20 plus 10 equals 30.
[tex] \pi x^{2} [/tex] = a
The formule is about area of a circle.
[tex]\pi x^{2} = a[/tex]
We need to solve the equation for x. Where x is the radius of the circle.
In order to solve it for x, we need isolate it for x on left side.
So, first we need to get rid pi from left side.
On dividing both sides by pi, we get
[tex]\frac{\pi x^2}\pi}=\frac{a}{\pi}[/tex]
[tex]x^2=\frac{a}{\pi}[/tex]
Taking square root on both sides, we get
[tex]\sqrt{x^2}=\sqrt{\frac{a}{\pi}}[/tex]
[tex]x=\sqrt{\frac{a}{\pi}}[/tex]
What are the converse, inverse and contrapositive of the statement? Which statements are true? Statement: If the figure is square, then the figure is quadrilateral
The converse, the inverse, and the contrapositive of the statement
"If the figure is square, then the figure is a quadrilateral." is given below.
We have,
The statement: "If the figure is square, then the figure is a quadrilateral."
Converse:
The converse of the statement switches the "if" and "then" parts of the original statement.
Converse: If the figure is a quadrilateral, then the figure is square.
Inverse:
The inverse of the statement negates both the "if" and "then" parts of the original statement.
Inverse: If the figure is not square, then the figure is not a quadrilateral.
Contrapositive:
The contrapositive of the statement also switches the "if" and "then" parts and negates both of them.
Contrapositive: If the figure is not a quadrilateral, then the figure is not square.
Thus,
Converse: If the figure is a quadrilateral, then the figure is square.
Inverse: If the figure is not square, then the figure is not a quadrilateral.
Contrapositive: If the figure is not a quadrilateral, then the figure is not square.
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what is the solution to this equation?
-6x+3=21
Select and place the symbol that will make the statement true -|y| ? |-y|
It's [tex]\leq[/tex]
The correct symbol to make the statement -|y|? |-y| true is '=', because the absolute value of 'y' and '-y' are always equal, regardless of whether 'y' is positive or negative.
Explanation:The correct symbol to make the statement true is '='. This is because the absolute value of any number, positive or negative, is always positive, or zero in the case of zero itself. So no matter what value 'y' takes on, |-y| and |y| will always be equal.
For example, let's consider that y = -5. Then |-5| = 5 and |5| = 5. Here |-y| and |y| are equal.
If y = 5, then |-5| = 5 and |5| = 5. Here too, |-y| and |y| are equal. Therefore, no matter if 'y' is positive or negative, the absolute value of 'y' and '-y' are always equal.
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The population of a city can be modeled with a linear equation, y = –80x + 3,450, where x is the number of years after 2000 and y is the city’s population. Write a description of the city’s population based on the equation.
Answer:
Initial population is 3450 in the year 2000 and it decreases 80 every year.
Step-by-step explanation:
We are given with y=-80x+3450 where y is city's population and x is the number of years after 2000.
That is x=0 means the year 2000.
Hence y-intercept will represent the initial population which is nothing but 3450.
Since our equation slope =-80 which is negative means y is decreasing as x increases.
For x raises by 1, y decreases by 80.
That means population decreases by 80 for every year.
Answer:
The y-intercept indicates the population in the year 2000, so 3,450 people lived in the city in 2000. The negative slope indicates that the city is losing population. It loses 80 people each year.
Step-by-step explanation:
i just did the assignment
Brittany is sell car magnets. She purchases them for $7.50 each and marks up the price by 30%. How much is Brittany planning to charge?
Considering that 30% of $7.50 is the same as 0.3/7.5, you would get $2.25 as the markup price. So by adding $7.50 with $2.25, Brittany would charge $9.75 per car magnet.
if amit started work at 6am and left at 1:45 pm how many hours should he record for the day on his time card?
6 hours in the morning (from 6 am to 12 am)
1:45 in the afternoon (from 12 am to 1:45 pm)
sum
6:00 + 1:45 =
7:45 ( 7hours and 45 minutes)
6 am to 12 pm is 6 hours.
12 pm to 1 pm is 1 hour.
So you have 7 hours 45 min.
Since 45 min is 3/4 of an hour you would add it up to get 7.75 hours.
Your answer is 7.75 hours.
Hope this Helps!!
Choose a fraction that makes the following sentence true. 0.1 is a rational number because it can be written as ___.
a. 1/10
b. 1/9
c. 0.1
d. 1/11
gUYS I FOUND THE RIGHT ANSWER ITS 1/9 ON GOD I JUST GOT IT RIGHT
The decimal 0.1 is a rational number because it can be expressed as the fraction 1/10, which is the correct answer to the student's question.
Explanation:The student asked to choose a fraction that correctly completes the sentence: 0.1 is a rational number because it can be written as ___. The correct choice is 1/10. This is because the decimal 0.1 can be converted directly to the fraction 1/10 by placing the digit 1 in the numerator and 10 in the denominator, which signifies the decimal's place value. Rational numbers are those that can be expressed as a fraction where both the numerator and the denominator are integers, and the denominator is not zero.
11.Bentley Manufacturing Company wants to rent a private club for its annual dance. The total cost will be $1,045. If the committee charges $9.50 per person, how many people need to attend the dance in order to cover the cost?
Answer:
110 people need to attend the dance in order to cover the cost.
Step-by-step explanation:
Bentley Manufacturing Company wants to rent a private club for its annual dance.
The total cost will be $1,045.
The committee charges $9.50 per person.
So, let the total number of persons attending be = x
So, this situation can be represented as:
[tex]9.50x=1045[/tex]
This gives x = 110
So, 110 people need to attend the dance in order to cover the cost.
Olympic swimming pools are rectangles measuring 164.042 feet in length and 82.021 feet in width. What is the perimeter of an Olympic pool pls help i have no clue how to do this
To find the perimeter of a rectangle, you use the equation 2(lxw) so 2(164.042+82.021)
2(246.063) which is 492.126
The perimeter of an Olympic pool is 492.126 feet if the Olympic swimming pools are rectangles measuring 164.042 feet in length and 82.021 feet in width.
What is a rectangle?It is defined as two-dimensional geometry in which the angle between the adjacent sides is 90 degrees. It is a type of quadrilateral.
It is defined as the area occupied by the rectangle in two-dimensional planner geometry.
The area of a rectangle can be calculated using the following formula:
Rectangle area = length x width
It is given that:
Olympic swimming pools are rectangles measuring 164.042 feet in length and 82.021 feet in width.
Perimeter = 2(length + width)
Perimeter = 2(164.042 + 82.021)
Perimeter = 2(246.063)
Perimeter = 492.126 feet
Thus, the perimeter of an Olympic pool is 492.126 feet if the Olympic swimming pools are rectangles measuring 164.042 feet in length and 82.021 feet in width.
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22.48 rounded to the nearest whole number
ANSWER
22
EXPLANATION
22.48 rounded to the nearest whole number is 22.
The reason is that the 4 after the decimal point is less than 5 so we won't round up.
Answer:
The round off number is 22.
Step-by-step explanation:
The number = 22.48
Nearest whole number = 22
Explanation:
A whole number is any number which is without any decimal or fraction.The question was to round off the nearest of 22.48.Now the rule is that if the number left to decimal is 5 or more than 5, round of the number by adding 1 to the number right to the decimal. If the number left to decimal is 4 or less than 4 then round off number simply by removing all left to decimal.Now in our question there was 4 left to decimal. So we apply the second rule and the rounded off number will be 22.if g=8, what is the value of the expression
[tex] \frac{g}{2} + 3[/tex]
A.
[tex] \frac{8}{5?} [/tex]
B.
[tex] \frac{11}{2} [/tex]
C.
[tex]7[/tex]
D.
[tex]19[/tex]
7-3x=x-4(2+x)
helppp
Convert the decimal 0.6333… to a fraction and classify it as either rational or irrational.
A. 57⁄9, irrational
B. 57⁄90, rational
C. 63⁄90, rational
D. 63⁄99, rational
answer B
We assume x= 0.6333
100x = 63.3333
10x= 6.333 33 (subtract it )
----------------------------
90x = 57 ( divide by 90 on both sides)
So x= [tex]\frac{57}{90}[/tex]
Answer : [tex]\frac{57}{90}[/tex]
When we can write a number in fraction form then it is a rational number.
We converted the decimal number into a fraction so it is rational
The answer is B. 57/90, rational.
The steps for solving the equation 2x-3=7
Step 1: Add 3 to both sides.
2x-3+3=7+3
2x=10
Step 2: Divide both sides by 2.
2x/2=10/2
x=5
Standard Form 2x-10=0
Factorization 2(x -5)=0
Solution x=10/2=5
Write
10/17 as a decimal and round to the nearest hundredth.
the answer to that is 0.59
Answer:
0,900 or 0,9
Step-by-step explanation:
10/17 = 10 ÷ 17 = 0,588235
Hope it helped,
BioTeacher101
this afternoon,sara noticed that the number of the page assigned for homework is divisble by both 12 and 2.what is the smallest possible page number tha
t could have been assigned
Answer:
The smallest possible page number that would have been assigned is 12.
Step-by-step explanation:
Number of pages assigned for homework = x
The 'x' is the number which divisible by both 2 and 12.
2 = 1 × 2 (prime number)
12 = 1 × 2 × 2 × 3 (Composite number)
The smallest possible page number that could have been assigned will be equal to lowest common multiple of 1, 1, 2, 2 and 3.
X = 1 × 1 × 2 × 2 × 3 = 12
The area of a rectangular vegetable garden is 200ft^2 . The width is 10 ft. What is the lenght of the vegetable garden?
The length of the rectangular vegetable garden will be 20 feet.
What is the area of the rectangle?Let W be the rectangle's width and L its length.
The area of the rectangle is the multiplication of the two different sides of the rectangle. Then the rectangle's area will be
Area of the rectangle = L × W square units
The region of a rectangular vegetable nursery is 200 square feet. The width is 10 feet.
The length of the rectangle will be given as,
200 = 10 L
L = 200 / 10
L = 20 feet
The length of the rectangular vegetable garden will be 20 feet.
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the arithmetic average of 10 numbers -2, -5,-2, 5, x , -3 10, 3, 8, -10 is 8 find x
AS
Arithmetic average = Sum of all the numbers /Total numbers
SO arithmetic average= {(-2)+(-5)+(-2)+(5)+(x)+(-3)+(10)+(3)+(8)+(-10)} / 10
={4x} /10
=0.4 x
As Given Arithmetic average= 8
so 0.4x =8
Dividing 0.4 Both sides
0.4x/0.4 = 8/0.4
x= 20
30 + (.0825 x 30) + (15% x 30) =
30×·15=4.50
then subtract 30 by 4.50 to get 25.50
.0825×30=2.475
now add 2.475+25.50+30= 57.975 round to 57.98
The final answer is 36.975. The expression simplifies to 36.975 when all calculations are completed.
1. 30 + (.0825 x 30):
To calculate this part, we first multiply 0.0825 (which is 8.25% written as a decimal) by 30. This gives us:
0.0825 x 30 = 2.475
Next, we add 30 to the result:
30 + 2.475 = 32.475
2. (15% x 30):
To calculate this part, we first convert 15% to a decimal by dividing it by 100:
15% = 15/100 = 0.15
Next, we multiply 0.15 by 30:
0.15 x 30 = 4.5
Now that we have the results from both parts, we add them together:
30 + (.0825 x 30) + (15% x 30) = 30 + 2.475 + 4.5 = 36.975
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Complete question is:
Solve the given expression: 30 + (.0825 x 30) + (15% x 30) =
True or False: For any two integers a and b, (a-b)^2 = a^2-b^2
Expanding the expression, it is found that the statement is false.
---------------------------
The statement given is: [tex](a - b)^2 = a^2 - b^2[/tex]Expanding the left side, we get:[tex](a - b)^2 = (a - b)(a - b) = a^2 - ab - ab + b^2 = a^2 - 2ab + b^2[/tex]
Which is different than the statement, and thus, the statement is false.The expression is also known as a notable product, the perfect square binomial.A similar problem is given by: https://brainly.com/question/17202374
The statement is false. The square of difference of two quantities is not equal to the difference of their squares. The correct expression for [tex](a-b)^2 is a^2 - 2ab + b^2, not a^2 - b^2.[/tex]
Explanation:The statement For any two integers a and b,[tex](a-b)^2 = a^2-b^2[/tex] is false. Let's illustrate why this is incorrect with an example. If we let a = 2 and b = 1, then the left-hand side of the equation [tex](a-b)^2[/tex] would give us [tex](2-1)^2[/tex] = 1 and the right-hand side of the equation [tex]a^2 - b^2[/tex] would give us 2² - 1² = 3 which are not equal.
It's important to note that (a - b)² can be expanded to a² - 2ab + b² in accordance with the square of a binomial formula, which is definitely not equal to [tex]a^2 - b^2[/tex]. A common mistake is to drop the middle term in the expansion (-2ab), which leads to this incorrect equation.
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50 POINTS! Arrange the steps to solve this problem. 9 steps. 50 POINTS!
[tex]\left\{\begin{array}{ccc}x+y=-2\\2x-3y=-9\end{array}\right\\\\\text{multiply the first equation by 3}\\3(x+y)=3(-2)\qquad|\text{use distributive property}\\3x+3y=-6\\\\\underline{+\left\{\begin{array}{ccc}3x+3y=-6\\2x-3y=-9\end{array}\right}\qquad\text{add 3x+3y=-6 to 2x-3y=-9, and solve for x}\\.\qquad5x=-15\qquad|:5\\.\qquad x=-3\\\\\text{Substitute the value of x in the first equation (x+y=-2)}\\\\-3+y=-2\qquad|+3\\y=1\\\\\text{The solution for the system of equations is (-3, 1)}[/tex]
Answer:
...
Step-by-step explanation:
Car dealerships claim to make most of their money from servicing cars. In a certain month, an Acura dealership sold fifteen less used cars than twice the number of new cars. In the smae month, they serviced fifty more than twelve times the number of new cars sold. If the dealership either sold or services a total of 335 cars that month, how many new cars were sold that month? How many use? How many serviced?
Answer:
New cars sold = 20,
Used cars sold = 25
Cars serviced = 290
Step-by-step explanation:
In a month they sold fifteen less used cars than twice the number of new cars.
Lets say 'x' number of new cars were sold, then:
The number of used car sold is:
[tex]2\times x-15=2x-15[/tex]
In the same month they serviced fifty more than twelve times the number of new cars sold. So the number of cars serviced is:
[tex]12\times x+50=12x+50[/tex]
Altogether they sold or serviced 335 cars, so the sum of all the cars sold and serviced should be 335:
[tex]x+(2x-15)+(12x+15)=335[/tex]
Solving for 'x' we get:
[tex]x+2x+12x-15+50=335[/tex]
[tex]15x+35=335[/tex]
[tex]15x=335-35=300[/tex]
[tex]x=\frac{300}{15}=20[/tex]
Therefore, the number of new cars sold in that month is 20.
Number of used car sold [tex]=2x-15=2\times 20-15=40-15=25[/tex]
Number of cars serviced [tex]=12\times x+50=12\times20+50=240+50=290[/tex]
We can also cross check by summing them up:
[tex]290+25+20=335[/tex]
which algebraic rule describes the 270° counter-clockwise rotation about the origin?
a) (x, y) → (−x, y)
b) (x, y) → (x, −y)
c) (x, y) → (y, −x)
d) (x, y) → (−y, x)
270 degree counter clockwise is the same as 90 degrees clockwise.
If you imagine the (x,y) axes rotating 90 clockwise, you will see that what x becomes y, and what was y becomes negative x (after the rotation).
So x-->y, and y-->-x
So the answer (c) is the correct one.
Answer:
option C
Step-by-step explanation:
the correct answer is option C
when a point (x, y ) means point lies in the first quadrant is rotated counter-clockwise to 270° means now the point will be in the fourth quadrant.
hence, in algebraic notation we interchange x by negative x
and y remains the same and their value interchanges so,
the best-suited answer will be (x, y) → (y, -x)
hence, the answer will be option C
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please explain how to do square roots
choosing the 6 winning lottery numbers when the numbers are chosen at random from 0 to 9 A) 1/1,000,000 B) 1/100,000 C) 1/10,000,000 D) 531,441
Answer:
A 1/1,000,000
Step-by-step explanation:
Evaluate (a + b)2 for a = 2 and b = 3
f(a,b) = 2(a+b)
f(2,3) = 2(2+3)
f(2,3) = 2(5)
f(2,3) = 10
Determine the x- and y-intercepts of the graph of y=−13x+3 . Then plot the intercepts to graph the equation.
To find the x-intercept of the equation y = -13x + 3, set y to zero and solve for x to get (3/13, 0). For the y-intercept, set x to zero and solve for y, resulting in (0, 3). These intercepts are then plotted and connected to graph the equation.
Determining X and Y Intercepts
To determine the x-intercept of the linear equation y = -13x + 3, we need to set y to zero and solve for x:
0 = -13x + 3
13x = 3
x = 3/13
So, the x-intercept is (3/13, 0).
To determine the y-intercept, we set x to zero and solve for y:
y = -13(0) + 3
y = 3
Thus, the y-intercept is (0, 3).
Plotting the Intercepts
On graph paper, mark the x-intercept at (3/13, 0) and the y-intercept at (0, 3). Then use a ruler to draw a straight line that passes through these points; this line represents the equation y = -13x + 3.
The slope is the rate of change along a line. However, in this scenario, the slope is not required to plot the line since we already have the intercepts. Nonetheless, for your reference, the slope (m) in the equation y = mx + b corresponds to -13, indicating a decline of 13 units in the y-direction for each single unit increase in the x-direction.
PLEASE HELP ME WITH THIS !!
the top one, use the vertical line test and if their are more than two points on the vertical line when testing the points then the relation is not a function. Which tells you that the last three are not a function.