The area of the semicircle table after it is cut in half [tex]=\frac{9}{2}\pi[/tex] square units.
What is a semicircle?A semicircle is a 2 -D shape which is obtained by cutting a circle along with its diameter. a circle has 2 semicircles when it is cut along with its diameter.
What is a formula for the area of a semicircle?The formula for finding the area of a semicircle is half of the area of a circle with the same radius.
area of semicircle = [tex]\frac{\pi r^{2} }{2}[/tex] square units
Given:
A table with a round top is cut in half so now its shape is a semicircle.
After it is cut, the edge along the wall is 6 ft means that the diameter of the semicircle is = 6 ft
Diameter = 6 ft
Radius = diameter / 2
Radius = 6/ 2
Radius = 3 ft
Therefore now we can calculate the area of the table after it is cut in half
Area of the semicircle table after it is cut in half =
[tex]=\frac{\pi r^{2} }{2} \\=\frac{\pi 3^{2} }{2} \\=\frac{9\pi }{2}\\= \frac{9}{2}\pi[/tex]
The area of the semicircle table after it is cut in half [tex]=\frac{9}{2}\pi[/tex] square units.
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A table with a round top is cut in half so that it can be used against a wall. After it is cut, the edge along the wall is 6 feet. What is the area of the table after it is cut in half? Give your answer in terms of pi.
EXERCISE 12.1 There are 20 girls and 15 boys in a class. (a) What is the ratio of number of girls to the number of boys? (b) What is the ratio of number of girls to the total number of students in the class?
Answer:
(a) 4 : 3
(b) 4 : 7
Step-by-step explanation:
a)
20:15
divide both by the HCF which is 5
4:3
b) 20 + 15 = 35
20 : 35
divide both by HCF which is 5
4:7
if a/b=c, then a= bc
A. If a/b ≠ c, then a ≠ bc.
B. If a =bc then a/b=c.
C.Ff a ≠ bc, then a/b ≠c
D. If a/b=c. then a≠ bc
Even though A and B are both square, AB always equals BA.
How to Prove that if ab=ac, then b=c ?Could someone please assist me in demonstrating that b=c follows from ab=ac and a does not equal 0. You can only apply the field axioms. Here is my try.
ab=ac then, ab-ac=0
a(b-c)=0
a(0)=0 Since a cannot equal zero (this has already been shown), (b-c) must also equal zero, leaving us with...
b-c=0
b=c
The only issue I have with the above is that I presupposed that a did not equal 0. I'm not sure if this is okay because the original theorem I'm attempting to prove includes the claim that "a does not equal 0."
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Can someone help with this and teach me how?
432x486
209952 is the value of 432x486
What is Multiplication?Multiplication is a method of finding the product of two or more numbers
We need to multiply 432 and 486
Steps to follow to find this
1. Line up both your numbers with one on top of the other.
2.Make sure that the places match up for the ones, tens, and hundreds
3. Multiply the top number by the last digit of the second number – the 'ones' unit.
432
×486
___________
2592
3456+
1728++
_____________
209952
Hence, 209952 is the value of 432x486
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What is the equation of the line that passes through the point (-1,-5) and has a slope of 1?
Answer:
y=x-4
Step-by-step explanation:
if the slope is 1, the y intercept is -4
What is the equation of the line that passes through the point (-1,-5) and has a slope of 1?
The equation of a line in slope-intercept form is given by y = mx + b, where m is the slope of the line and b is the y-intercept, which is the point where the line crosses the y-axis.
Since the line passes through the point (-1,-5) and has a slope of 1, we can substitute these values into the equation to solve for the y-intercept. We get:
y = 1x + b
(-5) = 1(-1) + b
-5 = -1 + b
-4 = b
Therefore, the equation of the line that passes through the point (-1,-5) and has a slope of 1 is y = 1x - 4.
Bart is writing lines on a chalkboard that is initially empty. It ordinarily takes Bart 50 minutes to cover the whole board; however, today, Nelson is erasing the board while Bart is writing. Nelson can erase the board in 80 minutes by himself. If they work simultaneously, how long will it be until the whole board is covered?
think about this conceptually first. The difference between their rates of work is going to be the total speed at which the chalk board fills up (speed of writing - speed of erasing).
Ok, so we need to find the speed that Bart is writing, and the speed at which Nelson is erasing.
Bart: 50 minutes/ 1 board
However, we want to find his speed, which will be in boards/minute. Flip the fraction to get 1 board/50 minutes. Then multiply top and bottom by 1/50 in order to get 1/50 board per minute.
Bart's Speed = 1/50 board per minute
Do the same for Nelson, to get 1/80 board per minute (erasing).
The difference between these will be 1/50 - 1/80 = 3/400 board per minute
Since we want to know how long it will take to fill the board at this rate, we multiply 1 board * 1/(3/400) minute per board - this is the same as 1 * 400/3
So, the answer is 400/3 minutes, or 133.33 minutes, or 2 hours, 13 minutes.
#2
This is the same idea as #1. His speed without the headwind is 2000 miles/5 hours = 400miles/hour.
His speed with the headwind is 2000 miles/8 hours = 250 miles/hour.
400m/h - 250m/h = 150m/h
The speed of the wind is 150 miles/hour.
2) AABC and ADEF are shown below. The
m/A=51°and m/F =39°. Is AABC~ADEF?
Fill in the blanks with words from the
word bank then read it to see if it
sounds correct.
the triangles are
because all angles
and the sides are
Word bank: yes, no, maybe, parallel,
vertical angles, corresponding,
complimentary, congruent, right angles,
similar, proportional.
Answer:
Yes, the triangles are similar, because all angles are congruent and the sides are proportional.
Step-by-step explanation:
In similar triangles the corresponding angles have the same measurement. The sum of the interior angles of a triangle is 180. Both triangles have a 90 angle. 180-90 = 90. The other two answer must add to 90.
90 - 51 = 39. So each triangle has a 90, 51 and 39 degree angle.
The sides are also proportional. The scale factor from the smaller triangle to the larger is 2 and if you go the other way the scale factor is 1/2
Please help me solve this I’ll give brainless
Answer:
a) Solving by factoring, you move 225 to the left side by subtracting then making the equation equal to 0.
b) x = -15
x = 15
Step-by-step explanation:
1. x^2 -225=0
2. Find what two numbers equal to -225 then factor by using the expression a^-b^2=(a-b)(a+b)
In this case, -15(15)=-225
(x-15)(x+15)=0
3. Find x
x-15=0
x+15=0
This equation has 2 solutions
x=-15
x=15
To check answer, one of the solutions into X
1) Triangle ABC has vertices A(6,2), B(3,4), and C (2,8). If the triangle is rotated
90° counterclockwise, what are the coordinates of the image A'B'C'?
The coordinates of the image A'B'C are A(-2, 6) B(-3, 4) C(-8, 2)
How do you find the coordinates of a triangle?A specific example of barycentric coordinates for a triangle is referred to as triangular coordinates, and it is also known as a ternary plot or areal coordinates. Triangular coordinates can also refer to any of at least three additional related systems of coordinates in the Euclidean plane.The coordinate geometry formula for the area of a triangle A = (1/2) |x1 1 (y2 2 y3 3) + x2 2 (y3 3 y1 1) + x3 3 (y1 1 y2 2)|, where (x1 1,y1 1), (x2 2,y2 2), and (x3 3,y3 3) are the coordinates of the triangle's vertices, gives the area of a triangle in coordinate geometry.y = mx + c. The points whose coordinates fulfil the equation y = mx + c, on the other hand, always lie on the line with gradient m and y-intercept c.Given data :
Triangle ABC has vertices A(6,2), B(3,4), and C (2,8).
Although I am aware that the coordinates must rotate around the origin, I am unsure of the signs (+ or -).
Consequently, the shape is in the second quadrant of the graph, and the 90-degree angle should be in the fourth quadrant rather than the first (which is 180 degrees anticlockwise) or third (.180 anticlockwise)
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PLEASE HELPPPP brainiest answer will be marked.
35/12 is the value of tanZ
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
Tanz is also given by ratio of sinz and cosz
The tangent formula for a right-angled triangle can be defined as the ratio of the opposite side of a triangle to the adjacent side.
tanz=opposite side/adjacent side
tanz=xy/yz
=35/12
Hence, 35/12 is the value of tanZ
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Graph the equation-5y=-6x+15
A.linear
B.quadratic
C.exponential
D.absolute value
The graph of the equation would be linear in nature.
Option (A) is correct.
What is a graph of an equation?
The picture is obtained by plotting all the points of an equation or inequality. If there is only one variable, the graph is on a number line. If there are two variables, the graph is on the coordinate plane. If there are three variables, the graph is in three-dimensional coordinates.
The given equation is
-5y = -6x + 15
Now arrange it properly, we get
6x - 5y = 15
Now draw the graph, we get
Hence, the degree of the equation is 1. so the graph of the equation would be linear in nature.
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If you rent a car from Caleb's Cars, you'll pay a $61 fee
and $24 per day. At Vinny's Vehicles, you'll pay a $105 fee and $20 per day. Determine the number of days you can rent a car from either place and pay the same amount. Use substitution or elimination.
11 days are required to rent a car at both locations at the same price.
What is a System of Equations?
A system of equations in algebra is made up of two or more equations that are solved together. "A group of equations satisfied by the same set of variables are called a system of linear equations. Finding the values of the variables employed in the system of equations is the first step towards solving it. While maintaining the balance of the equations on both sides, we compute the values of the unknown variables. Finding a variable whose value makes the condition of all the given equations true is the primary goal of solving an equation system.
1st equation: 61+24x=y
Equation 2: 105+ 20x Equals y
Eq. 1 - 2 - subtracted
105-61+20x-24x= 0
44-4x= 0
4x = 44
4 divided by both sides
x= 44/4
x= 11 days
Hence, 11 days are required to rent a car at both locations at the same price.
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Share 850 between 2
Give the answer in it's simplest form.
An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
850 ÷ 2 = 425
The amount each person got is 425.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
The total amount = 850
The number of people to share = 2
Now,
The amount each got.
= 850/2
= 425
Thus,
The amount each person got is 425.
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pls solve with solution(s)^^
1.) 2.25 divided by 2.5 =
2.) 35 divided by 0.05 =
3.) 45 divided by 0.15 =
4.) 630.21 divided by 0.07 =
5.) 0.29 divided by 9.28 =
The solutions for the given division are explained below:
What is meant by division?One of the four fundamental operations of arithmetic, or how to mix numbers to create new ones, is division. Addition, subtraction, and multiplication are the other operations.
In its most basic form, the division of two natural numbers involves counting the instances in which one number is contained inside another, among other possible applications. It is not required that this number be an integer. When two natural numbers are divided with a remainder, or in the Euclidean method, the result is an integer quotient, or the number of times the second number is entirely included in the first, and a remainder, or the portion of the first number.
1) 2.25/2.5=0.9
2) 35/0.05=700
3) 45/0.15=300
4) 630.21/0.07=9003
5) 0.29/9.28=0.03125
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A department store buys 400 shirts at a cost of $4,800 and sells them at a selling price of $20 each. Find the percent markup.
40% is the percent markup.
What does math mean by percentage?
A value or ratio that may be stated as a fraction of 100 is referred to in mathematics as a percentage. Divide the number by the total and multiply by 100 to find the percent of a given number. , a.
an a, the in the an in the an in the an in the an in the Per 100 is what the word percentage signifies.
= 1 - 4800 /20 ÷ 400
= 1 - 12/20
= 1 - 3/5
= 5 - 3/5
= 2/5
Multiply a number to both the numerator and the denominator
2 *20/5 *20
= 40/100
= 40%
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brainliest + ten points to first correct answer! word problem.
A high school soccer team has 18 players. There are 16 years, for juniors, four sophomores, and the rest are freshman. What is the ratio of seniors to freshman?
Incomplete question
What is the slope of the function
Y = -5/4x - 3
PLEASE HELP ASAP
What is the area of AUVW?
-10 -8
-6
W
-4
V
2
104
B
56
2
0
2 $
-6
-8
-10
U
A
6
6
8
00
10
The area of ΔUVW is 21 units.
What is the area of the triangle?
The total area bounded by a triangle's three sides is referred to as the triangle's area. In essence, it is equal to 1/2 of the base times the height, or A = 1/2 b x h. As a result, we need to know the triangular polygon's base (b) and height (h) in order to calculate its area.
From given figure we can see that WV is the height of the triangle and WU is the base.
W = (-3, 6), V = (-3, -8) and U = (0, 6).
To find the distance WV and WU by using the distance formula.
[tex]d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}[/tex]
So,
[tex]WV = \sqrt{(-3+3)^2 +(-8-6)^2} = \sqrt{(-14)^2} = 14\\ WU = \sqrt{((0+3)^2+(6-6)^2} = \sqrt{3^2} = 3[/tex]
Hence, the height is 14 units and the base is 3 units.
⇒
Area of triangle = 1/2 x base x height
= 1/2 x 3 x 14
Area of triangle = 21 units
Hence, the area of ΔUVW is 21 units.
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cos theta = 3/5 and sin theta < 0. Identify the quadrant of the terminal side of theta and
find sin theta
The angle is in 4th quadrant and the value of [tex]sin\theta[/tex] is -(4/5).
What is Trigonometry ?One of the most significant areas of mathematics, trigonometry has a wide range of applications. The study of the connection between the sides and angles of the right-angle triangle is essentially the focus of the field of mathematics known as "trigonometry." Therefore, employing trigonometric formulae, functions, or trigonometric identities can be helpful in determining the missing or unknown angles or sides of a right triangle. Angles in trigonometry can be expressed as either degrees or radians.
There are two other sub-branch classifications for trigonometry. The two varieties of trigonometry are as follows:
Plane TrigonometrySpherical TrigonometryEverything is normal in Quadrant I, and Sine, Cosine, and Tangent are all positive.
However, the x direction is negative and the cosine and tangent become negative in Quadrant II.
Sine and cosine have negative values in Quadrant III.
Sine and tangent are negative in Quadrant IV.
since,
[tex]cos\theta = 3/5 (+ve)\\\ sin\theta\ is\ ( -ve)[/tex].
So the angle is in 4th Quadrant.
we know,
[tex]sin^{2}\theta + cos^{2}\theta = 1[/tex]
⇒ [tex]sin^{2}\theta = 1 - (\frac{3}{5}) ^{2}[/tex]
⇒[tex]sin^{2}\theta = 1 - \frac{9}{25} = \frac{16}{25}[/tex]
⇒ [tex]sin\theta = -\frac{4}{5}[/tex] (since The angle is in 4th Quadrant)
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The sum of three consecutive integers is 42. Which of the equations could represent this relationship? Select the two correct answers. x + (x + 1) + (x + 2) = 42 x + (x + 2) + (x + 4) = 42 (x minus 1) + x + (x + 1) = 42 (x minus 2) + x + (x + 2) = 42 x + 2 x + 3 x = 42
There are two ways to represent this equation: "x + (x + 1) + (x + 2) = 42" and "(x minus 1) + x + (x + 1) = 42".
What is equation?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign. A mathematical phrase with two equal sides and an equal sign is called an equation. An example of an equation is 4 + 6 = 10.
Here,
There are 2 ways,
x+(x+1)+(x+2)=42
(x-1)+x+(x+1)=42
This equation can be written as "x + (x + 1) + (x + 2) = 42" or "(x minus 1) + x + (x + 1) = 42," respectively.
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What is the domain of this function?
Answer:
C) x >= 3
Step-by-step explanation:
The domain of the function is all the x's for this function/graph/equation.
Since you have a graph, it is all the x's where the graph exists. The graph exists from 3 to the right (forever), so x can be everthing 3 and greater.
x >=3
Name two sets of alternate interior angles
Answer:
1st and 3rd ones.
Step-by-step explanation:
<BAD and <ADE are equal because the transversal connects the two angles on alrenate sides. Also <CBA and <CED are equal, as they are again, alternate and the transversal (the diangonal line) connects them.
interval notation: -6.5 < x≤ 3
Answer:
(-6.5,3]
Step-by-step explanation:
Fred is playing tennis. For every 2 of his serves that land in, 3 serves land out. If he hit 22 serves in, how many serves landed out?
Please find the equation that fits this chart
Answer: y = 3/4x
Step-by-step explanation:
(100, 75)
(200, 150)
find slope
150 - 75 / 200 - 100
75 / 100 = 3/4
plug values into formula y=mx+b to find y-intercept
y = 3/4x + b
75 = 3/4(100) + b
75 = 75 + b
b = 0
question 3 a data analyst is working with the world happiness data in tableau. what tool do they use to select the area on the map representing finland?
Pan tool do the data analyst use to select the area on the map representing Finland.
What is data analyst?
A data analyst is working with the world happiness data in table. To use Pan tool to select the area on the map representing Finland.
A data professional examines data to uncover critical insights about a company's consumers and how the data may be utilized to address problems. They also share this information with corporate executives and other stakeholders.
Pan allows us to shift the map to focus on it or present the areas in the way we wish. Simply pick the Pan Option and move the map around to suit your needs. Alternatively, you may move the map by holding down the Shift key.
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DETERMINE WHICH ORDERED PAIRS ARE SOLUTIONS TO THE LINEAR INEQUALITY: 2x - 3y < 15
1: ( 2 , 5 )
2: ( -1 , -7 )
3: ( 3 , -4 )
4: ( 0 , 0 )
The two ordered pairs that are solutions of the inequality are:
( 2 , 5 ) and ( 0 , 0 )
Which ordered pairs are solutions of the inequality?Here we have the linear inequality:
2x - 3y < 15
To check which ordered pairs are solutions, we just need to evaluate these points on the inequality and see if it becomes true or not.
For example, with the first pair (2, 5) we will get:
2*2 - 3*5 < 15
4 - 15 < 15
-11 < 15
This is true, so (2, 5) is a solution.
The other solution is the fourth option (0, 0), so we get:
2*0 - 3*0 < 15
0 < 15
(0, 0) is also a solution.
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What is the minimum temperature?
STEM AND LEAF
I will appreciate your help!!
7) The minimum temperature is 31⁰F. So, the answer is option B.
What is stem and leaf plot?The frequency of various types of values can be easily observed using a stem and leaf plot, also known as a stem and leaf diagram. This graph displays numerical data that is arranged in chronological order. There is a stem and a leaf for each piece of data.
Each first or second digit of the data value is divided into a stem, and the last digit is represented by a leaf, in a stem and leaf plot, which is represented by a particular table. The stem and leaf plot key is the "|" symbol that is used to indicate the values of the stem and the leaf. In the case of 46, the stem is 4 and the leaf is 6.
7) The minimum value in the stem is 3
And the minimum value in the leaf is 1
So, according to the given key 4|3=43°F
Here | denotes the key symbol.
So, in this solution the minimum value of stem is 3 and the minimum value of leaf is 1
Therefore, it must be 3|1
Hence, from the given key
This can be written as 31⁰F
Therefore, the answer is option B.
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what is 2(x + 4) equivalent to
Answer:
2 x x = 2x
2 x 4 = 4
so 2x + 8 is the answer.
To solve this equation we must expand its terms so that we can then multiply and add.
¿What are the equations?Equations are those mathematical equalities divided between two expressions which are called members and separated by their equal sign, in which known elements and unknown or unknown data appear, related by mathematical operations.
We solve the problem:2 (x + 4)2x + 2 × 42x + 8So, our result of the equation is 2x + 8
¡Hope this helped!
below.
Enter your answer in the box below.
5432
2 3 4 5
Answer: 1/-4
Step-by-step explanation:
Find your initial y and x points (-2y and 0x) and then find another point that is equivalent (-1y and -4x) and use m=rise/run = y2-y1/x2/x1 to get your answer of 1/-4
I need an explanation on how to solve it!
The factored form of f(x) is f(x) = (x+2) (x+2)(x+4)
What is a factor?
A factor is a number/expression that divides another number/expression, leaves zero remainder . In other words, if multiplying two numbers/expressions gives us a product, then the numbers/expressions we are multiplying are factors of the product because they are divisible by the product.
f(x) = x³ +8x² + 20x + 16
The value of x at which f(x) is zero, is the root
x= -2 is a root
so, ( x- (-2) ) = ( x+2) is a factor
Divide the polynomial x³ +8x² + 20x + 16 by ( x+2) using long division method:
x+2) x³ +8x² + 20x + 16 ( x² + 6x + 8
x³ + 2x²
_______________________
6x² + 20x + 16
6 x² + 12x
____________________________
8x + 16
8x + 16
__________________________
00
f(x)= (x+2) (x² + 6x + 8 )
Factors of (x² + 6x + 8 ) are (x+2)(x+4)
f(x) = (x+2) (x+2)(x+4)
Thus, the factored form of f(x) is f(x) = (x+2) (x+2)(x+4)
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