Answer: y=10x+50
Step-by-step explanation:
A rectangle is placed around a semicircle as shown below. The width of the rectangle is 8 yd. Find the area of the shaded regiorUse the value 3.14 for 1, and do not round your answer. Be sure to include the correct unit in your answer.
It is given that,
[tex]\begin{gathered} Radius\text{ of semicircle = width of rectangle = 8 yd} \\ Diameter\text{ of semicircle = length of rectangle = 16 yd} \\ \pi\text{ = 3.14} \end{gathered}[/tex]The area of the semicircle is calculated as,
[tex]\begin{gathered} Area\text{ = }\pi\times r^2 \\ Area\text{ = 3.14 }\times\text{ 8 }\times\text{ 8/2} \\ Area\text{ = 100.48 yd}^2 \end{gathered}[/tex]The area of the rectangle is calculated as,
[tex]\begin{gathered} Area\text{ = Length }\times\text{ Breadth} \\ Area\text{ = 16 yd }\times\text{ 8 yd} \\ Area\text{ = 128 yd}^2 \end{gathered}[/tex]The area of the shaded region is calculated as,
[tex]\begin{gathered} Area\text{ of shaded region = Area of rectangle - Area of semicircle} \\ Area\text{ of shaded region = 128 yd}^2\text{ - 100.48 yd}^2 \\ Area\text{ of shaded region = 27.52 yd} \end{gathered}[/tex]Find the probability that a point chosen at random on LP is on MN
The length of LP is 12 units and the length of MN is 3 units; therefore the probability that a point chosen at random falls on MN is
[tex]\frac{MN}{LP}=\frac{3}{12}=0.25[/tex]
Yousef is cutting pieces of construction paper so he can make cards for his family . Each piece of paper is 11 1/2 inches wide. If he cuts that width so he would have two equal-sized smaller pieces, how wide will each smaller piece be? rocine she wants to try requires
The total width of each piece of paper:
[tex]\begin{gathered} W\text{ = 11}\frac{1}{2}\text{inches} \\ W\text{ = }\frac{23}{2}\text{inches} \end{gathered}[/tex]Yousef cuts the piece of paper into two pieces of paper of equal widths:
Let each of the smaller pieces have a width of w
W = 2w (since the smaller pieces have equal widths)
[tex]\begin{gathered} \frac{23}{2}=\text{ 2w} \\ 23\text{ = 4w} \\ \frac{23}{4}=\text{ w} \\ w\text{ = 5}\frac{3}{4}in \end{gathered}[/tex]An airplane pilot flies due north from Ft. Myers to Sarasota, a distance of 150 miles. She then turns N50°E and flies to Orlando, a distance of 100 miles How far is it from Ft. Myers to Orlando? Round to the nearest tenths
115 miles
1) Sketching this to better grasp it we have:
2) Since we could draw the route as a triangle, we can use the Law of Cosines to find out the distance between Fort Myers and Orlando:
[tex]\begin{gathered} a^2=b^2+c^2-2bc\cos (\alpha) \\ x^2=(100)^2+150^2-2(100)(150)\cos (50) \\ x^2=32500-2(100)(150)\cos (50) \\ x^2=13216.37 \\ \sqrt[]{x^2}=\sqrt[]{13216.37} \\ x\approx114.96\approx115 \end{gathered}[/tex]Note that we rounded off to the nearest tenth(114.9).
3) Hence, the answer is 115 miles
36. Let f(x) = x 4 x - 6 and g(x) = x - 2x – 15. Findf(x)•g(x)
f(x) = x^2 + x - 6
g(x) = x^2 - 2x - 15
Process
factor both functions
f(x) = (x + 3)(x - 2)
g(x) = (x - 5)(x + 3)
Divide them:
f(x) / g(x) = [(x + 3)(x - 2)] / [x - 5)(x + 3)]
Simplify like terms
f(x) / g(x) = (x - 2)/ (x - 5)
Find the terminal point on the unit circle determined by π2 radians.Use exact values, not decimal approximations.
Okay, here we have this:
Considering the provided information, we are going to determine the requested terminal point, so we obtain the following:
So for this we will first calculate how much the given angle is in degrees, from there then we proceed to observe in the unit circle, then we have:
(pi/2)*(180°/pi)=180°/2=90°
We can observe in the image of the unit circle that the terminal point of 90° is (0, 1).
Finally we obtain that the terminal point of pi/2 radians is (x,y)=(0, 1).
Grace and Maria are practicing for a fitness test. Each day, they do as many curl-ups as they can in 1 min. Which measures could best be used to argue that Maria is better at doing curl-ups than Grace is? Mean MAD Min Q1 Median Q3 Max Grace 36 3.25 30 32.5 37 38.5 43 38 4.5 Maria 24 35.5 39 42.5 45
For option A:
MAD and IQR:
MAD means Mean Absolute Deviation:
This is the measure that records the deviation from the average number of curl-ups that both girls can do.
Therefore, if the value of MAD is higher, it just means that the person tends to vary by a larger value, on the number of curl-ups she does.
In this question, Maria has a higher MAD of 4.5 while Grace's MAD is 3.25. This means that Grace's curl-ups tend to be closer to the average number of curl-ups she does over a period of time. While Mar
What is the area in simplest form? 5/6 ft 4/6 ft
We are given a rectangle with a length of 5/6 ft and a height of 4/6 ft. To determine the area let's remember that the area of a rectangle is the product of the length by the height. Therefore, the area is:
[tex]A=(\frac{5}{6}ft)(\frac{4}{6}ft)[/tex]Solving the product we get:
[tex]A=\frac{20}{36}ft^2[/tex]Now, we simplify the result by dividing both sides by 4:
[tex]A=\frac{\frac{20}{4}}{\frac{36}{4}}ft^2=\frac{5}{9}ft^2[/tex]Therefore, the area is 5/9 square feet.
if the inequality -8 < x > 10 was placed in interval notation it would be represented by
It would be represented by interval notation (-8,10].
Interval notation:
The collection of real numbers that are located between two numbers is known as an interval in mathematics. The starting and ending numbers will be shown using brackets in the interval notation method. There are two different styles of brackets on it: square and round. The end values are included if the interval is given in square brackets. The end values are not included when an interval is given in round brackets.
Instance: [7, 12] It refers to the range of values between 7 and 12, with 12 included but not 7.
Complete question:
If the inequality -8<x≤10 was placed in interval notation it would be represented by
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(3,5) and (-1,9) slope finding b and writing equation
Answer:
• Slope, m =-1
,• Equation: y=-x+8
Explanation:
Gien the points: (x1,y1)=(3,5) and (x2,y2)=(-1,9)
Slope
[tex]Slope,m=\frac{y_2-y_1}{x_2-x_1}[/tex]Substitute the points:
[tex]\begin{gathered} m=\frac{9-5}{-1-3} \\ =\frac{4}{-4} \\ m=-1 \end{gathered}[/tex]The slope of the line is -1.
Equation of the Line
We use the point-slope form to find the equation of the line.
Using point (3,5) and slope, m=-1
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-5=-1(x-3) \\ y-5=-x+3 \\ y=-x+3+5 \\ y=-x+8 \end{gathered}[/tex]The equation of the line is y=-x+8.
A professor decided he was only going to grade 8 out of 10 HW problems he assigned. How many different groupings of HW problems could he grade?
Answer:
The number of groupings is 45
Explanation:
Given that the professor decided he was only going to grade 8 out of 10 HW problems he assigned.
We want to calculate the number of ways the professor can grade the HW.
Which is a conbination;
[tex]10C8[/tex]Solving we have;
[tex]\begin{gathered} n=10C8=\frac{10!}{8!(10-8)!} \\ n=45 \end{gathered}[/tex]Therefore, the number of groupings is 45
Susan's Jewelry Shop is having a sale on necklaces. The store is offering a sale pack of 4 necklaces for $48.80. What is the unit price of a necklace in the sale pack?
Carly's ClothinStore is also having a sale on necklaces. The unit price of any necklace at Carly's Clothing Store is the same as the unit price of a necklace at Susan's Jewelry Shop How much would it
cost a customer for 10 necklaces at Carly's Clothing Shop?
Unit Price
The store offers a sales pack of 4 necklaces for $48.80. This means each necklace in this pack has a unit price of:
$48.80 / 4 = $12.20
Now we know the unit price of any necklace at Carly's Clothing Store is the same as the unit price at the competing store. This means each necklace at Carly's Clothing Store has a price of $12.20.
If a customer bought 10 of these necklaces, he would have to pay
10 * $12.20 = $122,00
For 10 necklaces at Carly's Clothing Store, a customer would pay $122
25% of what number w is 9?=25100
25 % of 36 is 9
Explanation
Step 1
the easy way to find the percentage of any number is:
[tex]\begin{gathered} y\text{ \% of x } \\ total\text{ =x*}\frac{y}{100} \end{gathered}[/tex]so
A) let
25% of what number w is 9?
let
[tex]\begin{gathered} nubmer(x)\text{ = W} \\ percentage\text{ \lparen y\rparen=25 \%} \\ total\text{ =}9 \end{gathered}[/tex]now, replace and solve for w:
[tex]\begin{gathered} y\text{ \% of x } \\ total\text{ =x*}\frac{y}{100} \\ 9=W*\frac{25}{100} \\ 9=W*0.25 \\ divide\text{ both sides by 0.25} \\ \frac{9}{0.25}=\frac{W\times0.25}{0.25} \\ 36=W \end{gathered}[/tex]therefore ,
25 % of 36 is 9
Examine the following graph, where the exponential function P(x) undergoes a transformation.The preimage of the transformation is labeled P(x), and the image is labeled I(x).
Explanation
For the function P(x), the value of x in the function is halved to get the values of x in the image.
This can be seen in the graphs below.
The red line represents the preimage and the blue line represents the image.
Answer: Option 4
all you need is on the photo pleaseeeee i really need help
We can find the y-intercept evaluating the function for x = 0, so:
[tex]\begin{gathered} y(x)=-5x^2+20x+60 \\ y(0)=-5(0)^2+20(0)+60=0+0+60 \\ y(0)=60 \end{gathered}[/tex]---------
We can find the zeros evaluating the function for y = 0. So using the factored form:
[tex]\begin{gathered} -5(x-6)(x+2)=0 \\ so\colon \\ x1=6 \\ and \\ x2=-2 \end{gathered}[/tex]-----------------------------------------------
The vertex V(h,k) is given by:
[tex]\begin{gathered} h=\frac{-b}{2a} \\ k=y(h) \end{gathered}[/tex]Or we can find it directly from the vertex form:
[tex]\begin{gathered} y=a(x-h)^2+k \\ so \\ for \\ y=-5(x-2)^2+80 \\ h=2 \\ k=80 \end{gathered}[/tex]So, the vertex is:
[tex](2,80)[/tex]---------
The symmetry axis is located at the same point of the x-coordinate of the vertex, so the axis of symmetry is:
[tex]x=2[/tex]-----------------------
The maximum value is located at the y-coordinate of the vertex (if it is positive) so, the maximum value is:
[tex]y=80[/tex]3 373,Consider the complex number z =+22What is 23?Hint: z has a modulus of 3 and an argument of 120°.Choose 1 answer:А-2727-13.5 +23.41-13.5 - 23.41
To answer this question, we can proceed as follows:
[tex]z=-\frac{3}{2}+\frac{3\sqrt[]{3}}{2}i^{}\Rightarrow z^3=(-\frac{3}{2}+\frac{3\sqrt[]{3}}{2}i)^3[/tex][tex](-\frac{3}{2}+\frac{3\sqrt[]{3}i}{2})^3=(\frac{-3+3\sqrt[]{3}i}{2})^3=\frac{(-3+3\sqrt[]{3}i)^3}{2^3}[/tex]We applied the exponent rule:
[tex](\frac{a}{b})^c=\frac{a^c}{b^c}[/tex]Then, we have:
[tex]\frac{(-3+3\sqrt[]{3}i)^3}{2^3}=\frac{(-3+3\sqrt[]{3}i)^3}{8}[/tex]Solving the numerator, we have:
[tex](a+b)^3=a^3+b^3+3ab(a+b)[/tex][tex](-3+3\sqrt[]{3}i)^3=(-3)^3+(3\sqrt[]{3}i)^3+3(-3)(3\sqrt[]{3}i)(-3+3\sqrt[]{3}i)[/tex][tex]-27+81\sqrt[]{3}i^3-27\sqrt[]{3}i(-3+3\sqrt[]{3}i)[/tex][tex]-27+81\sqrt[]{3}i^3+81\sqrt[]{3}i-27\cdot3\cdot(\sqrt[]{3})^2\cdot i^2[/tex][tex]-27+81\sqrt[]{3}i^2\cdot i+81\sqrt[]{3}i-81\cdot3\cdot(-1)[/tex][tex]-27+81\sqrt[]{3}(-1)\cdot i+81\sqrt[]{3}i+243[/tex][tex]-27-81\sqrt[]{3}i+81\sqrt[]{3}i+243[/tex][tex]-27+243=216[/tex]Then, the numerator is equal to 216. The complete expression is:
[tex]=\frac{(-3+3\sqrt[]{3}i)^3}{8}=\frac{216}{8}=27[/tex]Therefore, we have that:
[tex]z^3=(-\frac{3}{2}+\frac{3\sqrt[]{3}}{2}i)^3=27[/tex]In summary, therefore, the value for z³ = 27 (option B).
In ∆KLM, l= 56 inches , k =27 inches and < K=10°. Find all possible values of < L, to the nearest degree.
SOLUTION
In this question, we are meant to find the possible values of
This is just an application of SINE RULE, which says that:
[tex]\begin{gathered} \frac{L}{\sin\text{ L}}\text{ = }\frac{K}{\sin \text{ K}},\text{ we have that:} \\ \\ \frac{56}{\sin\text{ L }}\text{ = }\frac{27}{\sin \text{ 10}} \\ \text{cross}-\text{ multiplying, we have that;} \\ 27\text{ x sin L = 56 X sin 10} \\ \sin L\text{ =}\frac{56\text{ X sin 10}}{27} \\ \sin \text{ L = }\frac{56\text{ X 0.1736}}{27} \\ \\ \sin \text{ L = }\frac{9.\text{ 7216}}{27} \\ \sin L\text{ =0.3600} \\ \text{Taking sine inverse of both sides, we have:} \\ L=21.1^0 \\ L=21^{0\text{ }}(\text{correct to the nearest degr}ee) \end{gathered}[/tex]g(x)=1/2x. Graph the function and it's parent function and describe the transformation.
In order to graph the function, we need to know the degree from the function, since there are not exponents it means that this is a linear function that passes through the origin since there is not any y-intercept.
The parent function is
[tex]y(x)=x[/tex]The transformation of the function is to compress the function by a factor of 0.5
Can you please help me solve this? It is for HW
Use a rule of three to find the number of won games in a season of 120 games.
If the rate is the same, then, you can write:
[tex]\frac{20}{110}=\frac{x}{120}[/tex]Now, solve for x and simplify:
[tex]\begin{gathered} x=\frac{20}{110}\cdot120 \\ x=21.81 \\ x\approx22 \end{gathered}[/tex]Hence, the Panthers would win 22 games
Can u help this problem
True Or False? the y intercept for the line of the best fit for this scatterplot is 5
From the graph of the line we notice that if we prolong the line to the y-axis it will intercept it at approximately 4.5.
Therefore, the stament is False.
tem = 462-5 h 1995. Central High School had a student population of 2250 students. By 2005, the student population was only 1.800 students. What is the percent of decrease in the student population? A 2002 B. 25% C. 75% D. 80% tem = 119766
Central High School had a student population of 2250 students.
By 2005, the student population was only 1.800 students.
What is the percent of decrease in the student population?
A 2002
B. 25%
C. 75%
D. 80%
Percentage of decrease = 100 - 100 * (1800/2250) = 100 - 100 * 0.8 = 100 - 80 = 20%
The following data are an example of what type of regression?
x
1
2
4
6
8
10
12
OA. Exponential
OB. Quadratic
O C. Linear
OD. None of the above
Y
1.2
1.4
2.1
3.1
4.3
5.6
7.2
The given data is an example of Option C Linear regression equation,
y = 0.5438x + 0.2169
Given,
The data;
x ; 1 2 4 6 8 10 12
y ; 1.2 1.4 2.1 3.1 4.3 5.6 7.2
We have to find the type of regression of the given data;
Regression equation;
In statistics, a regression equation is used to determine whether or not there is a link between two sets of data.
Lets find regression equation first;
There are 7 number of pairs
The regression equation is;
y = 0.5438x + 0.2169
That is,
The given data is an example of Option C Linear regression equation,
y = 0.5438x + 0.2169
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Write the equation, (2)x+(3)y=(24) in slope-intercept form
the equation in slope- intercept form:
y = -2x/3 + 8
Explanation:
GIven: (2)x+(3)y=(24)
To write in slope intercept form, we apply the formula for a linear equation:
y = mx + c
where m = slope, c = intercept
2x + 3y = 24
Make y the subject of formula by taking x to the other side of the equation:
3y = -2x + 24
Divide through by 3:
[tex]\begin{gathered} \frac{3y}{3}=\frac{-2x}{3}+\frac{24}{3} \\ y\text{ = }\frac{-2x}{3}+8 \end{gathered}[/tex]when we compare the above equation with the equation of line, they are in alignment.
Hence, the equation in slope- intercept form:
y = -2x/3 + 8
4) Identify the LIKE terms: 7y + 5r-4r + 2w 7y and 2w 7y and 5 O -4r and 2w 51 and 41
Problem Statement
We are asked to identify the like terms from the following expression:
[tex]7y+5r-4r+2w[/tex]Concept
When we are asked to identify like terms, the question is asking us to find which terms have the same variables with the same power.
For example:
[tex]\begin{gathered} \text{Given the expression:} \\ x^2+2x+y+yx+y^3+y^2+2y+3x^2 \\ \\ 3x^2\text{ and }x^2\text{ are like terms because they have the same variable (x) and both have a power of 2.} \\ y\text{ and 2y are like terms because they have the same variable (y) and both have a power of 1.} \\ \\ \text{Those are the only like terms in the expression} \end{gathered}[/tex]With the above information, we can solve the question.
Implementation
By the explanation given above, the like terms from the given expression are:
[tex]5r\text{ and }-4r[/tex]derermine if the whole numbers exhibit the closure property for the indicated ooerations or not. if not provide a counter example to justify your conclusion
EXPLANATION
Addition:
If we add two or more whole numbers, the result will be also a whole number.
Hence, they exhibit the closure property.
Subtraction:
If we subtracti two or more whole numbers, the result will not necessarily be a whole number. For example, subtraction 5-10 give us -5 --> Not a whole number. [NOT CLOSURE PROPERTY]
Division:
The division of two whole numbers could not necessarily be a whole number, as for instance, 6/12 = 1/2 [NOT CLOSURE PROPERTY]
Write each equation in standard form10. y + 1 = x + 213. y - 4 = -(x - 1)16. y - 10 = -2(x - 3)
Standard form of a line:
Ax + By = C
where A is a positive integer, B is an integer and C is a constant.
10. y + 1 = x + 2
y + 1 - y = x + 2 - y subtracting y at both sides
1 = x + 2 - y
1 - 2 = x + 2 - y - 2 subtracting 2 at both sides
-1 = x - y
13. y - 4 = -(x - 1)
(y - 4)*(-1) = -(x - 1)*(-1) Multiplying by -1 at both sides
-y + 4 = x - 1
-y + 4 + y = x - 1 + y Adding y at both sides
4 = x - 1 + y
4 + 1 = x - 1 + y + 1 Adding 1 at both sides
5 = x + y
16. y - 10 = -2(x - 3)
(y - 10)/(-2) = -2(x - 3)/(-2) Dividing by -2 at both sides
y/-2 +5 = x - 3
2*(y/-2 +5) = 2*(x - 3) Multiplying by 2 at both sides
-y + 10 = 2x + 6
-y + 10 + y = 2x + 6 + y Adding y at both sides
10 = 2x + 6 + y
10 - 6 = 2x + 6 + y - 6 subtracting 6 at both sides
4 = 2x + y
Circle O shown below has an arc of length 34 inches subtended by an angle of 2.1 radians. Find the length of the radius, x, to the nearest tenth of an inch.
16.2 inches
Explanation
the arc length is given by the formula:
[tex]\begin{gathered} arclength=\theta r \\ where\text{ } \\ r\text{ is the radius } \\ \theta\text{ is the angle in radians} \end{gathered}[/tex]so
Step 1
a)let
[tex]\begin{gathered} r=x\text{ \lparen unknown\rparen} \\ angle=\theta=2.1\text{ rad} \\ arclength\text{ = 34 inches} \end{gathered}[/tex]b) now, replace in the formula and solve for x
[tex]\begin{gathered} arclength=\theta r \\ 34\text{ inches=2.1 rad*x} \\ divide\text{ both sides by 2.1 rad} \\ 16.19\text{ inches =x} \\ rounded \\ x=16.2\text{ inches} \end{gathered}[/tex]
therefore, the answer is
16.2 inches
I hope this helps you
on the unit circle, in standard position, an angle of which measure is coterminal with an angle that measures pi/4 radians?
Coterminal angles are defined as the angles which possess the same terminal side.
The given angle measure is π/4 radians.
Consider that one full circle constitutes an angle measure of 2π radians.
So if we add 2π to the given angle, the resultant will represent the same terminal side.
[tex]undefined[/tex]I am still confused on how to solve these problems please help.
Step 1: We have a line segment XZ, with point Y between X and Z.
Therefore, we have:
XY + YZ = XZ
Replacing with the values given:
7a + 5a = 6a + 24
Like terms:
7a + 5a - 6a = 24
6a = 24
Dividing by 6 at both sides:
6a/6 = 24/6
a = 4
Step 2: Now we can find the length of the line segment, this way:
YZ = 6a + 24
Replacing a by 4
YZ = You can finish the calculation