The area wiped by the wiper blade is 424.08 in².
How to find the area?Using this formula to find the area
A= 1/2r² Ф
Where:
A = Area
r = Radius
Let plug in the formula
A = [1/2 × (21)² × 135° ×π /180 ] - [1/2 × (21 -12)² × 135° ×π /180 ]
A = [1/2 × (21)² × 135° ×π /180 ] - [1/2 × (9)² × 135° ×π /180 ]
A = [1/2 × (441) × 135° ×π /180 ] - [1/2 × (81) × 135° ×π /180 ]
A = 519.54 - 95.43
A = 424.08 in²
Therefore the area is 424.08 in².
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Which expression would be easier to simplify if you used the associative property to change the grouping? OA. 6+ 1; +3) OB. I(-0.2) +(-0.6)] +1.7 O c.(2+)+-) O D. (60+ 40) +-27)
A.
[tex]6+\lbrack\frac{4}{9}+(-\frac{2}{9})\rbrack[/tex]Since both fractions have the same numerator, you can factorize 1/9 aout of the parentheses, because:
[tex]\begin{gathered} \frac{1}{9}\cdot4=\frac{4}{9} \\ \text{and} \\ \frac{1}{9}\cdot2=\frac{2}{9} \end{gathered}[/tex]Then you can simplify the expression as:
[tex]6+\frac{1}{9}\lbrack4+(-2)\rbrack=6+\frac{1}{9}\lbrack4-2\rbrack[/tex]using the digits -9 to 9, without repeating any numbers, place a number in each box to create a system of equations that has a solution in quadrant 2. Tip: in quadrant 2, the x - coordinate is negative and the y-coordinate is positive.
Okay, here we have this:
Considering the provided information and options, we are going to find the requested numbers, so we obtain the following:
So first we will choose two values for x and y that meet the given tip: in quadrant 2, the x - coordinate is negative and the y-coordinate is positive.
For our case we will take x=-1 and y=1, then we can write the following two equations:
1x+3y=2 -> 1(-1)+3(1)=2 -> -1+3=2 -> 2=2
y=7x+8 -> 1=7(-1)+8 -> 1=-7+8 -> 1=1
Solve x2 + 12x + 25Hias17 by completing the square. Select all the possible solutions.-6 + 70-6 + 2.7–6 – 276-606-270-6-77
we are given the following expression:
[tex]x^2+12x+25=17[/tex]First, we will subtract 17 to both sides:
[tex]\begin{gathered} x^2+12x+25-17=17-17 \\ x^2+12x+8=0 \end{gathered}[/tex]We get an expression of the form:
[tex]ax^2+bx+c=0[/tex]To complete the square we will add and subtract the following term:
[tex]\frac{b^2}{4a}[/tex]Replacing the values:
[tex]\frac{12^2}{4(1)}=36[/tex]Therefore, we will add and subtract 36:
[tex]x^2+12x+36-36+8=0[/tex]Now we associate the first three terms:
[tex](x^2+12x+36)-36+8=0[/tex]Now we factor in the associated terms:
[tex](x+6)^2-36+8=0[/tex]Solving the operations:
[tex](x+6)^2-28=0[/tex]Now we solve for "x", first by adding 28 to both sides:
[tex](x+6)^2=28[/tex]Now we take square root to both sides:
[tex](x+6)=\sqrt[]{28}[/tex]Now we subtract 6 to both sides:
[tex]x=-6\pm\sqrt[]{28}[/tex]Now we factor 28 as 7*4:
[tex]undefined[/tex]The dash in-front of the whole number is a negative sign, Just a little heads up :)
Okay, here we have this:
We need to solve the following expression:
[tex]\begin{gathered} -5\cdot2\text{ }\frac{1}{4} \\ =-5\cdot\frac{8+1}{4} \\ =-5\cdot\frac{9}{4} \\ =-\frac{45}{4} \\ =-11.25 \end{gathered}[/tex]Finally we obtain that the result is -11.25.
Reduce to the lowest terms by canceling -14/9 times -3/7
Answer:
2/3
Explanation:
Given the below;
[tex]\frac{-14}{9}\times\frac{(-3)}{7}[/tex]We can see from the above that 9 is divisible by 3 and that 14 is divisible by 7, let's go ahead and reduce to the lowest term as shown below;
[tex]\frac{-14}{9}\times\frac{(-3)}{7}=\frac{-2}{3}\times\frac{(-1)}{1}=\frac{2}{3}[/tex]Three people share 4/5 of a lasagna. What fraction of the lasagna does each person eat?
4/15
1) Since 3 people share 4/5 of a lasagna we can write:
[tex]\frac{\frac{4}{5}}{3}=\frac{4}{5}\times\frac{1}{3}=\frac{4}{15}[/tex]Remember that when dividing a fraction we must multiply the dividend (4/5) by the reciprocate of the divisor (3).
2) So each one ate 4/15 of a whole lasagna.
Use a calculator and inverse functions to find the radian measures of a given angle around your answer to the nearest hundredth.angles whose sign is -0.26
Answer
Option C is correct.
x = -0.26 + 2pn
OR
x = -2.88 + 2pn
Explanation
Using the calculator and inverse functions
Let the unknown angle be x
Sin x = -0.26
x = Sin⁻¹ (-0.26)
x = -0.26 or -2.88 (From the calculator)
In order to generalize it, we add 2pi to both of them.
x = -0.26 + 2pn
OR
x = -2.88 + 2pn
Hope this Helps!!!
using the change-of-base formula, which of the following is equivalent to the logarithmic expression below? log6 21
Given:
Log6 21.
We are asked to use change of base formula to determine form the options which is equivalent.
let's apply the base change formula:
For C:
Log10 10
Log10 21
Log10 10
Log10 6
Apply power law of logarithm to simplify the expression:
1
LOg10 21
1
Log10 6
ivide fraction by multiplying its reciprocal:
1 x Log10 6
Log10 21
Write as a single fraction:
Log10 6
Log10 21
Apply the base chande formula: log21 6
Check its equivalency: False.
Option A is False
Sam wants to cover a gift box with paper the top of the box is 8in wide and 15in long the box is 12in tall what is the minimum amount of paper Sam will need to cover the entire box?
In order to find the amount of paper that will be needed, we need to calculate the surface area of this rectangular prism.
The faces of this figure are:
- 2 rectangles with dimensions 8 in and 15 in,
- 2 rectangles with dimensions 15 in and 12 in,
- 2 rectangles with dimensions 12 in and 8 in.
Calculating the area of each rectangle, we have:
[tex]\begin{gathered} A_1=8\cdot15=120 \\ A_2=15\cdot12=180 \\ A_3=12\cdot8=96 \end{gathered}[/tex]Now, the surface area is:
[tex]\begin{gathered} S=2A_1+2A_2+2A_3 \\ S=240+360+192 \\ S=792\text{ in}^2 \end{gathered}[/tex]So the amount of paper needed is 792 in².
What is 3[cos(60)+isin60]*1/2[cos(15)+isin(15)]
1) Let's simplify this expression considering the trigonometric ratios and the complex numbers as well.
[tex]\begin{gathered} 3\left[\cos \left(60^{\circ \:}\right)+i\sin \left(60^{\circ \:}\right)\right]\frac{1}{2}\left[\cos \left(15^{\circ \:}\right)+i\sin \left(15^{\circ \:}\right)\right] \\ Convert\:to\:radians: \\ 3\left[\cos \left(\frac{\pi }{3}\right)+i\sin \left(\frac{\pi }{3}\right)\right]\frac{1}{2}\left[\cos \left(\frac{\pi }{12}\right)+i\sin \left(\frac{\pi }{12}\right)\right] \\ \quad \cos \left(x\right)+i\sin \left(x\right)=e^{ix} \\ 3\times\frac{1}{2}\lbrack\left[e^{i\frac{\pi}{3}}\right]\left[e^{i\frac{\pi}{12}}\right] \\ \frac{3\left(-1\right)^{\frac{5}{12}}}{2} \\ \end{gathered}[/tex]We have transitioned that to work with radians for convenience and used one identity. Note that we could have written our final answer in a radical form.
The function f is defined by the following rule.f(x) = 3x-3Complete the function table.хf(x)- 4-30145
Use inverse trig ratios to find the angle measures sinX = 0,259 [ Choose ] Cosx = 0,743 [ Choose ] < tanX = 4 [Choose < sinX = 4/7 [ Choose
ANSWER:
[tex]\begin{gathered} x=15.01\text{\degree} \\ x=42.01\text{\degree} \\ x=75.96\text{\degree} \\ x=34.85\text{\degree} \end{gathered}[/tex]STEP-BY-STEP EXPLANATION:
We calculate the value of the angles for each point as follows:
[tex]\begin{gathered} \sin x=0.259\rightarrow x=\arcsin 0.259\rightarrow x=15.01\text{\degree} \\ \cos x=0.743\rightarrow x=\arccos 0.753\rightarrow x=42.01\text{\degree} \\ \tan x=4\rightarrow x=\arctan 4\rightarrow x=75.96\text{\degree} \\ \sin x=\frac{4}{7}\rightarrow x=\arcsin \frac{4}{7}\rightarrow x=34.85\text{\degree} \end{gathered}[/tex]find a set of parametric equations for the rectangular equation
We have for the fisrt equation that
[tex]\begin{gathered} t\text{ = 2 -x } \\ x\text{ = 2 - t = -t + 2} \end{gathered}[/tex]Now knowing this we are going to replace in the second equation
[tex]\begin{gathered} y\text{ = 8x - 6} \\ y\text{ = 8(-t + 2) - 6 = -8t +16 -6} \\ y\text{ = -8t +10} \end{gathered}[/tex]So the answer is the fourth option.
Determine whether each parabola has a horizontal directrix or vertical directrix 1. (y-3)²= 1/8 (x+1) horizontal or vertical directrix2. (x-2)²=6(y-3) horizontal or vertical directrix 3. (y+4)²=-12(x+2)horizontal or vertical directrix4. (x+3)²= -8(y+2) horizontal or vertical directrix
Answer
1) Horizontal directrix.
2) Vertical directix.
3) Horizontal directix.
4) Vertical directrix.
Explanation
A parabola with a vertical axis will have a horizontal directrix.
A parabola with a horizontal axis will have a vertical directrix.
A parabola with a vertical axis will have a standard equation of the parabola as
(x - h)² = 4p (y - k),
where p ≠ 0.
The vertex of this parabola is at (h, k). The focus is at (h, k + p).
The directrix is the line y = k - p and it is a vertical directrix.
A parabola with a horizontal axis will have a standard equation of the parabola as
(y - k)² = 4p (x - h),
where p ≠ 0.
The vertex of this parabola is at (h, k). The focus is at (h + p, k).
The directrix is the line x = h - p and it is a horizontal directrix.
So, for this questions,
1.) (y - 3)² = 1/8 (x + 1)
This is of the form (y - k)² = 4p (x - h), so, we can easily see that this parabola has a horizontal directrix.
2.) (x - 2)²= 6 (y - 3)
This is of the form (x - h)² = 4p (y - k), so, we can easily see that this parabola has a vertical directrix.
3.) (y + 4)² = -12 (x + 2)
This is of the form (y - k)² = 4p (x - h), so, we can easily see that this parabola has a horizontal directrix.
4.) (x+3)²= -8(y+2)
This is of the form (x - h)² = 4p (y - k), so, we can easily see that this parabola has a vertical directrix.
Hope this Helps!!!
The waiter places a bowl of soup in front of Lacy. In a counterclockwise direction, she passes the soup 90°. The person receiving the soup passes it 30°. After the two passes, the soup is in front of which person ?○ Haifa○darcy○garret○igor
Notice that we have 12 people evenly distributed in a round table (360°).
This way, each person would be
[tex]\frac{360}{12}=30[/tex]30° from each other.
After the two passes, the soup would have moved 120°, meaning that
[tex]\frac{120}{30}=4[/tex]It would have moved 4 places.
Now, the person sitting 4 places away from Lacy, if the soup is passed counterclockwise, is Haifa
Therefore, the soup would be in front of Haifa.
Amber has a job babysitting. She makes 7.50 per hour. What is the constant rate of change?
Remember that the constant rate of change refers to the change between the variable.
In this case, the constant rate of change is $7.50 per hour, in other words, it's 7.50. As an equation would be
[tex]y=\frac{15}{2}x[/tex]On your fifteenth birthday you discover you have a rich aunt sally aunt sally is a very generous women and wants to provide for your future she has decided that she will initially give you $1 then $2 the next year and so on doubling the amount each year until your 30. Use a chart to keep track how much money she will give you each year for the first 5 years.
Let's fill a table with the first two years, we already know those
So, we need to complete the chart for years 3,4, and 5. We know that in year 3, will receive double the money than we get in year 2, this is 2*$2=$4. Now we write that result on our table.
In year 4 we'll get double the money than in year 3, this is 2*$4=$8
Similarly, in year 5 we get double the money than what we got in year 4: 2*$8=$16
And we have filled in the table!
Now, a bonus, the pattern here seems to be an equation, notice this:
year 1 -> $1 = $2^0
year 2 ->$2 = $2^1
year 3 -> $4 = $2^2
year 4 -> $8 = $2^3
year 5 -> $16 = $2^4
This means that the amount of money we'll receive each year is given by
[tex]2^{t-1}[/tex]Where t is the year! (year 1, year 2, etc)
Solve for y. y - 10 = 7 - X
We are given the following expression:
[tex]y-10=7-x[/tex]To solve for "y" we will add 10 to both sides:
[tex]y-10+10=7-x+10[/tex]Adding like terms:
[tex]y=17-x[/tex]Find the slope of the line that passes through (4, 3) and (9, 10). Simplify your answer and write it as a proper fraction, improper fraction
Answer:
Slope = 7/5
Explanation:
The slope of a line that passes through the points (x1, y1) and (x2, y2) can be calculated as:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]So, replacing (x1, y1) by (4, 3) and (x2, y2) by (9, 10), we get that the slope of the line is equal to:
[tex]m=\frac{10-3}{9-4}=\frac{7}{5}[/tex]Therefore, the slope is equal to 7/5
Find the value of b.a=5 and c = 10A.9.5B.10C.9D.8.7Please can you explain.
1) Assuming this is a right triangle, we can find the missing leg by making use of the Pythagorean Theorem.
2) Thus, we can write out this:
[tex]\begin{gathered} c^2=a^2+b^2 \\ \\ (10)^2=5^2+b^2 \\ \\ 100=25+b^2 \\ \\ b^2=100-25 \\ \\ b=\sqrt{75} \\ \\ b\approx8.7 \end{gathered}[/tex]Note that the hypotenuse (the largest side) is always on the left side. And that this is an approximation rounded off to the nearest tenth.
3) Thus, the answer is:
[tex]D.\:8.7[/tex]Point L is on line segment KM. Given LM = 5 and KL = 12, determine the length KM.
ANSWER
KM = 17
EXPLANATION
We have that point L is on the line segment KM.
Let us draw a diagram to represent it:
From the diagram, we see that the length of KM is the sum of the lengths of KL and LM.
This means that:
KM = KL + LM
KM = 12 + 5
KM = 17
That is the value of the length of KM.
Find the inverse function of F(x)=2 arccos xF^-1(x)=
Given the inverse function
[tex]f(x)\text{ = 2arccosx}[/tex]A function g is the inverse of f if for y = f(x) , x = g(y)
[tex]\begin{gathered} y\text{ = 2arccosx} \\ \arccos x\text{ = }\frac{y}{2} \\ \arccos a\text{ = b} \\ a=\cos (b) \end{gathered}[/tex][tex]\begin{gathered} x=\text{ cos(}\frac{y}{2}) \\ \text{substitute y = x} \\ y=\cos (\frac{x}{2}) \end{gathered}[/tex]Hence the correct answer is Option B
what is the probability of a student owning a car that is not blue or green round to two decimal places
0.83
Explanation
The probability of an event is the number of favorable outcomes divided by the total number of outcomes possible
[tex]P=\frac{favorable\text{ ourcomes}}{\text{total possible outcomes}}[/tex]Step |
Let
[tex]\begin{gathered} \text{favorable outcomes=car that is not blue or gre}en,\text{ so} \\ \text{favorable outcomes=}red\text{ cars+yellow cars+white cars+other} \\ \text{favorable outcomes=}40+29+26+14 \\ \text{favorable outcomes=}109 \end{gathered}[/tex]now, the total outcomes is the total of cars
[tex]\text{total outcomes=40+13+29+26+10+14=132}[/tex]Finally, replace in the equation
[tex]\begin{gathered} P=\frac{favorable\text{ ourcomes}}{\text{total possible outcomes}} \\ p=\frac{109}{132} \\ P=0.83 \end{gathered}[/tex]so, the answer is 0.83
I hope this helps you
I need help with this please thank you number 14
Answer:
The question is given below as
Concept:
The question will be solved using the linear pair theorem below
The Linear Pair Theorem states that two angles that form a linear pair are supplementary; that is, their measures add up to 180 degrees.
By applying the principle, we will have that
[tex]\begin{gathered} \angle x+88^0=180^0 \\ collect\text{ similar terms,} \\ subtract\text{ 88 from both sides} \\ \operatorname{\angle}x+88^0-88^0=180^0-88^0 \\ \angle x=92^0 \end{gathered}[/tex]Hence,
The value of x= 92°
Step 2:
By applying the linear pair theorem, we will also have that
[tex]\begin{gathered} \angle z+88^0=180^0 \\ collect\text{ similar terms, } \\ subtract\text{ 88 from both sides} \\ \operatorname{\angle}z+88^0-88=180^0-88 \\ \angle z=92^0 \end{gathered}[/tex]Hence,
The value of z= 92°
Step 3:
By applying the linear pair theorem also, we will have that
[tex]\begin{gathered} \angle x+\angle y=180^0 \\ 92^0+\angle y=180^0 \\ collect\text{ similar terms,} \\ substract\text{ 92 from both sides} \\ 92^0-92^0+\operatorname{\angle}y=180^0-92^0 \\ \angle y=88^0 \end{gathered}[/tex]Hence,
The value of y= 88°
I need help with question 3, the model is above it.
we have Pattern A
0,4,8,12,
In this problem we have an arithmetic sequence
the common factor d=4
therefore
in step 4
there are 12+4=16 dots
answer is 16 dotsPoss Combine like terms to create an equivalent expression. Skill 4 3 2 m 5 m т 5 5 Over Introl Subs Quiz 80% Take Com
Collecting like terms =>
[tex]\begin{gathered} (\frac{2m}{5}-\frac{3m}{5})\text{- }\frac{4}{5} \\ we\text{ can simplify the terms with m coefficient} \\ \frac{2}{5}m\text{ -}\frac{3}{5}m \\ =\text{ find the lowest common multiple of the denominator} \\ =\text{ lowest common multiple of 5 and 5 is 5} \\ =\text{ }\frac{2m\text{ - 3m}}{5} \\ \Rightarrow\text{ }\frac{-m}{5} \\ \\ \\ \end{gathered}[/tex][tex]\begin{gathered} \text{Then we will obtain} \\ \frac{-m}{5}\text{ -}\frac{4}{5} \end{gathered}[/tex]We may decide to further simplify the expression or leave the answer as it is shown above,
On simplification we will need to get the lowest common multiple of the denominator which is 5
[tex]\frac{-m}{5}\text{ -}\frac{4}{5}\Rightarrow\text{ }\frac{-m\text{ - 4}}{5}[/tex]identify the terms, like terms, coefficients and constants 2c - 2b + c + 3 + b - 4
1) In this expression, we have
1.1 ) Terms: We have 6 terms in total.
2c -2b +c +3 + b -4 Combining like terms we can rewrite them as
c -b -1
1.2) Like terms are the ones that share the same variable
2c, c
-2b, b
1.3) Coefficients the numbers that multiply the variables
2c - 2b + c + 3 + b - 4
So we have:
2, -2, 1
1.4) The constants. Simply put in this case, the numbers that do not vary
-4 and 3
The local water slides have 40 employees,of which 95% are temporary.How many temporary employees are there?
Mul,tiply the number of employees by the percentage in decimal form (divided by 100)
40 x (95/100) = 40 x 0.95 = 38 employees
need help with math
Here, we want to get the solution to the inequality
To do this, we simply move on to collect like terms
We simply have to bring -4 to the other side
Mathematically, we have this as;
[tex]\begin{gathered} 2x\text{ -4 }\leq\text{ 12} \\ 2x\leq\text{ 12 + 4} \\ 2x\leq\text{ 16} \\ \text{ x }\leq\frac{16}{2} \\ x\leq8 \end{gathered}[/tex]Simplify the inequality. Graph it, write it in interval notation, and then inequality notation. Write your answer in interval notation.3x+2<−4 or 3x+3>27Clear All Draw: Line segments interval inequality
given the inequality
[tex]3x+2<−4\text{ }or\text{ }3x+3>27[/tex]then
[tex]3x<−4-2\text{ }or\text{ }3x>27-3[/tex][tex]3x<−6\text{ }or\text{ }3x>24[/tex][tex]x<−2\text{ }or\text{ }x>8[/tex]Graph:
notice the empty circle because the ineqaulity does not have equal symbol
interval:
[tex]\left(-\infty \:,\:-2\right)\cup \left(8,\:\infty \:\right)[/tex]inequality:
[tex]x<-2\text{ }or\text{ }x>8[/tex]