A rectangle is placed around a semicircle as shown below. The width of the rectangle is 4 yd. Find the area of the shaded region.
Use the value 3.14 for pi, and do not round your answer. Be sure to include the correct unit in your answer.
The area of the shaded region is calculated as: 6.88 yd²
How to Find the Area of a Shaded Region?The area of the shaded region in the diagram = area of rectangle - area of semicircle.
Given the following:
Width of rectangle = 4 ydRadius of the semicircle (r) = 4 ydLength of the rectangle = 2(4) = 8 ydArea of the semicircle = 1/2(πr²) = 1/2 × 3.14 × 4² = 25.12 yd²
Area of the rectangle = length × width = 8 × 4 = 32 yd²
The area of the shaded region = 32 - 25.12 = 6.88 yd²
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The acceleration function (in m/s2) and the initial velocity are given for a particle moving along a line. a(t) = t + 6, v(0) = 7, 0 ≤ t ≤ 10 (a) Find the velocity at time t. v(t) = Correct: Your answer is correct. m/s (b) Find the distance traveled during the given time interval.
a) The function velocity of the particle is v(t) = 0.5 · t² + 6 · t + 7, b) The distance traveled by the particle is 467 feet.
How to determine the velocity and the distance traveled by a particleIn this problem we have the equation that represents the acceleration of a particle. The function velocity (v) is obtained by integrating the function acceleration (a) and the function position is obtained by integrating the function velocity. Now we present the definitions of each function:
Velocity
v(t) = ∫ a(t) + C
Position
s(t) = ∫ v(t) + C
Where C is the integration constant.
The distance traveled during the time interval is found means of definite integrals:
Δs = [tex]\int\limits^b_a {v(x)} \, dx[/tex]= s(b) - s(a)
a) First, determine the function velocity of the particle:
v(t) = ∫ (t + 6) dt + C
v(t) = 0.5 · t² + 6 · t + C
7 = C
v(t) = 0.5 · t² + 6 · t + 7
b) Second, determine the distance traveled in the given time interval:
Δs = s(10) - s(0)
Δs = 0.167 · 10³ + 3 · 10² + 7 - 0.167 · 0³ - 3 · 0² - 7
Δs = 467
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What is function definition with example?
A function is defined as a relation between a set of inputs having one output each.
Say, there is an element x in the sets of input, now it can be paired with no more than one y in the sets of output. We should note that the same y can be paired with different x's, but not the reverse. All linear equations, with the exception of vertical and horizontal lines, are functions.
The function is generally written as "f(x)" where x is the input value.
let us take an example-
f(x) = x/2
here, f(x) is a function because each input "x" has a single output "x/2":
• f(2) = 1
• f(5) = 2.5
• f(−12) = −6
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A model rocket is shot straight up from the roof of a school. The height, h, in meters, after t seconds can be approximated by h(t)=-5t2+22t+15. Answer the following questions algebraically, showing all of your work
How long does it take for the rocket to pass a window that is 10m above the ground? (hint: make h=10, group like terms, then solve the quadratic equation)
Answer: [tex]\frac{11+\sqrt{146}}{5}[/tex] seconds
Step-by-step explanation:
[tex]10=-5t^2 +22t+15\\\\5t^2 -22t-5=0\\\\t=\frac{22 \pm \sqrt{(-22)^2 -4(5)(-5)}}{2(5)}\\\\t=\frac{11+\sqrt{146}}{5} \text{ } (t > 0)[/tex]
find the value of x 20 3x 5
The value of x is 5
What are algebric expressions?
Algebraic expressions are the idea of expressing numbers using letters or alphabets without specifying their actual values.
The given expression is 20 - 3x = 5
We need to calculate the value of x
20 - 3x = 5
20 - 5 = 3x
15 = 3x
3x = 15
x = 5
Therefore, the value of x is in the algebric expression is 5
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How do you match equivalent expressions?
To match equivalent expression is the fractions with distinct numerators and denominators but the same value are said to be equivalent fractions.
In mathematics, equivalent fractions are those with the same denominator and differing numerators.
According to equivalent fractions, two or more fractions are considered to be equal if both provide the same fraction following simplification. Let's imagine that two fractions, a/b and c/d, were simplified to provide comparable fractions, e/f. In this case, the two fractions are equal to one another.
For instance, if we simplify 5/15, we get a fraction that is equal to 1/3, which is equal to 5/15.
We have to find how do we match equivalent expression.
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Think About the Process Van purchased a DVD player on sale. The original selling price was $179.30. The sale price was
$157.17. What is the first step in finding the percent markdown? Find the percent markdown.
What is the first step in finding the percent markdown?
OA. Find the cost.
OB. Find the greatest markdown possible.
C. Find the markdown.
The percent markdown was%. (Round to the nearest whole number as needed.)
Answer:19.26%
Step-by-step explanation: yeah
Answer:
19%
Step-by-step explanation:
There are only 5 steps here they are:
1. Divide 144.77 by 179.30
2. You get the answer 0.80741773...
3. You round it to 0.81.
4. You turn it into a percent by moving the dot(decimal) to the right four times.
5. And then you subtract it from 100 and you get 19% for the discount.
so therefore the answer is 19%
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please I need help on question 9
Applying the definition of congruent triangles, the values of x and y are:
x = 11; y = 6
What are Congruent Triangles?If two triangles are congruent, all of it corresponding parts, which are angles and sides, will have equal measure.
Since triangles RWS and TUV are congruent triangles, therefore:
<R = <T
<W = <U
<S = <V
RW = TU
WS = UV
RS = TV
Thus, find the value of x:
90 + 8x - 27 + 29 = 180
92 + 8x = 180
8x = 180 - 92
8x = 88
Divide both sides by 8
8x/8 = 88/8
x = 11
Find the value of y:
RS = TV
Substitute
25 = 3y + 7
25 - 7 = 3y
18 = 3y
18/3 = y
y = 6
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Ace Guitars produces acoustic and electric guitars. Each acoustic guitar yields a profit of $30 and requires 2 work hours in Factory A and 1 work hours in Factory B. Each electric guitar yields a profit of $50 and requires 2 work hours in Factory A and 3 work hours in Factory B. Each factory operates for at most 12 hours each day. Graph the feasible region. Then, find the number of each type of guitar that should be produced each day to maximize the company’s profit.
Choose all equations that would be needed to graph the feasible region.
Inequalities to support the questions
2x + y ≤ 12 2x+ 3y ≤ 12x ≥ 0, y ≥ 0What is Inequality?Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.
Given:
Each factory operates for at most 12 hours each day.
let maximum profit by factory A be x and Factory B be y.
Then, Inequalities to support the questions
2x + y ≤ 12
and, 2x+ 3y ≤ 12
and, x ≥ 0, y ≥ 0
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What is the formula for finding an obtuse angle?
We can find the obtuse angle by using the lengths of the sides of the triangle.
What is an obtuse angle?
Any angle greater than 90° is considered obtuse: A straight angle is one that measures 180°: A zero angle is one with a measurement of 0°: Complementary angles are those whose measures add up to 90°: Supplementary angles are those with measures that add up to 180°.
The lengths of the triangle's sides can be used to calculate an obtuse triangle. Add the squares of the lengths of both sides of the triangle that intersect to form the obtuse angle. For example, if the lengths of the sides are 3 and 2, squaring them yields 9 and 4.
Hence, we can find the obtuse angle by using the lengths of the sides of the triangle.
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Convert to standard form y+4= -3(x+1)
Answer:
3x + y = - 7-----------------------------------
The standard form of linear equation is:
ax + by = cConvert the given equation in below steps:
y + 4 = - 3(x + 1) Distributey + 4 = - 3x - 33x + y = - 3 - 4 Collect variables in one side3x + y = - 7 SimplifyWhat is the point of a triangle called?
The points of a triangle are known as vertices, and various triangle points are centroid, circumcenter, incenter and orthocenter.
A triangle is a three-sided polygon.
The triangle's three points are known as vertices.
Several triangle-related points:
A triangle's centroid is the point where three medians cut each other. A median is the line that connects a vertex to the opposite side's midpoint.At the circumcenter, the three perpendicular bisectors of a triangle's sides meet. The circumcenter is also the center of the circle formed by passing through the three vertices of the triangle. The orthocenter is the point at which the triangle's altitudes, or the perpendicular lines between each vertex and the opposite side, intersect.The incenter of a triangle is the point at which the three bisectors of the triangle's interior angles intersect. This is also the center of the inscribed circle, also known as the triangle's incircle.A triangle's Euler line is the line that connects the orthocenter, circumcenter, and centroid. It also contains the Nine Point Circle's center.Thus, the points of a triangle are known as vertices, and various triangle points are centroid, circumcenter, incenter and orthocenter.
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A magician makes potions by combining maple syrup from a magical maple tree with ordinary water. The magician starts with a large supply of two potions: a red potion, which is 50% magical syrup by volume (and the rest is just water), and blue potion, which is 10% magical syrup by volume. (Perhaps you're wondering how the same syrup can produce both red and blue potions. That's why it's magic syrup!)
(a) Find the amount of red potion (in mL) that must be added to 200 mL of blue potion in order to produce potion that is 30% magical syrup by volume.
(b) Find the amounts of red potion and blue potion (in mL) that can be combined in order to produce 150 mL of a potion that is 30% magical syrup by volume.
(c) Does there exist a combination of red potion and blue potion that can produce a potion that is 20% magical syrup by volume?
Answer:
Step-by-step explanation:
its a
Which symbol is represent function?
The value of a function f at an element x of X, denoted by the symbol f(x), is regarded to as the picture of x as per f or the value of f implemented to the input x.
In the given question we have to define which symbol is represent function.
The notation f: X→Y denotes a function, its domain, and its codomain. The value of a function f at an element x of X, denoted by the symbol f(x), is regarded to as the picture of x as per f or the value of f implemented to the input x.
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Solve each system of equations by graphing. Identify all possible solutions.
y=x²+6x
y=x-4
So the solution of equations y = x² + 6x and y = x - 4 are (-1,-5) and (-1,-5), respectively (-4,-8).
What is system of equations?For a solution to be a solution to a system, it must satisfy all of that system's equations, and because all points satisfying an equation are in their graphs, a solution to a system is the intersection of all of its equations at a single point (as we need a common point, which will be an intersection of course) (this can be one or many, or sometimes none)Given 2 equations,
y = x² + 6x
y = x - 4
x² + 6x = x -4
x² + 5x + 4 = 0
By solving this equation we get x = -1 and x = -4
By substituting x in equation we can find values of y
y = x² + 6x
y = -1² + 6(-1)
= 1 - 6
= -5
Similarly substituting x = -4
y = -4² + 6(-4)
= 16 - 24
= -8
So the points of equation y = x² + 6x and y = x - 4 are (-1,-5) and (-4,-8).
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Answer:
The possible solutions for the given equations y=x²+6x and y=x-4 are (-1, -5) and (-4, -8).
Solve the system of equations:Given,
y=x²+6x ⇒ equation 1
y=x-4 ⇒ equation 2
Substitute equation 2 in equation 1....
x - 4 = x²+6x
x²+6x - x + 4 = 0
x²+ 5x + 4 = 0
x² + x + 4x + 4 = 0
x (x + 1) + 4 (x + 1) = 0
(x + 1) (x + 4) = 0
x + 1 = 0 ; x + 4 = 0
x = -1 ; x = -4
Substitute x = -1 and x = - 4 in 2nd equation:
y = x - 4
When x = -1;
y = -1 - 4
y = -5
When x = -4
y = - 4 - 4
y = -8
So, the solutions for the equations y=x²+6x and y=x-4 is (-1, -5) and (-4, -8)
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Cole and Maggie play table tennis. Maggie has won 4 more games than Cole. Is it possible for Cole to have won 13 games if the sum of the games Cole and Maggie have won together is 30?
*
1 point
Yes; Cole could have won 13 games because 2x + 4 = 30.
Yes; Cole could have won 13 games because 13 + 4 is less than 30.
No; Cole could not have won 13 games because 2x + 13 ≠ 30.
No; Cole could not have won 13 games because 2x + 4 ≠ 30
The answer to this Question is A we can use basic knowledge from linear equations to find the answer
What is Linear Equation?
Linear Equation is a equation in which degree of variables is 1 only
Yes the given case is possible only under some conditions that we can define as follows and as given in Linear Equations from Options
together cole and maggie have won 30 games and we are also given that out of those 30 maggie has won 4 games
we should closely see at Linear Equations given in Options.
therefore cole has won 26 games which is more than 13
Hence the answer to the Question is Yes
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(-4x4+6+3/3)x6
What is the solution
Answer:___(-4x⁴+9)x⁶
3
What is Incentre of triangle ABC?
The Incenter of triangle ABC is I = (ax1+bx2+cx3 / a+b+c , ay1+by2+cy3 / a+b+c).
Given:
Let I be the incenter of triangle ABC.
Let A(x1,y1) ,B(x2,y2) and C(x3,y3) are vertices.
Let a,b and c are lengths of the sides AB,BC and AC.
we know that:
Incenter I = (ax1+bx2+cx3 / a+b+c , ay1+by2+cy3 / a+b+c)
we can find a, b and c values using the distance formula between the vertices.
AB = a = [tex]\sqrt{(x2-x1)^2 + (y2-y1)^2}[/tex]
BC = b = [tex]\sqrt{(x3-x2)^2 + (y3-y2)^2}[/tex]
AC = c = [tex]\sqrt{(x3-x1)^2 + (y3-y1)^2}[/tex]
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Is the exponential function 5 x?
It is Growing Exponential function because the base is greater than 1 and the exponent has a positive sign.
What is exponential decay function?
A exponential decay is a function that, as the name implies, decays exponentially. So it decays fast at the beginning and slower as the value of the variable increases.
[tex]y=5^x[/tex]
It is a function called "Exponential function". The base determines the growth or decay of the function.
If base > 1, then the function grows, otherwise if base is between 0 and 1, the function decays.
Here, the base is positive and it's not 1 or 0.
If we have
[tex]y=5^{-x}[/tex]
this function can be rewritten in this way:
[tex]y=(1/5)^x[/tex]
Here, base between 0 and 1, the function decays
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What does m<2 mean in geometry?
Answer: I hope this is helpful mark me brainlist if this apply to you
Step-by-step explanation:
The square meter, also called the meter squared, is the International System of Units (SI) unit of area. The symbol for square meters is m2. Less formally, square meter is sometimes abbreviated as sq m.A metre square is a square with sides one metre in length – it refers to the shape and the side length, not the area. By contrast, a square metre is an area and can be any shape.The basic unit of length is the meter and is denoted as. In geometry, can be used as a variable to denote a line and can be used to name a point. In algebra, denotes the slope of a line in the equation y = m x + c .
If m<1 = 128, then m<8=
Answer:
m<8=1024
Step-by-step explanation:
Since they are asking for m<8, we do 128*8=1024.
If P(x,6) and Q(14,-2) are two points and distance between them in 10 units, find the possible values of x.
Answer:
x = 8 , x = 20
Step-by-step explanation:
Calculate PQ using the distance formula and equate to 10
d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = Q (14, - 2 ) and (x₂, y₂ ) = P (x, 6 )
PQ = [tex]\sqrt{x-14)^2+(6-(-2))^2}[/tex]
= [tex]\sqrt{(x-14)^2+(6+2)^2}[/tex]
= [tex]\sqrt{(x-14)^2+8^2}[/tex]
= [tex]\sqrt{(x-14)^2+64}[/tex]
Equating to 10
[tex]\sqrt{(x-14)^2+64}[/tex] = 10 ( square both sides to clear the radical )
(x - 14)² + 64 = 10² = 100 ( subtract 64 from both sides )
(x - 14)² = 36 ( take square root of both sides )
x - 14 = ± [tex]\sqrt{36}[/tex] = ± 6 ( add 14 to both sides )
x = 14 ± 6
then
x = 14 - 6 = 8 or x = 14 + 6 = 20
blank = blank x 0.1 + 8 x blank
Answer:
0
Step-by-step explanation:
0 = 0×0.1+8×0
0 = 0+8×0
0= 8×0
0=0
The equation of a parabola is y = a(x - 1)^2 + k and the points (2, 6.5) and (-1, -1) lie on the parabola. Determine the maximum value of the parabola.
The maximum value of the parabola is represented by y-vertex whose value is 9.
What is a Quadratic Function?
The quadratic function can represent a quadratic equation in the Standard form: ax²+bx+c=0 where: a, b and c are your respective coefficients. In the quadratic function, the coefficient "a" must be different than zero (a≠0) and the degree of the function must be equal to 2.
For solving a quadratic function you should find the discriminant: Δ=b²-4ac . And after that you should apply the discriminant in the formula:[tex]x=\frac{-b\pm\sqrt{\Delta} }{2a}[/tex] .
The question gives a quadratic equation and two points, but you do not know some coefficients. Then, you should find the unknown coefficients and after that, you should find the y-vertex of the parabola ([tex]y_v=\frac{-{\Delta} }{4a}[/tex]).
For finding the coefficients, you should solve the system of equations.
y = a(x - 1)² + k -> points (2, 6.5) and (-1, -1), thus
6.5=a(2-1)² + k (1)
-1=a(-1-1)² + k (2)
Simplifying the equations
6.5=a(1)² + k ( 1 )
-1=a(-2)² + k (2)
6.5=a+ k ( 1 )
-1=4a+ k (2)
Multiply equation 1 by -1
-6.5=-a- k ( 1 )
-1=4a+ k (2)
Sum equations 1 and 2
-7.5=3a
a= -2.5
If a= -2.5, from equation 1, you have
-6.5=-a- k
-6.5=-(-2.5)- k
-6.5=2.5- k
k=2.5+6.5
k=9
Then , the parabola equation is y= -2.5 (x-1)² +9. You can rewrite it as:
y=-2.5(x²-2x+1)+9
y= -2.5x²+5x-2.5+9
y= -2.5x²+5x+6.5
Find y-vertex[tex]y_v=\frac{-{\Delta} }{4a}=y_v=\frac{-{(b^2-4ac)} }{4a}=\frac{-{(5^2-4*(-2.5)*(6.5))} }{4*(-2.5)}=\frac{-90}{-10} =9[/tex]
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Can someone help me please? I would really appreciate the person to help me.
The system of linear equations have variable unique solutions, infinitely many solutions and no solutions.
System of Linear EquationIn algebra, a system of equations comprises two or more equations and seeks common solutions to the equations. "A system of linear equations is a set of equations which are satisfied by the same set of variables."
A system of equations as discussed above is a set of equations that seek a common solution for the variables included.
1.
y = -2x + 3 ...eq(i)
y = 1/2x - 7 ...eq(ii)
The solutions to the linear equations (x,y) are (4, -5)
2.
y = 2x - 7 ...eq(i)
y = 5x + 5 ...eq(ii)
The solutions to the linear equations (x,y) are (-4, -15)
3.
3y = -12x + 6 ...eq(i)
y = -4x + 2 ...eq(ii)
The linear equations (x, y) have infinitely many solutions
4.
y = -2x + 3 ...eq(i)
y = 2x - 1 ...eq(ii)
The linear equations (x,y) have solutions of (1, 1)
5.
y = 5x + 4 ...eq(i)
y = 5x - 2 ...eq(ii)
The linear equations have no solutions
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A car is traveling at a rate of 20 meters per second. What is the car's rate in kilometers per hour? How many kilometers will the car travel in 2 hours? Do not round your answers.
Rate:
Distance traveled in 2 hours:
Answer:
Rate = 72 km per hour
Distance traveled in 2 hours = 144 km
Step-by-step explanation:
The car speed is given as 20 meters per second
There are 3600 seconds in an hour
So in 1 hour the car would travel 20 x 3600 = 72,000 meters. This is equivalent to 72,000 meters per hour
There are 1000 meters in a kilometer
So, in terms of kilometers, the car would travel 72,000/1000 = 72 km i one hour. This is equivalent to a speed of 72 km per hour
In 2 hours the car would travel 72 x 2 = 144 km
write the equation in logarithmic form 62554
The logarithmic form of the equation is log₅ 4 = 625.
Logarithmic form
In math, a way to write an exponential function in reverse is called as logarithmic functions.
Given,
Here we have to convert the given equation
615 = 5⁴
Now, we have to convert this into the logarithmic form .
The general form of the logarithmic form is written as,
f(x) = logₐ x
Where a refers the base and x refers the exponent.
Here the value of base is 5 and the value of exponent is 4.
And the value of f(x) = 25,
Therefore, the logarithmic form is written as,
=> log₅ 4 = 625.
I HAVE ANSWERED THE QUESTION IN GENERAL AS GIVEN QUESTION IS INCOMPLETE.
Complete Question:
Convert the equation into logarithmic form: 615 = 5⁴
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What is a quadrilateral mention 6 types of quadrilaterals?
A four-sided polygon with four angles is known as a quadrilateral. Parallelogram, rhombus, rectangle, trapezoid, square, and isosceles trapezoid are the six different forms of quadrilaterals.
What is Quadrilateral?
A two-dimensional shape called a quadrilateral is described as having four sides, four vertices, and four angles. Concave and convex are the two primary varieties. Convex quadrilaterals also fall under a number of other categories, including trapezoids, parallelograms, rectangles, rhombus, and squares.
A parallelogram is a particular kind of quadrilateral in geometry. It has four sides and is a two-dimensional figure. The opposite sides of a parallelogram must be parallel, congruent, and have equal opposite angles as these are its most crucial characteristics.
A quadrilateral with all equal sides is a rhombus. Rhombuses are a particular kind of parallelogram in which all of the sides are equal because the opposite sides of a parallelogram are equal.
An enclosed 2-D shape called a rectangle has four sides, four corners, and four right angles (90°). A rectangle has equal and parallel opposite sides. A rectangle has two dimensions—length and width—because it is a two-dimensional form. The rectangle's longer side is its length, while its shorter side is its breadth.
An open, flat object with four straight sides and one pair of parallel sides is referred to as a trapezoid or trapezium. A trapezium's non-parallel sides are referred to as the legs, while its parallel sides are referred to as the bases.
A square is a quadrilateral with four equal sides and four equal angles that is a regular quadrilateral. The square's angles are at a straight angle or 90 degrees. The square's diagonals are also equal and split at a 90-degree angle.
An isosceles trapezoid is a trapezoid in which the left and right side lengths are also equal since the base angles are equal.
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We are looking to factor 23x^2 + kx - 5 + x^2 - 3. Some values of k allow us to factor it as a product of linear binomials with integer coefficients. What are all such values of k?
The values of k that allow us to factor it as a product of linear binomials with integer coefficients are k ≥ -16√3
What are linear binomials?Linear binomials are mathematical expression that contain only two terms. Examples include x + 3.
What is a quadratic equation?A quadratic equation is an equation in which the highest power of unknown is 2.
How to find the values of k?Since we have the quadratic equation 23x² + kx - 5 + x² - 3, to determine the value of k which makes it a linear binomial, we simplify and find the discriminant.
What is the discriminant of a quadratic equation?The discriminant of a quadratic equation ax² + bx + c is D = b² - 4ac
Simplifying the quadratic equation, we have
23x² + kx - 5 + x² - 3 = 23x² + x² + kx - 5 - 3
= 24x² + kx - 8
Comparing the above quadratic equation with ax² + bx + c, we have that
a = 24b = k and c = -8So the discriminant, D = b² - 4ac
= k² - 4 × 24 × 8
= k² - 768
The allowable values of k are gotten when the discriminant D ≥ 0
So, D ≥ 0
⇒ k² - 768 ≥ 0
⇒ k² ≥ 768
⇒ k ≥ ±√768
⇒ k ≥ ±√(256 × 3)
⇒ k ≥ ±16√3
⇒ k ≥ -16√3
So, the values of k are k ≥ -16√3
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please help me answer this question
Answer:
this 1
Step-by-step explanation:
same doubt pease any help
