A rectangle's length is 4 inches greater than its breadth.. If the perimeter of the rectangle is 36. Area will be 77[tex]cm^{2}[/tex].
Why isn't a rectangle a square?A quadrilateral with in all four of its angles being right angles is a rectangle. A quadrilateral with four right angles and four equal-length sides is called a square. As a result, a square is indeed a particular form of rectangle since it has rectangles with equal-length sides.As a result, a square is indeed a particular form of rectangle since it has rectangles with equal-length sides. Because a square is indeed a quadrilateral with in all four angles at right angles, every square is also a rectangle. To be a square, a rectangle's sides must all be the same length, hence not all rectangles are squares.
Finding the Area , we obtain:
Let the rectangle's breadth be x cm.
Its length is then x+4 cm.
According to the problem,
2{x+x+4}=36
or, 2x+4=18
or, x=7.
So, breadth is 7 cm and length is 11 cm.
So, the area is 7×11=77 [tex]cm^{2}[/tex].
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A cell phone plan charges $47.35 per month plus $13.94 in taxes, plus $0.60 per minute for calls beyond the 400-minute monthly limit. Write a piecewise-
defined function to model the monthly cost C(x) (in S) as a function of the number of minutes used for the month.
CG)-{8
for (Choose one) ▼
for (Choose one)
X
The piecewise function for the given problem is;
C(x) = $61.29 x ≥ 400
C(x) = $61.29 + 0.6(x - 400) if x ≥ 400
How to identify the Piecewise Function?A piecewise function is defined as a function that has different definitions depending on which values of x are being used. Piecewise functions are called "piecewise" due to the fact that they are made of "pieces" with different function definitions. To evaluate a piecewise function for a given value of x, find which interval your value fits in, and then use that definition of the function to evaluate.
First, we will find the monthly cost if the 400-minute monthly limit is not exceeded. Then, the total cost would be;
47.35 + 13.94 = 61.29 with just the plan and taxes. So if x ≤ 400, then;
C(x) = 61.29
Now if the 400 minutes is exceeded, the bill will also include $0.60 per additional minute. To find the number of additional minutes, we can take the total number of minutes x and subtract 400. In general, the cost would be;
C(x) = $61.29 + 0.6(x - 400) if x ≥ 400
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Need help quick with this problem!!!!
The product of a, b, and c is 27/8.
What is an expression?
In mathematics, an expression is a combination of numbers, symbols, and operators (such as +, -, ×, ÷, and parentheses) that represents a quantity or a mathematical relationship. Expressions can be simple or complex, depending on the number of terms and the complexity of the operations involved.
The given expression is
[tex]\frac{6x^2y^{-1}}{\sqrt[4]{16x^5y^2} }[/tex]
To simplify the given expression and write it in the form of ax^by^c, we can start by using the properties of exponents and simplifying the numerator and denominator separately:
Numerator: [tex]6x^2y^(-1) = \frac{6x^2}{y}[/tex]
Denominator: [tex]\sqrt[4]{(16x^5y^2)} = (16x^5y^2)^{(1/4)} = 2x^{(5/4)}y^{(1/2)}[/tex]
Putting the simplified numerator and denominator together, we have:
[tex]\frac{6x^2y^{-1}}{\sqrt[4]{16x^5y^2}} = \frac{6x^2}{y} \cdot \frac{1}{2x^{5/4}y^{1/2}} = \frac{3}{\sqrt{2} \cdot x^{3/4}y^{3/2}}[/tex]
Now we can see that the given expression can be written in the form of ax^by^c, where a = 3, b = -3/4, and c = -3/2. Therefore, the product of a, b, and c is:
a * b * c = 3 * (-3/4) * (-3/2) = 27/8.
Hence, the product of a, b, and c is 27/8.
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7x + 14y = 28
5x+10y= 20
Solve for x and y using elimination
The value of x is [0,∞] and y is [0,∞]. The solution has been obtained by using the elimination method.
What is elimination method?
The elimination approach involves removing one of the variables from the system of linear equations by employing addition or subtraction together with multiplication or division of the variable coefficients.
We are given two equations as
7x + 14y = 28 ....(1)
5x + 10y = 20 ....(2)
Now, on multiplying equation (1) by 10, we get the equation as
70x + 140y = 280 ....(3)
On multiplying equation (2) by 14, we get the equation as
70x + 140y = 280 ....(4)
Since, we are getting the same equations so, the system has infinitely many solutions.
Hence, the value of x is [0,∞] and y is [0,∞].
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The correct mix for a batch of concrete is 6:3:2 in terms of sand, gravel and cement. The batch is to have 3300 pounds of these ingredients. How many of each are needed?
pounds of sand
pounds of gravel
pounds of cement
Answer:
1,800 lbs of sand
900 lbs of gravel
600 lbs of cement
Step-by-step explanation: 11*300=3,300. 300*6=1,800, 300*3=900, and 300*2=600. This is correct because if you add 1,800+900+600 you get 3,300.
Explain how to find 20% of 160
Answer: 20% of 160 is 32.
Step-by-step explanation:
The percentage is from the word percent which means one part in a hundred. It is a part of the base or the whole determined by the rate. Usually, the percentage is smaller than the base. However, there are also cases where the percentage is greater than the base. This happens when the percent is greater than 100%.
To find the percentage, you have to multiply the base and the rate. The base is the 100% or original amount or the whole while the rate is the ratio of the percentage to the base and it has the percent sign (%). Remember that you have to convert the rate to a decimal number by moving the decimal point twice to the left.
Let us now find the 20% of 160.
20% = 0.2
percentage = 160 × 0.2
= 32
What are the outliers in the data set? How do you know that they are outliers?
Step-by-step explanation:
you have to find your five number summary
I need help with this problem
The estimate of the number 7th grader who play in the school band will be 120.
How to calculate the valueIt is important to note that an expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator.
Some of the mathematical operations that are illustrated in this case include addition, subtraction, etc. The estimate of the number 7th grader who play in the school band will be:
= 60 / 200 × 400
= 120
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Solve for x. Round to the nearest tenth.
xº
54
12
The required measure of the angle x in the given right triangle is 12.38°.
What are trig ratios?If you know the lengths of two sides of a right triangle, you can use trigonometric ratios to calculate the measures of one (or both) of the acute angles.
Here,
Since the question seems to be incomplete the complete question has been attached after the solution.
We have given a triangle where x° is the angle of the right triangle where the hypotenuse is 54 and one legs is 12. With the help of trig ratios
sin x = 12 / 54
x = sin⁻¹(12/54)
x = 12.38°
Thus, the required measure of the angle x in the given right triangle is 12.38°.
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BUDGET
Income
Expenses
Rent
Groceries
Utilities
Total Expenses
Net income
Instruction
Class Activity 1
January February March
$2200
$1200
$125
$69.51
$2200
$1225
$110.1
$82.71
$2200
$1225
$79.16
$73.04
1) Bold and center align the column headings and "merge and center" the title.
2) Format all numbers with "$" to 2 decimal places.
3) Calculate totals for each type of expense and for each month. Also, calculate a grand total for all 3 months of
expenses.
4) Calculate net income for each month (total income minus total expenses).
Class Activity (Contd.)
5) Add another column to calculate the percentage of total expenses for each category by
dividing each category's total by the grand total.
6) Create two different unique charts. Each chart must represent different information on the
table.
7) Each chart must be on a different Excel page and each page tab must be labelled
according to the chart.
Here are the steps to complete the budget, as described in the instructions:
Bold and center align the column headings:Highlight the column headings (Income, Expenses, Rent, Groceries, Utilities, Total Expenses, Net Income)Right-click and select "Format Cells"In the "Font" tab, select "Bold" and "Center" alignClick "OK"How to merge and center the title:Type the title "BUDGET" in cell A1Highlight cells A1 to G1Right-click and select "Merge and Center"The title will now be centered across the entire rowFormat all numbers with "$" to 2 decimal places:Highlight the cells containing numbersRight-click and select "Format Cells"In the "Number" tab, select "Currency" and set decimal places to 2Click "OK"Calculate totals for each type of expense and for each month:
To calculate the total expenses for each month, add up the amounts in the Rent, Groceries, and Utilities columnsFor example, in January the total expenses would be $125 + $69.51 + $82.71 = $277.22To calculate the grand total expenses for all 3 months, add up the total expenses for each monthFor example, the grand total expenses would be $277.22 + $110.10 + $73.04 = $460.36Calculate net income for each month:
To calculate the net income for each month, subtract the total expenses from the total incomeFor example, in January the net income would be $2200 - $277.22 = $1922.78Add another column to calculate the percentage of total expenses for each category:
Create a new column to the right of the Utilities columnLabel this new column "Percentage of Total Expenses"In the first cell of this column, divide the value in the Rent column by the grand total expenses and multiply by 100For example, in January the calculation would be =($125/$460.36)*100 = 27.11%Copy this formula down to the last row of dataCreate two different unique charts:
Go to the "Insert" tab and select the type of chart you want to create (e.g. bar chart, pie chart, line chart, etc.)Highlight the data you want to include in the chartClick the "Insert" button to create the chartRepeat the process to create a second chart on a different Excel pageLabel each page tab according to the chart:
Right-click on the first chart's page tab and select "Rename"Type in a descriptive label for the chart (e.g. "Expense Breakdown Chart")Repeat the process for the second chart page tab.Read more about budgets here:
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How do we find X and Y?
Step-by-step explanation:
answer is in the picture
Decide which of the two given prices is better and explain why. Storage locker A rents for $33/yd^2 per month. Storage locker B rents for $1.49/ft^2 per week. (Assume 1 month=4 weeks.)
B is significantly more affordable and better than A, renting for $1.62 per square foot.
Yard and feet conversion:Yard and feet are used to estimate the length. Both of the units are used in the royal and US customary system of measurements. The value of one yard is equal to three feet.
To compute Square yard to Square Feet, where Square yard is equal to 9 Square Feet, multiply the value in Square yard by 9. one can also use the Square yard to Square Feet calculator.
1 yard² = 9 feet²
A rents for $33 per yard squared
hence A rents $33 for 9 feet squared
hence A rents $3.67 per feet squared( $33/9) which is costlier than $1.49 per feet squared
Thus, as B is more economical, it is better.
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what is the pattern for each hypotenuse in the pythagorean spiral?
i have:
Hypotenuse = (Triangle # + 1) X 9
(square root the answer)
does this make sense?
The pattern for the hypotenuse in the Pythagorean spiral is √(a² + b²)
How to get the patternThe Pythagorean spiral is formed by drawing squares whose side lengths are given by the Pythagorean triples, which are sets of three positive integers (a, b, c) that satisfy the equation a² + b² = c².
In the Pythagorean spiral, the hypotenuse of each square is the diagonal of the square, which is given by the square root of the sum of the squares of the sides. For a square with side lengths a and b, the hypotenuse (diagonal) is given by:
√(a² + b²)
Since the side lengths of each square in the Pythagorean spiral are given by the Pythagorean triples, the hypotenuse of each square can be calculated using the Pythagorean theorem. Therefore, the pattern for each hypotenuse in the Pythagorean spiral is that it is given by the square root of the sum of the squares of the side lengths, where the side lengths are integers that form a Pythagorean triple.
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Solve for y
Y-18=b
Need help please.
Answer:
y = 18 + b
Step-by-step explanation:
Add 18 to both sides
y = 18 + b
2. The cost of an ad in a local paper is given by the piecewise function.
x ≤ 51
40,
(40+7(x-4), x>5)
Find the difference in cost between a one-line ad and a four-line ad.
c(x) = {40
please help
The difference in cost between a one-line ad and a four-line ad is 0
How to find the difference in cost between a one-line ad and a four-line ad.From the question, we have the following parameters that can be used in our computation:
c(x) = 40 x ≤ 5
c(x) = 40 + 7(x-4), x>5)
For one line add, we make use of the function
c(x) = 40 x ≤ 5
This is so because 1 is in the domain of x ≤ 5
For four line add, we make use of the function
c(x) = 40 x ≤ 5
This is so because 4 is in the domain of x ≤ 5
So, we have
C(1) = 40 and C(4) = 40
The difference, it
Difference = 40 - 40
Evaluate
Difference = 0
Hence, the difference is 0
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Examine the figure below, solve for a, round to the nearest whole number.
T
37
A
46⁰
28
D
The measure of a from the triangle ATD is 27 units. Therefore, the option B is the correct answer.
What is sine rule?Law of Sines In trigonometry, the law of sines, sine law, sine formula, or sine rule is an equation relating the lengths of the sides of any triangle to the sines of its angles.
The formula for sine rule is sinA/a=sinB/b=sinC/c
From the given triangle ADT, ∠A=46°, ∠D=84°, AT=37, AD=t and TD=a.
By angle sum property,
∠A+∠D+∠T=180°
46°+84°+∠T=180°
130°+∠T=180°
∠T=50°
sin46°/a=sin84°/37=sin50°/t
0.7193/a=0.9945/37=0.7660/t
0.7193/a=0.9945/37
0.9945a=0.7193×37
0.9945a=26.6141
a=26.6141/0.9945
a=26.76
≈27
0.9945/37=0.7660/t
0.9945t=0.7660×37
0.9945t=28.342
t=28.342/0.9945
t=28.5
Therefore, the option B is the correct answer.
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NEED HELP ASAP!!!
Due today
Answer:
20 cubic yards
Step-by-step explanation:
You want to know the volume in cubic yards of a layer of topsoil that is 6 inches deep over an area 31 feet by 34 feet.
UnitsYou know that ...
36 inches = 1 yard3 feet = 1 yardThen the dimensions of the volume being applied are ...
6 inches = 6/36 yards
31 feet = 31/3 yards
34 feet = 34/3 yards
VolumeThe volume is the product of the dimensions of the space:
V = LWH
V = (31/3 yd)(34/3 yd)(6/36 yd) ≈ 19.519 yd³
About 20 cubic yards are needed to fill the garden.
Hannah has to make 168 gallons of punch for a big party. The punch is made of soda and fruit drink. The cost of the soda is $1.57 per gallon and the cost of the fruit drink is $2.41 per gallon. Hannah's budget requires that the punch cost $1.66 per gallon. How many gallons of soda and how many gallons of fruit drink does she need?
Gallons of soda =
Gallons of fruit punch =
Hannah needs 150.71 gallons of soda and 17.29 gallons of fruit drink to make 168 gallons of punch that costs $1.66 per gallon.
What is meant by budget?
Budget is a planning and monitoring tool used by management to coordinate all of the company's activities. Budgeting is the process of estimating income and expenses for a given time frame.For any individual, group of people, organisation, or government. A budget is a plan for financial calculations for a specified time period, usually a month or a year, but not always.Budgeting is the process of estimating a company's revenues and expenses for a given time period.Examples of budgets prepared for this purpose include the sales budget, which makes a projection of the company's sales, and the production budget, which makes a projection of the company's production, among others.Let's assume that Hannah needs to use x gallons of soda and y gallons of fruit drink to make 168 gallons of punch.
We know that the cost of soda is $1.57 per gallon and the cost of fruit drink is $2.41 per gallon, and Hannah's budget requires that the punch cost $1.66 per gallon.
So we can set up the following system of equations:
x + y = 168 (total amount of punch)
1.57x + 2.41y = 1.66(168) (total cost of punch)
Simplifying the second equation:
1.57x + 2.41y = 278.88
Now we can use substitution or elimination method to solve for x and y.
Using substitution:
x = 168 - y
1.57(168 - y) + 2.41y = 278.88
264.36 - 1.57y + 2.41y = 278.88
0.84y = 14.52
y = 17.29
So Hannah needs 17.29 gallons of fruit drink.
Using x + y = 168, we can find that she needs 150.71 gallons of soda.
Therefore, Hannah needs 150.71 gallons of soda and 17.29 gallons of fruit drink to make 168 gallons of punch that costs $1.66 per gallon.
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The "-8" and "+8" on the left
cancel, leaving x by itself. What
number do we get on the right?
Enter the number that belongs in the green box.
X-8=6
+8+8
x = [?]
ha
Neeed help!!!!!!!!!!!!!!
An area of a rectangle is 32x¹²y⁹ square inches and the length is 8x⁴y³ therefore the expression which represents the width of the rectangle in inches is 4x⁸y⁶.
What is a Rectangle?
This is referred to as a quadrilateral with four right angles.
Area of rectangle = Length × width
Width = Area/ Length
= 32x¹²y⁹ / 8x⁴y³
= 4x⁸y⁶
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A boat heading out to sea starts out at Point A, at a horizontal distance of 1246 feet
from a lighthouse/the shore. From that point, the boat's crew measures the angle of
elevation to the lighthouse's beacon-light from that point to be 14°. At some later
time, the crew measures the angle of elevation from point B to be 5°. Find the
distance from point A to point B. Round your answer to the nearest tenth of a foot if
necessary.
Answer:2304.9
Step-by-step explanation:
Answer:
2304.9 ft
Step-by-step explanation:
You want the distance from point A, which is 1246 ft horizontally from a lighthouse to point B, given the angles of elevation to the light are 14° and 5° from points A and B, respectively.
TangentThe tangent relation for sides in a right triangle is ...
Tan = Opposite/Adjacent
In a model of this geometry, the height (h) of the lighthouse is the side opposite the angle of elevation. This lets us write two equations:
tan(14°) = h/1246
tan(5°) = h/(1246 +d) . . . . . where d is the distance from A to B
SolutionSolving these equations for d, we have ...
h = 1246·tan(14°) = (1246+d)·tan(5°)
d·tan(5°) = 1246·(tan(14°) -tan(5°))
d = 1246·(tan(14°)/tan(5°) -1) ≈ 2304.9 . . . . feet
The distance from point A to point B is about 2304.9 feet.
<95141404393>
MODELING REAL LIFE: You have a total of 42 math and science problems for homework. You have 10 more math problems than science problems. How many problems do you have in each subject. a) Use x to represent math problems and y to represent science problems. Write an equation that represents the number of problems you have.
Solve by elimination. {4x+2y=−6
{3x−2y=13
A. (−2,−5)
B. (1,−5)
C. infinite number of solutions
D. (0,−3)
Answer:
[B]. (1,-5)
Step-by-step explanation:
Given:
[tex]\begin{bmatrix}4x+2y=-6\\ 3x-2y=13\end{bmatrix}[/tex]
Solve:
[tex]\begin{bmatrix}4x+2y=-6\\ 3x-2y=13\end{bmatrix}[/tex] Since 2y - 2y = 0 we take that away now we have;
[tex]4x=-6\\3x=13[/tex] Add 4x + 3x = 7x
[tex]\frac{7x}{7} =\frac{7}{7}[/tex] Divide both sides by 7.
[tex]x=1[/tex]
Now substitute x to find y.
[tex]4(1)+2y=-6[/tex]
[tex]4 + 2y =-6[/tex] Add 6 to the other side.
[tex]10 = 2y[/tex] Divide both sides by 2.
[tex]\frac{10}{2} =\frac{2y}{2}[/tex]
[tex]y = 5[/tex]
Hence, the answer is [B]. (1,-5)
RevyBreeze
For every 3 lemons you buy at a farm stand, the total cost increases by $1.80.
The constant of proportionality is
An equation that relates the total cost y and the number of lemons x is y=____x
Use the equation you wrote to complete the table.
Answer:
he constant of proportionality is $1.80, since for every 3 lemons the total cost increases by $1.80.
The equation that relates the total cost, y, and the number of lemons, x, is:
y = 1.80 * (x/3) + b
where b is the y-intercept, which represents the cost of 0 lemons. We'll need additional information to determine the value of b.
Here is a table with the values of y and x, assuming b = 0:
x (Number of Lemons) y (Total Cost)
0 0
3 1.80
6 3.60
9 5.40
... ...
Step-by-step explanation:
Algebra 2, Exponental Funtction.
The numeric value of the exponential function at x = 19.5 is given as follows:
f(19.5) = 178.41.
How to model an exponential function?The standard definition of an exponential function is given as follows:
y = ab^x.
In which:
a is the initial value, the value of y when x = 0.b is the rate of change.Considering that f(4.5) = 25 and f(14) = 85, the two equations are given as follows:
ab^(4.5) = 25.ab^(14) = 85.Hence:
a = 25b^(-4.5).
Then the value of b is obtained as follows:
25b^(-4.5)b^(14) = 85.
b^(9.5) = 85/25
b = (85/25)^(1/9.5)
b = 1.14.
Then the value of a is obtained as follows:
a = 25 x (1.14)^(-4.5)
a = 13.86.
Then the function is defined as follows:
y = 13.86(1.14)^x.
At x = 19.5, the numeric value is given as follows:
y = 13.86(1.14)^19.5
y = 178.41.
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The table of values shows the height of a Ferris wheel car as it travels in a circular motion. Select each true statement.
A:The car makes a complete revolution in 10 seconds
B:The maximum height of the Ferris wheel is 65 feet
C:The radius of the Ferris wheel is 35 feet
D:If the car is loaded at 0 seconds, then the people are loaded at the lowest point of the Ferris wheel.
The following statements are true:
A:The car makes a complete revolution in 10 seconds
B:The maximum height of the Ferris wheel is 65 feet
What is revolution ?A full rotation or turning around a focal point is referred to as a revolution. Revolution is the act of rotating around a fixed point or axis . Examples of this include the rotation of a planet around its star or a wheel around its axle.
A. The car makes a complete revolution in 10 seconds:
This can be deduced from the fact that the height of the Ferris wheel car returns to 35 feet after 10 seconds, which means that it has completed one full revolution.
B. The maximum height of the Ferris wheel is 65 feet:
This can be seen from the table, where the height of the Ferris wheel car reaches 65 feet at 2.5 seconds and 12.5 seconds.
C. If the car is loaded at 0 seconds, then the people are loaded at the lowest point of the Ferris wheel: This can be seen from the table, where the height of the Ferris wheel car is 35 feet at 0 seconds.
It is not possible to determine the radius of the Ferris wheel based on the given information alone.
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what is 3 1/4-1 3/4 on number line place a point on 3 1/4 and on the difference may use skip counter to show 1 3/4
The difference between 3.25 and 1.75 is done and marked on the number line as below.
What is meant by a number line?
A number line is a representation of a graduated straight line that is used to represent real numbers visually. It is assumed that every point on a number line corresponds to a real number and that every real number corresponds to a point. This line is used to compare integers on an endless line that extends on both sides, either horizontally or vertically, at equal intervals.
We are asked to plot the difference between 3 [tex]\frac{1}{4}[/tex] and 1 [tex]\frac{3}{4}[/tex] on the number line.
3 [tex]\frac{1}{4}[/tex] = 3 + 1/4 = 3 + 0.25 = 3.25
1 [tex]\frac{3}{4}[/tex] = 1 + 3/4 = 1 + 0.75 = 1.75
Difference = 3.25 - 1.75 = 1.5 = 1 [tex]\frac{1}{2}[/tex]
This can be shown on the number line below.
Each division has the value of 1/4 = 0.25.
We have marked 3[tex]\frac{1}{4}[/tex] = 3.25 on the number line.
Since we are subtracting 1 [tex]\frac{3}{4}[/tex] = 1.75 from 3.25, we move 7 divisions backward from 3.25 as 7 * 0.25 = 1.75.
So after moving 7 divisions backwards, we land on 1.5, which is the difference we found earlier.
Therefore the difference between 3.25 and 1.75 is done and marked on the number line as below.
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HELP ASAP TIMED!! hurry
Answer:
3rd choice (x + 8)² + (y - 11)² = 4
Step-by-step explanation:
(x - -8)² + (y - 11)² = 2²
(x + 8)² + (y - 11)² = 4
Step-by-step explanation:
(x - h)² + (y - k)² = r²
h = -8
k = 11
r = 2
(x + 8)² + (y - 11)² = 2²
(x + 8)² + (y - 11)² = 4
The answer is C. (x+8)² + (y-11)² = 4
When number is multiplied by 9 the product is 72. find the number
Answer: 8
Step-by-step explanation: 9 x 8 = 72
Naomi has seven times as many marbles as Cindy. Naomi has 42 marbles. Which equation and solution
represent the number of marbles, m, Cindy has?
Faith invests £800 for 3 years in a bank account. The account pays simple interest at a rate of 0.4% per year Work out the total amount of interest Faith has got at the end of the 3 years.
