find the area of figure using 3.14 for pi. round your answer to nearest tenth if necessary.
Answers
Given a figure to find the area of the figure.
The given figure is the combination of two triangles and a semi-circle.
Here the radius and the base of the triangle is 10 yd and the height of the triangle is 21 yd. So, the area of the figure is;
[tex]\begin{gathered} A=2\times\frac{1}{2}\times\text{base}\times\text{height}+\frac{\pi r^2}{2} \\ =10\times21+\frac{3.14\times10^2}{2} \\ =210+\frac{314}{2} \\ =210+157 \\ =367 \end{gathered}[/tex]Thus, the area of the figure is 367 yd^2.
Related Questions
This graph shows the solution to which inequality?3.2)(-3,-5)O A. ys fx-2B. vfx-2O c. vfx-2OD. yzfx-2
Answers
First, find the equation of the line, given that the points (3,2) and (-3,-6) belong to that line. To do so, use the slope formula and then substitute the value of the slope and the coordinates of a point on the slope-point formula of a line:
[tex]y=m(x-x_0)+y_0[/tex]The slope of the line, is:
[tex]\begin{gathered} m=\frac{\Delta y}{\Delta x} \\ =\frac{(2)-(-6)}{(3)-(-3)} \\ =\frac{2+6}{3+3} \\ =\frac{8}{6} \\ =\frac{4}{3} \end{gathered}[/tex]Therefore, the equation of a line (using the point (3,2)) is:
[tex]\begin{gathered} y=\frac{4}{3}(x-3)+2 \\ =\frac{4}{3}x-\frac{4}{3}\times3+2 \\ =\frac{4}{3}x-4+2 \\ =\frac{4}{3}x-2 \end{gathered}[/tex]Since the colored region on the coordinate plane is placed above the line
y=(4/3)x-2, then the equation of the inequality is:}
[tex]undefined[/tex]Find a degree 3 polynomial that has zeros -2,3 and 6 and in which the coefficient of x^2 is -14. The polynomial is: _____
Answers
Given:
The zeros of degree 3 polynomial are -2, 3 , 6.
The coefficient of x² is -14.
Let the degree 3 polynomial be,
[tex]\begin{gathered} p(x)=(x-x_1)(x-x_2)(x-x_3) \\ =(x-(-2))(x-3)(x-6) \\ =\mleft(x+2\mright)\mleft(x-3\mright)\mleft(x-6\mright) \\ =\mleft(x^2-x-6\mright)\mleft(x-6\mright) \\ =x^3-x^2-6x-6x^2+6x+36 \\ =x^3-7x^2+36 \end{gathered}[/tex]But given that, coefficient of x² is -14 so, multiply the above polynomial by 2.
[tex]\begin{gathered} p(x)=x^3-7x^2+36 \\ 2p(x)=2(x^3-7x^2+36) \\ =2x^3-14x^2+72 \end{gathered}[/tex]Answer: The polynomial is,
[tex]p(x)=2x^3-14x^2+72[/tex]Enter the equation for the graph.АА- 112y = [?] cos([ ]x)Enter
Answers
A cosine function has the form.
[tex]y=A\cos (Bx)[/tex]Where A refers to the changes of the y-coordinate along the curve, that is, the amplitude. And B refers to the period, that is, the repetition period of the curve.
According to the graph, the amplitude is 1, so A = 1.
Notice that from 0 to 2(pi) the function completes two cycles, which means B = 3.
Therefore, the function is [tex]y=1\cdot\cos (3x)[/tex]1 point Esther thinks she understands how to find the midpoint of a segment on a graph. "I always look for the middle of the line segment. But what should I do if the coordinates are not easy to graph?" she asks. Find the midpoint of KL if (2.125) and L(98, 15). *
Answers
In this case, we can write out the parameters
[tex]\begin{gathered} x_1=2,_{}y_1=125, \\ x_2=98,y_2=15 \end{gathered}[/tex]Thus, substitute the coordinates in the mid-point formula and simplify
[tex]\begin{gathered} x_m=\frac{98+2}{2}=\frac{100}{2}=50 \\ y_m=\frac{125+15}{2}=\frac{140}{2}=70 \end{gathered}[/tex]Hence, the coordinate of the mid-point is (50, 70)
Andre drew a plan of a courtyard at a scale of 1 to 60. On his drawing, one side of the courtyard is 2.75 inches. What is the actual measurement of that side of the courtyard? Show your work.
Answers
Okay, here we have this:
Considering that the scale is of 1 to 60, we obtain the following:
2.75 inches * 60 =165.
Show all work to solve the equation for x. If a solution is extraneous, be sure to identify it
Answers
So we need to solve the following equation for x:
[tex]\sqrt[]{x-2}+8=x[/tex]The first step would be substracting 8 from each side of the equation:
[tex]\begin{gathered} \sqrt[]{x-2}+8-8=x-8 \\ \sqrt[]{x-2}=x-8 \end{gathered}[/tex]The next step is to square
Kara categorized her spending for this month into four categories: Rent, Food, Fun, and Other. Theamounts she spent in each category are pictured here.Food$333Rent$417Other$500Fun$250What percent of her total spending did she spend on Fun? Answer to the nearest whole percent.
Answers
In this problem we have to calculate the total spences so we add all the costs so:
[tex]\begin{gathered} T=333+417+500+250 \\ T=1500 \end{gathered}[/tex]So 1500 is the 100% so now we can calculate which percentage correspount to 250 so:
[tex]\begin{gathered} 1500\to100 \\ 250\to x \end{gathered}[/tex]so the equation is:
[tex]\begin{gathered} x=\frac{250\cdot100}{1500} \\ x=16.66 \end{gathered}[/tex]So she spend 16.66% in fun
Solve each system of equations "-x+y+2z=-5" 5x+4y-4z=4 x-3y-2z=3
show your work please so i can understand how to do it!
Answers
x=-4, y=1 and z=-5 are solutions of x+y+2z=-5" 5x+4y-4z=4 x-3y-2z=3
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The given three equations are
-x+y+2z=-5.....(1)
5x+4y-4z=4....(2)
x-3y-2z=3....(3)
Add equations (1) and (3)
-x+y+2z+x-3y-2z=-5+3
Add the like terms
-2y=-2
y=1
Now put value of y in equations (1) and (2)
-x+2z=-6..(4)
5x-4z=0...(5)
Multiply with 5 on equation 4 and add with equation 5
-5x+10z+5x-4z=-30
6z=-30
z=-5
Now put y and z values in equation (1)
-x+1+2(-5)=-5
-x+1-10=-5
-x-9=-5
-x=4
x=-4
Hence x=-4, y=1 and z=-5 are solutions of x+y+2z=-5" 5x+4y-4z=4 x-3y-2z=3
To learn more on Equation:
https://brainly.com/question/10413253
#SPJ1
A piece of paper is folded into half repeatedly. The thickness of the paper in inches is modeled by the function y = 2x/1000, where x is the number of folds. How thick will the paper be if you could fold it 10 times?About an inchAbout 2 inchesAbout 3 inchesAbout 4 inches
Answers
Given: A piece of paper is folded into half repeatedly. The thickness of the paper in inches is modeled by the function y = 2x/1000, where x is the number of folds.
Required: To determine the thickness of the paper if the paper is folded 10 times.
Explanation: The thickness of the paper is given by the function
[tex]y=\frac{2x}{1000}[/tex]Here, x is the number of folds=10
Hence,
[tex]\begin{gathered} y=\frac{2\times10}{1000} \\ =0.02\text{ inches} \end{gathered}[/tex]Final Answer: After 10 folds, the thickness of the paper is 0.02 inches.
1. Ms. Oates is going to plant grass in her backyard. It is 14feet wide and 20.5 feet long. What is the area of thebackyard that will need to be covered with grass?
Answers
Area of a rectangle is given by the expression:
[tex]A=\text{base}\times height[/tex]Then:
[tex]\begin{gathered} A=20.5\times14 \\ A=287\text{ square f}eet \end{gathered}[/tex]The area that will need to be covered is 287 square feet.
P(-3,-5) and Q(1.–3) represent points in a coordinate plane. Find the midpoint of Pe.
Answers
By formula,
Midpoint between two points PQ =
[tex](\frac{x_2+x_1}{2},\text{ }\frac{y_2+y_1}{2})[/tex][tex]\begin{gathered} (\frac{1+-3}{2},\text{ }\frac{-3+\text{ -5}}{2}) \\ \\ \frac{-2}{2},\text{ }\frac{-8}{2}\text{ = (-1,-4)} \\ \\ \end{gathered}[/tex]So, (-1,-4) (option 3)
please show and explain this please
Answers
only answer ;( c.
Step-by-step explanation:
so hope it help
f(x) = (x + 2)(x - 3)(x - 1)(x - 1)
so the correct answer is C
Find the volume of a cylinder and cinema given the following dimensions
Answers
Given:
The radius , r=20 ft.
The height , h=23 ft.
The volume of the cylinder can be calculated as,
[tex]\begin{gathered} V=\pi r^2h \\ =\pi\times20^2\times23 \\ =28902.65ft^2 \end{gathered}[/tex]Therefore, the volume of the cylinder is 28902.65 sq.ft.
The volume of the cone can be calculated as,
[tex]\begin{gathered} V=\frac{1}{3}\pi\times r^2h \\ =\frac{1}{3}\pi\times20^2\times23 \\ =9634.22ft^2 \end{gathered}[/tex]Therefore, the volume of the cone is 9634.22 sq.ft.
Find the volume of 12 cm
Answers
Answer:
1728 cm ^ 3.
Step-by-step explanation:
we are given 12 cm
As we know formula of volume of cube = s ^3 ( side * side * side ) So = 12 * 12* 12 = 1728 cm ^ 3.
Find the Volume cylinder (8cm) (12cm) h = 8cm r = 12cm h = 8 cm r = 12 cm. The volume of a cylinder is equal to the area of the base πr2 π r 2 times the height. π⋅(radius)2 ⋅(height) π ⋅ ( r a d i u s) 2 ⋅ ( h e i g h t) Substitute the values of the radius r = 12 r = 12 and height h = 8 h = 8 into the formula to find the volume of the cylinder
P.s hopes this helps
How do I do this ? I need to find the solution for it
Answers
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given equations
[tex]\begin{gathered} y=-\frac{4}{3}x \\ y=\frac{3}{2}x \end{gathered}[/tex]STEP 2: Define the point that is the solution for the given functions on the graph
The solution of such a system is the ordered pair that is a solution to both equations. To solve a system of linear equations graphically we graph both equations in the same coordinate system. The solution to the system will be in the point where the two lines intersect.
STEP 3: Determine the solution for the system of equations
It can be seen from the image below that the two lines intersect at the origin and hence they are given as the solutions to the given system of equations.
Hence, the solutions are:
[tex]x=0,y=0[/tex]
The height, in feet, of a particle from the ground is given by the function s(t) = 1.512 + 20r, where 0 ≤ ≤ 17.
Find the velocity of the particle at t = 4.
Answer
feet per second
Answers
The velocity is v= 30.6 ft/ sec.
What is a velocity?Velocity defines the direction of the movement of the body or the object. Speed is primarily a scalar quantity. Velocity is essentially a vector quantity. It is the rate of change of distance. It is the rate of change of displacement.
Given that,
We have given the height
s(t) = 0.2[tex]t^{3}[/tex] + 21t, where 0 ≤ [tex]x[/tex] ≤ 17.
To find the velocity we have to differentiate s(t) wrt to t.
s(t) = 0.2[tex]t^{3}[/tex] + 21t
= 0.6[tex]t^{2}[/tex]+21
velocity of the particle at t = 4
s(4) = 0.6*[tex]4^{2}[/tex]+21
= 9.6+21
= 30.6
v= 30.6 ft/ sec
Hence, The velocity is v= 30.6 ft/ sec.
To learn more about velocity from the given link:
https://brainly.com/question/25749514
#SPJ13
The graph shows a dilation of trapezoid TRAP with respect to the origin which statements are true about the figures select three
Answers
A dilation means an elongation of the sides of a figure
So in a dilation the sides are bigger than at the original figure
A key formula for found dilation is Pithagoras theorem
For calculate T'R'
T'R' is the exact diagonal of OT' and OR', that means
OT' + OR' = T'R' in vectorial sum
OT'^ 2 + OR'^ 2 = T'R'^2. In numerical sum
So then T'R'^2 = 5^2 + 5^2 = 50.
and T'R'= √50
Now find TR to find the factor of dilation that is
T'R'/TR
Ninas math classroom is 6 and 4/5 meters long and 1 and 3/8 meters wide. What is the area of the classroom?
Answers
The most appropriate choice for area of rectangle will be given by -
Area of classroom = [tex]4\frac{27}{40}[/tex] [tex]m^2[/tex]
What is area of rectangle?
Rectangle is a four sided figure whose parallel sides are equal and whose every angle is 90°
The total space taken by the rectangle is called area of the rectangle.
If the length of the rectangle be l and the breadth of the rectangle be b, then area of the rectangle is given by
Area = [tex]l \times b[/tex]
Here,
Length of classroom = [tex]6\frac{4}{5}[/tex] m = [tex]\frac{34}{5}[/tex] m
Width of classroom = [tex]1\frac{3}{8}[/tex] m = [tex]\frac{11}{8}[/tex] m
Area of classroom = [tex]\frac{34}{5} \times \frac{11}{8}[/tex]
= [tex]\frac{187}{40}[/tex]
= [tex]4\frac{27}{40}[/tex] [tex]m^2[/tex]
To learn more about area of rectangle, refer to the link-
https://brainly.com/question/25292087
#SPJ13
Suppose Yolanda places $9000 in an account that pays 8% interest compounded each year. Assume that no withdrawals are made from the account. Follow the instructions below. Do not do any rounding. (a) Find the amount in the account at the end of 1 year. $ (b) Find the amount in the account at the end of 2 years. $0 X S
Answers
Compound interest - The amount in the account at the end of 1st year is $9720 and The amount in the account at the end of 2nd years is $10497.6
What is compound interest?
The interest earned on savings that is calculated using both the initial principal and the interest accrued over time is known as compound interest. It is thought that Italy in the 17th century is where the concept of "interest on interest" or compound interest first appeared. It will accelerate the growth of a sum more quickly than simple interest, which is only calculated on the principal sum. Money multiplies more quickly thanks to compounding, and the more compounding periods there are, the higher the compound interest will be.
We are given that the principal amount is $9000
An the interest is 8%
Hence after 1 year the amount will be
[tex]A=9000(1+0.08)\\A=9000(1.08)\\A=9720\\[/tex]
After 1 year the amount becomes $9720
Now After 2 years we will get interest on $9720
Hence the amount after 2 years will be
[tex]B=9720(1+0.08)\\B=9720(1.08)\\B=10497.6[/tex]
Therefore the amount after 2 years is $10497.6
To learn more about the compound interest please refer
https://brainly.com/question/24924853
#SPJ13
Given that the height of a trapezoid is 16 m and one base’s length is 25 m. Calculate the dimension of the other base of the trapezoid if its area is 352 m².
Answers
ANSWER:
19 m
STEP-BY-STEP EXPLANATION:
We have that the formula for the area of a trapezoid is the following:
[tex]A=\frac{B+b}{2}\cdot h[/tex]We substitute each value and calculate the length of the other base, like so:
[tex]\begin{gathered} 352=\frac{25+b}{2}\cdot16 \\ \\ 25+b=352\cdot\frac{2}{16}\frac{}{} \\ \\ b=44-25 \\ \\ b=19 \end{gathered}[/tex]The dimension of the other base of the trapezoid is 19 m
How do you write 6 tens + 4 ones + 5 tenths + 2 hundredths + 8 thousandths
Answers
Answer:64.528 is the decimal
Step-by-step explanation:
1 a) is the above sequence arithmetic? Justify your answer. b) Write the explicit formula for the above sequence. c) Find the 18th term.
Answers
First, we count the number of boxes.
We have: 4,8,12,16
(a)Now:
• 8-4=4
,• 12-8=4
,• 16-12=4
Since the difference is the same, the sequence is an arithmetic sequence.
(b)In the sequence
First term, a =4
Common difference, d=4
The nth term of an arithmetic sequence is:
[tex]\begin{gathered} U_n=a+(n-1)d \\ =4+4(n-1) \\ =4+4n-4 \\ =4n \end{gathered}[/tex]The explicit formula for the above sequence, f(n)= 4n.
(c)18th term
f(18)= 4 x 18
=72
The 18th term is 72.
HELP HELP! PLEASE, MY MOM WANT ME TO BE DONE!
Answers
From least to greatest, we have:
2 to 3, 3:4, and 7/8
Explanation:Given the following:
7/8, 2 to 3, and 3:4
The least is 2 to 3, followed by 3:4, then 7/8
Given the following dataset, determine the mode 6056605570546055
Answers
Answer:
5
Step-by-step explanation:
put it in order
6056605570546055
and the one that appears the most is the mode
Question 7, pre calc, include the answer in bold please. I have bad WiFi so please finish question if I get disconnected so I can see it, thanks
Answers
Given the following function
[tex]f(x)=x^4-x^3+7x^2-9x-18[/tex]We want to find its roots. Since we already know that (x + 1) and (x - 2) are factors of this polynomial, we can divide our polynomial by those factors and factorize the result to get the other roots.
Let's start by dividing by the first factor
[tex]\frac{x^4-x^3+7x^2-9x-18}{x+1}[/tex]To divide a polynomial by other, we start by dividing the leading term of the dividend by the leading term of the divisor(this will be the first term of our result)
[tex]\frac{x^4}{x}=x^3[/tex]Then, we ultiply it by the divisor
[tex]x^3(x+1)=x^4+x^3[/tex]Subtracting this result from the dividend, we have
[tex](x^4-x^3+7x^2-9x-18)-(x^4+x^3)=-2x^3+7x^2-9x-18[/tex]This means that our division is
[tex]\frac{x^4-x^3+7x^2-9x-18}{x+1}=x^3+\frac{-2x^3+7x^2-9x-18}{x+1}[/tex]Repeating the whole process of division with the second term, we have
[tex]\begin{gathered} x^3+\frac{-2x^3+7x^2-9x-18}{x+1}=x^3-2x^2+\frac{9x^2-9x-18}{x+1} \\ \Rightarrow\frac{x^4-x^3+7x^2-9x-18}{x+1}=x^3-2x^2+9x-18 \end{gathered}[/tex]From this result, we can rewrite our function as
[tex]x^4-x^3+7x^2-9x-18=(x+1)(x^3-2x^2+9x-18)[/tex]Repeating this same process with the other know factor, the other division we have to solve is
[tex]\frac{(x^3-2x^2+9x-18)}{x-2}=x^2+9[/tex]Then, our function is
[tex]f(x)=(x^4-x^3+7x^2-9x-18)=(x+1)(x-2)(x^2+9)[/tex]Then, to find the roots we need to solve the following equation
[tex](x+1)(x-2)(x^2+9)=0[/tex]Since we have a product of 3 terms, the result will be zero if and only if one of the terms is zero. This means that the roots can be found by assuming each one is zero. The solutions for this equation are the same solutions for the following system
[tex]\begin{cases}x+1=0 \\ x-2=0 \\ x^2+9=0\end{cases}\Rightarrow\begin{cases}x=-1 \\ x=2 \\ x=\pm\sqrt[]{-9}=\pm3i\end{cases}[/tex]And those are the roots for our function. x = -1, 2, +-3i.
I solved for Part A and the correct graph was answer A I just need Part B to be solved (at the bottom)
Answers
In Part (b) of this problem, we want to determine which function is the bes representation for the graph and table.
We are given:
To determine which function matches best, we can look at the parent function of a linear, logarithmic, and exponential function.
(see comparisons below):
Notice that our graph most closely resembles that of the exponential function. Therefore, the best model for the data would be an exponential function.
Jenelle invests $8,000 at 3% simple interest for 48 years. How much is in the account at the end ofthe 48 year period? Round your answer to the nearest cent.Answer: $Submit Question
Answers
Given
Principal = $8,000
Rate = 3%
Time = 48 years
Find
Amount at the end of the 48 years
Explanation
Amount = Simple interest + Principal
Simple Interest is given by
[tex]S.I=\frac{P\times R\times T}{100}[/tex]now substitute the values ,
[tex]\begin{gathered} S.I=\frac{8000\times3\times48}{100} \\ \\ S.I=11520 \end{gathered}[/tex]amount = 11,520 + 8000 = $19,520.00
Final Answer
Therefore , the amount at the end of the 48 years will be $19,520.00
URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS
Jimmy ran 20 meters west
from home and then turned
north to jog 25 meters. Jimmy
ran 45 meters, but could have
arrived at the same point by in
a straight line. How many
meters could he have using a
line distance?
A. 3.5 meters
B7 meters
C. 32 meters
D. 45 meters
Answers
Answer:
32m
Step-by-step explanation:
The distance he would've covered is 32m if he ran through a straight line.
What is Pythagoras's Theorem?
In mathematics, the Pythagorean theorem, or Pythagoras' theorem, is a fundamental relation in Euclidean geometry among the three sides of a right triangle. It states that the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides.
We can proceed to use this to find the distance from point a to point b assuming he ran through a straight line.
Mathematically, the theorem can be expressed as
Let's substitute the values into the equation and solve.
Jimmy would've jogged 32m if he ran through a straight line.
Learn more on Pythagoras theorem here;
brainly.com/question/231802
Give the slope and the y-intercept of the line y=– 8x+7. Make sure the y-intercept is written as a coordinate.
Answers
Solution
We have the following function given:
y =-8x+7
If we compare this with the general formula for a slope given by:
y= mx+b
We can see that the slope m is:
m =-8
And the y-intercept would be: (0,7)
is 2÷2 4 or am I wrong
Answers
2/2 = 1
The answer would be 1
