Answer:
If area of sector = area of circle
1/3π(r+4)^2= πr^2
r^2-4r-8 =0
what is a sector?A sector is a cut out section of a circle. It is of two radii and an arc .
The area of a sector is angle substended/ 360 x area of a circle
area of a circle is πr^2
if area of circle is equal to the area of sector
120/360×π(r+4)^2=πr^2
divide both side by π
1/3(r+4)^2=r^2
multiply both sides by 3
(r+4)^2=3r^2
opening the bracket
(r+4)(r+4)=3r^2
r^2+ 8r +16=3r^2
3r^2-r^2- 8r -16=0
2r^2- 8r -16=0
divide all by 2
r^2- 4r -8=0
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Cam's Cupboard grocery store is having a sale on canned goods. Tiana decides to stock up and purchases 12 cans of soup. During the sale, cans of soup sell for $0.55 less than full price. Tiana pays a total of $13.20 for the cans of soup.
Which equation can you use to find the amount, f, each can of soup costs at full price?
How much does each can of soup cost at full price?
$
PLEASE HELP MAN I CANT USE A HW PASS ON THISSS
If during the sale, cans of soup sell for $0.55 less than full price. Tiana pays a total of $13.20 for the cans of soup. The equation that can you use to find the amount, f, each can of soup costs at full price is 12(f−0.55)=13.20 and the amount that each can of soup cost at full price is $1.65.
EquationGiven data:
Number of cans = 12 can
Cost of can less than full price = $0.55
Total amount paid = $13.20
Let f represent the full price
Now let formulate an equation that will be use to find the amount:
Equation :
12(f−0.55)=13.20
Let let determine the amount that each can of soup cost at full price using the equation
12(f−0.55)=13.20
12f−6.6=13.20
Collect like terms
12f = 19.8
Divide both side by 12f
f = 19.8 / 12
f = $1.65
Therefore the can of soup at full price costs is $1.65.
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State the domain and range of f(x) = |x-1| +3.
The domain and range of the function f(x) = |x-1| +3 are-
domain: (−∞,∞)range: [3,∞)What is defined as the domain and range of the function?The domain of the a function would be the collection of values that can be plugged into it. This set contains the x values inside a function like f(x). A function's range is the number of values which the function can take.For the given expression for the function;
f(x) = |x-1| +3.
Domain: Unless the expression is undefined, the domain of the representation is all real numbers. Because there is no real number in this case, the expression is undefined.
Interval Notation:(−∞,∞)
Set-Builder Notation:{x| x ∈ R}
Range: The range is indeed the collection of all possible y values. To determine the range, consult the graph.
Interval Notation:[3,∞)
Set-Builder Notation:{y| y ≥ 3}
Thus, the domain and the range of the function is estimated.
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Estimate 87x403 pls help
An easy way to estimate would be to choose numbers close such as 90x400, which equals 36,000.
The true answer is 87*403 = 35,061.
3 600
Step-by-step explanation:
First multiply 87 to the nearest ten then multiply 403 to the nearest hundred which will give you 90 and 400. Multiply the two to get your answer
If £1 is equal to 99.72 rupees and the post office only has 500 rupee papers how much can I change out of £450
£1 = 99.72 rupees -> £450 = 44874 rupees.
As the post office only has 500 rupee papers, once we calculate out the result, we have to round down to the nearest whole number.
The amount of rupee papers we can change out is : 44874 : 500 = 89.748 (papers)
We round down to 89 papers.
Use the picture below.
How many lines of symmetry does the picture have?
O A. 1
OB. 3
о с. 0
OD. 2
Answer:
It has one line of folding symmetry
soledad says 3 (2-2)-1=36. what area did she make? explain.
In case whereby Soledad says 3 (2-2)-1=36 the error she made was that she does not perform, the calculation base PEDMAS rule of mathematics.
What is a mathematical error?The mathematical error can be described as the error that can be made when making a calculation, and the expected rule in mathematics in solving the particular problem is not followed.
From the given mathematical expression, 3 (2-2)-1=36, if we are to solve it, we will need to open the parenthesis first which will give us 6-6-1=-1, therefore it can be concluded that she make the mistake by not following the rules required.
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If f(x) = 1/x which equation describes the graphed function?
If f(x) = 1/x, then the function representing the graph plotted will be -
y = f(x + 2) - 1.
What is the name of the function represented by - f(x) = 1/x?The function f(x) = 1/x is called the multiplicative inverse function, because for each input it returns the multiplicative inverse or reciprocal of that input.
Given is function f(x) = 1/x.
The graph of the function f(x) = 1/x is plotted in the graph. If we plot the graph for f(x + 2) = 1/(x + 2), than the graph will shift towards left. If we subtract 1 from the f(x + 2), than the graph will shift downwards.
Therefore, if f(x) = 1/x, then the function representing the graph plotted will be -
y = f(x + 2) - 1
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4 1/6 divided by 8/9
4 1/6 divided by 8/9 is 4 11/16
The division of the fractions can be calculated as follows ?The first step is to change the mixed fraction (4 1/6) to a proper fraction
4 1/6
= 4 × 6
= 24 + 1
= 25
= 25/6
The Fraction can be divided as follows
25/6 ÷ 8/9
= 25/6 × 9/8
= 75/16
= 4 11/16
Hence the result of the division of 4 1/6 and 8/9 is 4 11/16
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The slope of a line is -5. What is the slope of any line parallel to this line? (If an answer is undefined, write Undefined.)
Answer:
Since both lines are parallel, they must have the same slope, which in this case is -5.
Solve the inequality and graph the solution on
the line provided.
15+ 3x <-3
the area of a triangle is 10x^2 - 4x. If the height of the triangle is 2x, determine an expression for the base.
A = base x height divided by 2.
The expression representing the base is b = 2(10x² - 4x)/x
How to determine the expression for the baseIt is important to note that the formula for area of a triangle is expressed as;
Area = 1/2 bh
Where;
b is the base of the triangleh is the height of the triangleGiven the parameters as;
Area = 10x² - 4x
Height = x
Substitute the values into the formula
10x² - 4x = 1/2(x)b
10x² - 4x = xb/2
cross multiply
2(10x² - 4x) = xb
Now, to determine the expression, make 'b' the subject of formula by dividing both sides by the coefficient of b, we have;
b = 2(10x² - 4x)/x
Hence, the expression is 2(10x² - 4x)/x
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80 points please help
Answer:
216
Step-by-step explanation:
gof(6) means g(f(6))
f(6)=2(6)-6=6
g(6)=6^3=216
The diagram shows a shaded parollelgram drawn inside a rectangle
Given h(x)= |1 - 7x|, find the following.
h(1)
h(-7)
h(9)
Solve them all
The values of the expression h(1), h(-7) and h(9) are 6, 50 and 62
Function and valuesAfter dividing one number by another, the modulo operation yields the remainder or signed remainder of the division.
Given the following modulus function shown below;
h(x)= |1 - 7x|, we are to find the following.
h(1)
h(-7)
h(9)
If x = 1, then;
h(x)= |1 - 7(1)|
h(1) = |1-7|
h(1) = |-6|
h(1) = 6
If x = -7, then;
h(-7)= |1 - 7(-7)|
h(-7) = |1--49)|
h(-7) = |1+49|
h(-7) = |50|
h(-7) = 50
If x = 9, then;
h(x)= |1 - 7(7)|
h(1) = |1-63|
h(1) = |-62|
h(1) = 62
This gives the equivalent values of the expression
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16. The department manager recorded the number of sick days taken last year by cach
employee, as shown in the table.
Employee Sick Days
Kailynn 4
Josh 5
Brian 1
Bill 3
Jacob 2
Pete 2
Sasha 3
What is the mean number of days employees were sick? Round to the nearest
hundredth.
The mean number of days employees were sick is 3 days.
Mean:-Mean is the average of numbers. The calculation is easy. Add all the digits and then divide by the number of digits. That is, the sum divided by the count.
As We have count for number of days by each employee given as follows
Kailynn 4days
Josh 5days
Brian 1days
Bill 3days
Jacob 2days
Pete 2days
Sasha 3days
∴ Total number of days will = 4 + 5 + 1 + 3 + 2 + 2 + 3 = 20 days
∴ Total employee count is 7.
∴ Mean Will be [tex] \frac{20}{7} [/tex]
= 2.85714
≈ 3 --(rounding to nearest hundred).
∴ The mean number of days employees were sick is 3 days.
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i need help with this, thanks
Answer:
9
Step-by-step explanation:
Vertical angles are congruent, so:
[tex]16y=18y-18 \\ \\ -2y=-18 \\ \\ y=9[/tex]
Answer:
y = 9
Step-by-step explanation:
Vertical Angles Theorem
When two straight lines intersect, the opposite vertical angles are congruent.
Therefore, equate the expressions and solve for y:
[tex]\begin{aligned}(18y-18)^{\circ}&=16y^{\circ}\\18y-18&=16y\\18y-18+18&=16y+18\\18y&=16y+18\\18y-16y&=16y+18-16y\\2y&=18\\2y \div 2 &=18 \div 2 \\y&=9\end{aligned}[/tex]
Therefore, the value of y is 9.
Which expression represents the prime factorization of 276? 7TH Grade Math!
A. 2 x 2 x 3 x 23
B. 2 x 3 x 3 x 23
C. 2 x 2 x 2 x 3 x 23
D. 2 x 2 x 3 x 3 x 23
Answer:
a
Step-by-step explanation:
The scale of a map is 1: 250000 the actual distance between two cities is 80km calculate the distance on the map give your answer in centimeters
PLS SOMEONE ANSWER❗️
The scale of a map exists 1: 250000 the actual distance between two cities exists 80km then the two cities exists 72 cm apart on the map.
How to estimate the actual distance?Given that the representative fraction exists 1/250000.
We know that the representative fraction exists the ratio of map distance to the corresponding ground distance exists independent of units of measurement.
This implies that 1 cm on the map exists actually 250000 cm distance.
We will convert this 250000 cm into m as 1 m = 100 cm.
[tex]\[250000 \times \dfrac{1}{{100}}[/tex] m = 2500 m
To convert this into km as 1 km = 1000 m.
[tex]\[2500 \times \dfrac{1}{{1000}}[/tex] km = 2.5 km
So, 1 cm on the map exists 2.5 km actual distance.
To find the distance on the map corresponding to 180 km on ground.
[tex]\dfrac{{180}}{{2.5}}[/tex] cm = [tex]$\frac{{1800}}{{25}}[/tex] cm = 72 cm
Therefore, the two cities exists 72 cm apart on the map.
We exists supposed to scale the representative fraction properly to avoid any miscalculation. Also, we will take care of the scales properly i.e. kilometers, meters and centimeters.
The complete question is:
The scale of a map is 1: 250 000.
(a) The actual distance between two cities is 80 km. Calculate this distance on the map. Give your answer in centimeters.
(b) On the map a large forest has an area of 6 cm?
Calculate the actual area of the forest. Give your answer in Square kilometres.
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solve for x from the picture please
x = 9
x + 3 + x - 1 = 20
2x + 2 = 20
2x = 18
x = 9
Please help me I will give you extra points and the crown
What is the special angle pair relationship between <1 and <3
From the given figure , the special angle pair relationship between ∠1 and ∠3 are known as corresponding angles and are congruent.
As given in the question,
From the given figure:
line l is parallel to line m.
t is the transversal of line l and m
Relationship between angles for the parallel lines
∠1 and ∠2 are straight angles and are supplementary
∠3 and ∠2 are interior angles and are supplementary
⇒m(∠1 + ∠2) = m(∠3+∠2)
⇒m∠1= m∠3
Therefore, from the given figure , the special angle pair relationship between ∠1 and ∠3 are known as corresponding angles and are congruent.
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32^1/25 x2^x = 8^1/4
Work out the exact value of x.
Answer:
Is 23
Step-by-step explanation:
His name 721 6 the y 8th 7th in his 6th grade 6th class and I was
The value of the x for the given expression [tex](32)^{1/25}\times (2)^x = (8)^{1/4}[/tex] is 19/20.
What is an algebraic expression?An algebraic expression is consists of variables, numbers with various mathematical operations,
The given expression is
[tex](32)^{1/25}\times (2)^x = (8)^{1/4}[/tex]
Simplify the expression,
[tex]((2)^5)^{1/25}\times (2)^x = (2^3)^{1/4}\\\\(2)^{5/25}\times(2)^x =(2)^{3/4}\\\\(2)^{1/5}\times(2)^x = (2)^{3/4}\\(2)^{1/5 + x} = (2)^{3/4}\\[/tex]
The base is same, so the expression can be written as,
1/5 + x = 3/4
x - 3/4 = 1/5
x = 1/5 + 3/4
x = (4 + 15)/20
x = 19 / 20
The required value of x is 19/20.
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( x+5) * (x ^3+6x ^2+18x)
The value of (x + 5) * (x^3 + 6x^2 + 18x) is x^4 + 11x^3 + 48x^2 + 90x
What are polynomial expressions?Polynomial expressions are mathematical statements that are represented by variables, coefficients and operators
How to evaluate the polynomial expression?
The polynomial expression is given as
(x + 5) * (x^3 + 6x^2 + 18x)
Express the polynomial expression as a product of factors
So, we have the following equation
(x + 5) * (x^3 + 6x^2 + 18x) = x * (x^3 + 6x^2 + 18x) + 5 * (x^3 + 6x^2 + 18x)
Open the brackets in the polynomial expression
So, we have the following equation
(x + 5) * (x^3 + 6x^2 + 18x) = x^4 + 6x^3 + 18x^2 + 5x^3 + 30x^2 + 90x
Collect the like terms in the polynomial expression
So, we have the following equation
(x + 5) * (x^3 + 6x^2 + 18x) = x^4 + 6x^3 + 5x^3 + 18x^2 + 30x^2 + 90x
Evaluate the like terms in the polynomial expression
So, we have the following equation
(x + 5) * (x^3 + 6x^2 + 18x) = x^4 + 11x^3 + 48x^2 + 90x
Hence, the solution is x^4 + 11x^3 + 48x^2 + 90x
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Find the value of x show your steps
The model represents an equation. What value of x makes the equation true?
PLEASE HELP
The value of x that makes the equation shown in the model true is x = -3.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Equations are classified based on degree (value of highest exponents) as linear, quadratic, cubic and so on. Variables can be dependent or independent. Dependent variables depend on other variable while an independent variable do not depend.
The model shown can be represented by the equation:
4(-x) + 9(1) = 8(-x) + 3(-1)
-4x + 9 = -8x - 3
-4x + 8x = -3 - 9
4x = -12
x = -3
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Solve the simultaneous equations 4 x + 3 y = − 10 4 x + y = − 14
Answer:
x = - 4, y = 2
Step-by-step explanation:
First equation: 4x + 3y = - 10
Second equation: 4x+y= - 14
To solve simultaneously:
Rearrange one of the equations and substitute the equation to another equation, I prefer rearranging the second equation because it is easier.
Rearranging the second equation to get y, and then substitute back to the first equation to find x:
y = - 14 - 4x ------> new second equation
Substitute y (new second equation) into the first equation to find x:
4x +3(-14 -4x) = - 10
4x - 42 - 12 x = - 10
- 8x - 42 = -10
-8x = - 10 + 42
- 8x = 32
8x = - 32
x = - 4
Now we substitute x = - 4 to the second equation to find y:
4x + y = - 14
y = - 14 - 4(-4)
y = - 14 - (-16)
y = - 14 + 16
y = 2
there is a problem with this equation in solving equations in Qhere it is if 1/5x=2
Q is the set of the rational numbers
Rational numbers are all numbers that can be put in the form of a/, where b is not equal to zero.
Examples:
[tex]\frac{3}{4},5\frac{2}{7},5.4,2[/tex]The given equation is
[tex](\frac{1}{5})^x=2[/tex]Insert log on both sides
[tex]log\mleft(\frac{1}{5}\mright)^x=log\mleft(2\mright)[/tex]Use the rule of power with a log
[tex]xlog(\frac{1}{5})=log\mleft(2\mright)[/tex]Divide both sides by log(1/5)
[tex]\begin{gathered} x=\frac{log\mleft(2\mright)}{log\mleft(\frac{1}{5}\mright)} \\ x=-0.43067655 \end{gathered}[/tex]Since we can not put the value of x in the form of a/b, then
The equation has NO solution in Q (or empty set { } or Nul)
What is Curtis's net pay?
Employee: Curtis R. Evans
SSN: 555-55-5555
Earnings
Regular Earnings:
Overtime
Gross Earnings:
O $589.23
Pay period: 8/20/2005 to 8/26/2005
O $407.86
$382.86
$421.00
O $426.16
78.00
Federal Taxes:
FICA
State Tax
Insurance:
Retirement:
Union Dues:
NET PAY:
?
$29.50
$30.75
$18.30
$25.00
$7.50
$6.00
If the Employee: Curtis R. Evan with SSN: 5 5 5-55-5 5 55 has regular earning of $421 and overtime of $78. Curtis's net pay is $499.
What is net pay ?Net pay can be defined as the amount a person received or earn as a salary after all deduction has been substracted.
Using this formula to determine the net pay
Net pay = Regular earnings + Overtime
Where :
Regular earning = $421
Overtime = $78
Let plug in the formula
Net pay = $421 + $78
Net pay = $499
Therefore we can conclude that the net pay or take home amount is the amount of $499.
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find thesum using a number line -4+(-3)=
Answer:
-7
Step-by-step explanation:
Answer:
Step-by-step explanation:
-4 + (-3) is basically -4 - 3
-4 - 3 = -7
A rectangle is 8m longer than it is wide. If the length is increased by 2m and the width is increased 2m, the area is
increase by 68m 2. Find the original dimensions.
The original dimensions are 12 m and 20 m.
What is area of rectangle?
Area of rectangle is the region occupied by a rectangle within its four sides or boundaries.
The area of a rectangle depends on its sides. Basically, the formula for area is equal to the product of length and breadth of the rectangle.
Let x be the width of the rectangle.
Length of the rectangle = x+8
Area of the rectangle = x(x+8)
According to question, new width= x+2
New length = x+2+8 = x+10
New area = (x+2)(x+10)
Area increased = (x+2)(x+10) – x(x+8)
x^2+12x+20-x^2-8x=68
4x-20=68
4x=48
x=12
Hence, the width = 12m and length = 12+8 = 20 m
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Which symbol creates a true sentence? (16 - 8) ÷ 2 ___ 16 – 8 ÷ 2??
The symbol that creates a true sentence for the expression is (16 - 8) ÷ 2 < 16 – 8 ÷ 2.
What is an expression?It should be noted that an expression is used to show the relationship between the values or the data given. This will be illustrated as thus:
It should be noted that (16 - 8) ÷ 2 will be:
(16 - 8) ÷ 2
= 2 ÷ 2
= 1
On the other hand, 16 - 8 ÷ 2 will be;
= 16 - 8 ÷ 2
= 16 - 4
= 12
It should be noted that 1 is less than 12. The symbol will be less than.
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