = 180 - 115
a = 65
applying sum of angles in a triangle equal to 180, b is calculated as follows
a + b + 90 = 180 right angle triangle
substituting for a
65 + b + 90 = 180
b + 155 = 180
b = 180 - 155
b = 25
applying vertical angle theorem
angle c = angle b
angle c = 25
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Andrea put $52 in the savings account that pays 4% interest how much interest will she earn in one year
Answer: $2.08
Step-by-step explanation: First multiply $52 by 4% as a decimal or 0.04. Then, multiply that by the number of years.
=52(0.04)(1)
=2.08
The price of a pair of Nike Panda's
increases from $52 to $64. What is the
percent increase to the nearest
percent?
Answer: 23%
PLEASE GIVE BRAINLIEST THANK YOU VERY MUCH!!
Directions: Match the situation provided to the correct equation/inequa
Situation:
Wyatt is saving up
money for a new
game. It costs $60,
including tax. He has
already saved $20.
At least how much
more money, X,
does he need to
save?
Inequality/Equation:
Innquality/Equation:
Solution
Graphed Solution:
Solution
The equation can be given as X+20 = 60
Wyatt needs to save $40 to buy the new game.
What is an equation?
An equation is an expression which has an equality symbol in it.
We are given that, Wyatt is saving up money for a new game. It costs $60,
including tax.
He has already saved $20. At least how much more money, X, does he need to save
Hence the equation can be given as
X + 20 = 60
On solving the equation X = 40
Hence Wyatt needs to save $40 to buy the new game
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Nathan and Jorge are working on a decimal division problem in
math class. After finishing the problem, it looked like this: 4.76 ÷
2.5 = 0.19. Nathan said that the decimal is incorrectly placed in the
quotient, and Jorge disagrees. Who is right? Explain your answer
Answer:
Nathan
Step-by-step explanation:
4.76 / 2.5
= (476/100) / (25/10)
= (476/100) * (10/25)
= 238/125
= 1.904
Thus, Nathan is right in saying that the decimal is incorrectly placed in the quotient of the given answer 0.19
What’s 1,598 fewer then 25,876
Answer:
24,278
Step-by-step explanation:
Select the correct answer.
What is the y-intercept of function f?
select function or not a function
Answer:
The graph is a function.
Step-by-step explanation:
square tile measures 12 inches on each side. If 1 inch = 2.54 centimeters, determine the area of the tile in square centimeters. Round the answer to the nearest square centimeter. 30 cm2 144 cm2 366 cm2 929 cm2
The area of the tile in square centimeters is 929cm2
The area in square centimeters is calculated as follows
First, let convert the tile measures 12 inches on each side into centimeters
1 inch = 2.54 centimeters
= 12 x 2.54
= 30.48 centimeters
Next is to find the area of the tile in square centimeters
The area of square = (side) x (side) square units
= 30.48 centimeters x 30.48 centimeters
= 929.0304
= 929 square centimeters (rounded)
So, the area of the tile in square centimeters is 929 square centimeters
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Answer:
The area of the tile in square centimeters is 929cm2
Step-by-step explanation:
I took the exam and got it right
Here are the first 4 terms of a sequence.
3 9 15 21
a) (i) Write down the next term in the sequence.
(ii) Explain how you got your answer.
b) Work out the 10th term of the sequence.
simplify (-5)∧5(-5)∧-6
Answer:
-5 with the exponet of 11
Answer:
-1/5 or -0.2 if you are going by fraction or decimal
Use three unit multipliers to convert 5280ft to meters
The three-unit multipliers are follows, 5280ft × 12 inches × 2.54 cm × 0.01 meter and it will be 1609.344 meters.
What is unit conversion?To convert any unit into another is called a unit conversion.
In order to convert units, we need to care about their dimensions their dimension should not be changed.
For example conversion of a kilometer to a meter is to multiply by 1000 but meter and kilometer both unit is for distance only.
As per the given,5280ft
It is known that 1 ft = 12 inches.
5280ft = 5280 x 12 inches
It is known that 1 inch = 2.54 cm
5280 x 12 inches = 5280 x 12 x 2.54 cm
It is known that 1 cm = 0.01 meter
5280 x 12 x 2.54 cm = 5280 x 12 x 2.54 x 0.01 meter
⇒ 1609.344 meters
Hence "The three-unit multipliers are as follows, 5280ft × 12 inches × 2.54 cm × 0.01 meter and it will be 1609.344 meters".
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