Answers
8.1
Remember cos = adjacent side (in this case X) / hypotenuse (10)
Related Questions
25 mice were involved in a biology experiment involving exposure to chemicals found in ciggarette smoke. developed at least tumor, 9 suffered re[iratory failure, and 4 suffered from tumors and had respiratory failure. A) how many only got tumors? B) how many didn't get a tumor? C) how many suffered from at least one of these effects?
Answers
Explanation:
The total number of mice for the experiment is
[tex]Universalset=25[/tex]How to know how many mice didn't have a tumor?
Identify the total mice who did not have any effects or the effects did not include a tumor.
The number of mice that had respiratory failur is
[tex]n(R)=9[/tex]Based on this, it can be concluded 9 mice did not have a tumor,
Hence,
The number of mice that didnt have a tumor is 9
To figure out the number that got only tutmor, we will consider the number that has both tumors and respiratory failure
[tex]n(T\cap R)=4[/tex]The number that developed tumors is given below as
[tex]n(T)=15[/tex]Hence,
The number that got
What is the zero of function f?f(x)=3 square root of x+3 -6
Answers
Solution:
Given:
[tex]f(x)=3\sqrt{x+3}-6[/tex]The zeros of a function are the values of x when f(x) is equal to 0.
Hence,
[tex]\begin{gathered} 0=3\sqrt{x+3}-6 \\ \\ Collecting\text{ the like terms,} \\ 0+6=3\sqrt{x+3} \\ 6=3\sqrt{x+3} \\ \\ Divide\text{ both sides by 3;} \\ \frac{6}{3}=\sqrt{x+3} \\ 2=\sqrt{x+3} \\ \\ Taking\text{ the square of both sides;} \\ 2^2=x+3 \\ 4=x+3 \\ \\ Collecting\text{ the like terms;} \\ 4-3=x \\ 1=x \\ x=1 \end{gathered}[/tex]Therefore, x = 1
The correct answer is OPTION A.
True Or False? the y intercept for the line of the best fit for this scatterplot is 5
Answers
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.
Line LM is the midsegment of trapezoid ABCD. AB = x + 8, LM = 4x + 3, and DC = 187. What is the value of x? (image attached)thank you ! :)
Answers
To solve that question we must remember that
Then
[tex]\text{ LM = }\frac{\text{ AB + DC}}{2}[/tex]Using the value the problem gives, we get the following equation
[tex]4x+3=\frac{(x+8)+187}{2}[/tex]Solving that equation for x
[tex]\begin{gathered} 4x+3=\frac{(x+8)+187}{2} \\ \\ 8x+6=(x+8)+187 \\ \\ 7x=2+187 \\ \\ 7x=189 \\ \\ x=\frac{189}{7} \\ \\ x=27 \end{gathered}[/tex]The value of x is 27.
y = 2x - 9 y = -1/2x + 1Graph both equations to find the solutionfor this system.
Answers
To answer this question, we can graph both lines equations using the intercepts of both lines. The intercepts are the x- and the y-intercepts for both lines.
The x-intercept is the point where the line passes through the x-axis. At this point, y = 0. Likewise, the y-intercept is the point where the line passes through the y-axis. At this point, x = 0.
Therefore, we can proceed as follows:
1. Graphing the line y = 2x - 9First, we can find the x-intercept. For this, y = 0.
[tex]\begin{gathered} y=2x-9\Rightarrow y=0 \\ 0=2x-9 \\ 9=2x \\ \frac{9}{2}=\frac{2}{2}x \\ \frac{9}{2}=x\Rightarrow x=\frac{9}{2}=4.5 \end{gathered}[/tex]Therefore, the x-intercept is (4.5, 0).
The y-intercept is:
[tex]y=2(0)-9\Rightarrow y=-9[/tex]Therefore, the y-intercept is (0, -9).
With these two points (4.5, 0) and (0, -9) we can graph the line y = 2x - 9.
2. Graphing the line y = -(1/2)x +1We can proceed similarly here.
Finding the x-intercept:
[tex]\begin{gathered} 0=-\frac{1}{2}x+1 \\ \frac{1}{2}x=1 \\ 2\cdot\frac{1}{2}x=2\cdot1 \\ \frac{2}{2}x=2\Rightarrow x=2 \end{gathered}[/tex]Therefore, the x-intercept is (2, 0).
Finding the y-intercept:
[tex]\begin{gathered} y=-\frac{1}{2}(0)+1 \\ y=1 \end{gathered}[/tex]Then the y-intercept is (0, 1).
Now we can graph this line by using the points (2, 0) and (0, 1).
Graphing both linesTo graph the line y = 2x - 9, we have the following coordinates (4.5, 0) and (0, -9) ---> Red line.
To graph the line y = -(1/2)x + 1, we have the coordinates (2, 0) and (0, 1) ---> Blue line.
We graph both lines, and the point where the two lines intersect will be the solution of the system:
We can see that the point where the two lines intersect is the point (4, -1). Therefore, the solution for this system is (4, -1).
We can check this if we substitute the solution into the original equations as follows:
[tex]\begin{gathered} y=2x-9 \\ -2x+y=-9\Rightarrow x=4,y=-1 \\ -2(4)+(-1)=-9 \\ -8-1=-9 \\ -9=-9\Rightarrow This\text{ is True.} \end{gathered}[/tex]And
[tex]\begin{gathered} y=-\frac{1}{2}x+1 \\ \frac{1}{2}x+y=1\Rightarrow x=4,y=-1 \\ \frac{1}{2}(4)+(-1)=1 \\ 2-1=1 \\ 1=1\Rightarrow This\text{ is True.} \end{gathered}[/tex]In summary, we found the solution of the system:
[tex]\begin{gathered} \begin{cases}y=2x-9 \\ y=-\frac{1}{2}x+1\end{cases} \\ \end{gathered}[/tex]Using the intercepts of the lines, graphing the lines, and the point where the two lines intersect is the solution for the system. In this case, the solution is (4, -1) or x = 4, and y = -1.
Point Q is shown on the coordinate grid belowWhich statement correctly describes the relationship between the point (-3,2) and point G
Answers
The coordinate of Q is (-3,-2)
The relationship between (-3, -2) and (-3, 2)
(x,y) changes into (x,-y) which is the reflection along x axis
The point (-3, 2) is a reflection of point Q across the x-axis
Answer : The point (-3, 2) is a reflection of point Q across the x-axis
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
Answers
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).
When you have a figure like this how you find the slope
Answers
Hello there. To find the slope of the line, we have to figure out two points of the line and plug in the formula for the slope.
Given two points (x0, y0) and (x1, y1) from the line, the slope m can be found with the following formula:
[tex]m=\frac{y_1-y_0}{x_1-x_0}[/tex]In this case, the image gave us two points from the line: (-4, -2) and (3, -4)
Plugging in the values, we have:
[tex]m=\frac{-4-(-2)}{3-(-4)}[/tex]Add the values
[tex]m=\frac{-4+2}{3+4}=\frac{-2}{7}[/tex]This is the slope of this line.
The food service manager at a large hospital is concerned about maintaining reasonable food costs. The following table lists the cost per serving, in cents, for items on four menu's. On particular day, a dietician orders 68 meals from menu 1, 43 meals from menu 2, 97 meals from menu 3, and 55 meals from menu 4.Part AWrite the information in the table as a 4x5 matrix M. Maintain the ordering of foods and menu's from the table.M=[__]Part BWrite a row matrix N that represents the number of meals ordered from each menu. Maintain the ordering of menu's from the tableN=[___]Part CFind the product NMNM=[___]1st blank options (average or total)2nd blank (each food, food, or each menu)
Answers
Answer and step by step:
a) To write the information in the table as a 4x5 matrix:
b) Write a row matrix N that represents the number of meals ordered from each menu.
c) Find the product NM:
To find the product of two matrices, the matrices have to be the same number of columns and rows. Then it cannot be solved.
can you please help me with the both of them?
Answers
The values of x and angle in triangle STU are 11 and 123, 65, and the values of x and angle in triangle BCD is 3 and 70, 50
The inner of two angles are formed where two sides of a polygon meet are called the interior angle
Given that in two triangles
S = 58, T= 5x + 10 and U = 11x +2
B = 22x + 4, C = 15x + 5 and D =120
In the Triangle STU Formula to find out the value of x is
Sum of interior angles = exterior angle
= 5x + 10 + 58 = 11x +2
= 5x + 68 = 11x + 2
11x -5x = 68 -2
6x = 66
X = 11
Now substitute x value in T & U
T = 5(11) +10 U = 11(11) + 2
T= 55 +10 U = 121 + 2
U = 123 T = 65
In the Triangle BCD Formula to find out the value of x is
Sum of interior angles = exterior angle
22x + 4 + 15x + 5 = 120
37x + 9 = 120
37x = 111
X = 3
Now substitute x value in B & C
B = 22(3) +4 U = 15(3) + 5
T= 66 +4 U = 45 + 5
U = 70 T = 50
Therefore the values of x and angle in triangle STU are 11 and 123, 65, and the values of x and angle in triangle BCD are 3 and 70, 50
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Two airplanes leave the same airport. One heads north, and the other heads east. After some time, the northbound airplane has traveled 15 miles. If the two airplanes are 39 miles apart, the eastbound airplane has traveled __ miles.
Answers
Answer:
36 miles
Explanation:
Let's go ahead sketch the given problem as shown below;
From the above diagram, we can go ahead and determine x, which is the distance the eastbound plane has traveled, using the Pythagorean theorem;
[tex]\begin{gathered} 39^2=x^2+15^2 \\ 1521=x^2+225 \\ x^2=1521-225 \\ x=\sqrt[]{1296} \\ x=36\text{miles} \end{gathered}[/tex]What is the slope? y= x+2
Answers
The given equation is
[tex]y=x+2[/tex]It is important to know that the slope is the coefficient of x when it's expressed in slope-intercept form like this case.
Hence, the slope is 1.Suppose that $2500 is invested at an interest rate of 7.2%. How much is the investment worth after 5 years if interest is compounded monthly? (Do not use the money sign and round to the hundredths place (2 spots))
Answers
The investment worth after 5 years if interest is compounded monthly is $3,579.47.
Calculation:-
FV = P (1+ r/m)^mt
= $2500 ( 1 + 7.2/12)¹²ˣ⁵
= $3,579.47.
The Future value is $3,579.47.
The total compound interest is $1,079.47.
FV - the future value of the investment, in our calculator it is the final stability
P - the preliminary stability (the fee of the funding)
r - the once-a-year interest charge (in decimal)
m - the variety of instances the interest is compounded in keeping with 12 months (compounding frequency)
t - the wide variety of years the cash is invested for 5 years
Compound interest, may be calculated with the use of the method FV = P*(1+R/N)^(N*T), wherein FV is the destiny price of the mortgage or investment, P is the initial important amount, R is the yearly interest charge, N represents the variety of times hobby is compounded in keeping with year, and T represents time in years.
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Agrocery store bought milk for $2.20 perhalf gallon and stored it in two refrigerators. During the night one refrigerator malfunctioned and ruined 13 half gallons. If the remaining milk is sold for $3.96 per half gallon, how many half gallons did the store buy if they made a profit of $121.00
Answers
Answer
The store bought 98 half gallon milks
Explanation
Let the number of half gallon nilks they bought be x
They bought each half gallon milk at a rate of 2.2 dollars each
13 half gallons got spoilt.
They then sold the rest of the half gallone (x - 13) gallons at 3.96 dollars per half gallon
Profit = Revenue - Cost
Revenue = (Amount of half gallons sold) × (Price of each one)
Revenue = (x - 13) × 3.96
Revenue = (3.96x - 51.48)
Cost = (Amount of half gallons bought) × (Price of each one)
Cost = x × 2.20
Cost = 2.20x
Profit = 121 dollars
Profit = Revenue - Cost
121 = (3.96x - 51.48) - 2.20x
121 = 3.96x - 51.48 - 2.20x
121 = 1.76x - 51.48
1.76x - 51.48 = 121
1.76x = 121 + 51.48
1.76x = 172.48
Divide both sides by 1.76
(1.76x/1.76) = (172.48/1.76)
x = 98 half gallon milks
Hope this Helps!!!
Find f (-9) if f (x) = (20+x)/5
Answers
The given function is expressed as
f(x) = (20 + x)/5
We want to find f(- 9). To do this, we would substitute x = - 9 into the function. It becomes
f(- 9) = (20 + - 9)/5 = (20 - 9)/5
f(- 9) = 11/5
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
Answers
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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Find the third side in simplest radical form: 3 789
Answers
Apply the Pythagorean theorem:
c^2 = a^2 + b^2
Where:
c = hypotenuse (longest side )
a & b = the other 2 legs of the triangle
Replacing:
c^2 = 3^2 + (√89)^2
c^2 = 9 + 89
c ^2 = 98
c = √98 = √(49x2) = √49 √2 = 7 √2
Third side = 7 √2
I am supposed to give the reasons why these triangles are equal.
Answers
Statements Reasons.
1. NL bisects angles KNM and KLM. 1. Given.
2. KNL = MNL 2. Definition of angle bisector
KLN = MLN
3. NKL = NML 3. Parallelogram theorem.
4. Triangles NKL and NML are congruent. 4. AAA postulate.
The parallelogram theorem mentioned states that opposite interior angles are congruent.
The AAA postulate of congruence states that two triangles are congruent if all three interior angles are congruent correspondingly.
myself and my daughter is having issues with this problem. we keep coming up 11.96 and rounding it to 12 but it saying it is wrong
Answers
using trigonometric ratio
[tex]\tan 23^{\circ}=\frac{13}{y}[/tex][tex]\begin{gathered} y=\frac{13}{\tan 23^{\circ}} \\ y=\frac{13}{0.42447481621} \\ y=30.6260807557 \\ y\approx30.6 \end{gathered}[/tex]Note
tan 23 = opposite/adjacent
Dion makes and sells stained glass suncatchers in different shapes. For one of his designs, he attaches semicircles to each side of a square that has a side length of 4 centimeters. He builds a frame around the outside of each suncatcher to hold it together.What is the approximate length of the frame that Dion used on this suncatcher?
Answers
Designs shape is:
So length is :
Perimeter of half circle is:
[tex]\text{ Perimeter =}\pi r+2r[/tex]Radius of circle is:
[tex]\begin{gathered} r=\frac{D}{2} \\ r=\frac{4}{2} \\ r=2 \end{gathered}[/tex]So the length is:
[tex]\begin{gathered} =4(\pi r+2r) \\ =4(2\pi+2(2)) \\ =4(2\pi+4) \\ =4(6.283+4) \\ =4\times10.283 \\ =41.132 \end{gathered}[/tex]So the approximate length is 41 centimeter.
Which of the following sequences represents an arithmetic sequence with a common difference d = –4? 768, 192, 48, 12, 3 35, 31, 27, 23, 19 24, 20, 16, 4, 0 5, –20, 80, –320, 1,280
Answers
The general formula of an arithmetic sequence is:
[tex]a_n=a_1+(n-1)\cdot d[/tex]Where d is known as the common difference and it represents the distance between consecutive terms of the sequence. So we can calculate this distance for each of the four options:
[tex]\begin{gathered} 768,192,48,12,3 \\ 768-192=576 \\ 192-48=144 \end{gathered}[/tex]So in the first sequence the difference between terms is not even constant so this is not the correct option.
[tex]\begin{gathered} 31-35=-4 \\ 27-31=-4 \\ 23-27=-4 \\ 19-23=-4 \end{gathered}[/tex]In the second sequence the distance is -4 so this is a possible answer.
[tex]\begin{gathered} 20-24=-4 \\ 16-20=-4 \\ 4-16=-12 \\ 0-4=-4 \end{gathered}[/tex]In the third sequence the distance is not always the same so we can discard this option.
[tex]\begin{gathered} -20-5=-25 \\ 80-(-20)=100 \end{gathered}[/tex]Here the distance isn't constant so the fourth option can also be discarded.
Then the only sequence with a distance d=-4 is the second option.
Find the product of (x+3)^2
Answers
Find the product of (x+3)^2
Remember that
(x+a)^2=x^2+2xa+a^2
therefore
(x+3)^2=x^2+6x+9
answer is
x^2+6x+9At its first meeting, the math club had 16 students attend. At its second meeting, 25 students attended. What was the percent of increase?
Answers
First, subtract 16 to 25:
25 - 16 = 9
next, calculate the associated percentage of 9 to 16, as follow:
(9/16)(100) = 56.25
Hence, the increase was of 56.25%
-3 (2x + 4) - (2x + 4) < -4(2x +3)
Answers
-3 (2x + 4) - (2x + 4) < -4(2x +3)
expand
-6x - 12 - 2x - 4 < -8x - 12
Collect like terms
-6x + 8x - 2x < 12 + 4 -12
The is no solution
The vertices of ABC are A(2,-5), B(-3, - 1), and C(3,2). For the translation below, give the vertices of AA'B'C'. T * - 1) (ABC) The vertices of AA'B'C' are A'B', and c'| (Simplify your answers. Type ordered pairs.)
Answers
In order to calculate the translation of <-4, -1> to the triangle ABC, we just need to add these coordinates to all vertices of the triangle, that is, add -4 to the x-coordinate and -1 to the y-coordinate. So we have that:
[tex]\begin{gathered} A(2,-5)\to A^{\prime}(2-4,-5-1)=A^{\prime}(-2,-6) \\ B(-3,-1)\to B^{\prime}(-3-4,-1-1)=B^{\prime}(-7,-2) \\ C(3,2)\to C^{\prime}(3-4,2-1)=C^{\prime}(-1,1) \end{gathered}[/tex]So the vertices after the translation are A'(-2, -6), B'(-7, -2) and C'(-1, 1).
The barrel of a rifle has a length of 0.983m. A bullet leaves the
muzzle of a rifle with a speed of 602m/s. What is the
acceleration of the bullet while in the barrel? A bullet in a rifle
barrel does not have constant acceleration, but constant
acceleration is to be assumed for this problem.
Answer in units of m/s^2
Answers
The acceleration of the bullet while in the barrel is 184335.7 m/s^2.
First, let us understand the acceleration:
Any action where the velocity changes are said to it as acceleration. There are only two ways to accelerate: altering your speed or altering your direction, or altering both. This happens because velocity is both a speed and a direction.
We are given;
The length of the barrel of the rifle is 0.983 m.
The speed of the bullet is 602m/s.
From the third equation of motion, we know that,
v^2 = u^2+ 2aS
Initial velocity, u=0
Final velocity, v = 602m/s.
Distance, S = 0.983 m.
Substitute the given values in the above formula,
v^2 = u^2 + 2aS
(602)^2 = 0 + 2 * a * 0.983
1.966a = 362404
a = 362404/1.966
a = 184335.7 m/s^2.
Thus, the acceleration of the bullet while in the barrel is 184335.7 m/s^2.
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Write a rule for the nth term of the sequence, then find a_20. 7, 12, 17, 22, ...
Answers
Problem
To find the 20th term of the sequence: 7, 12, 17, 22.
The rule for the nth term of the sequence is addding 5 to the term before to get the next term.
Concept
This is an arithmetic sequence since there is a common difference between each term. In this case .
Common ratio = 5
The term to term rule of a sequence describes how to get from one term to the next.
Final answer
The first term is 7. The term to term rule is 'add 5'.
The perimeter of rhombus EFGH is 48 cm and the measure of
Answers
Given data
Perimeter = 48cm
perimeter of a rhombus is the sum of all length of the outer boundary.
A rhombus has equal length
Perimeter = 4L
4L = 48
L = 48/4
L = 12cm
a) GH = 12cm
b)
c)
To find
Opposite = 6 side facing the given angle
Hypotenuse = 12 side facing right angle
[tex]\begin{gathered} \text{Apply trigonometry ratio formula} \\ \sin \theta\text{ = }\frac{Opposite}{\text{Hypotenuse}} \\ \sin \theta\text{ = }\frac{6}{12} \\ \sin \theta\text{ = 0.5} \\ \theta\text{ = }\sin ^{-1}0.5 \\ \theta\text{ = 30} \end{gathered}[/tex]Therefore,
Angle
Write the translation of point P(2, -9) to point P'(0, -12). [A] (x, y) =(x-3, y – 2) [B] (x, y) = (x+3, y +2) [C] (x, y) = (x+ 2, y + 3) [D] (x, y) = (x-2, y-3)
Answers
Applying the transformation (x, y) → (x - 2, y - 3) to point P, we get:
P(2, -9) → (2 - 2, -9 - 3) → P'(0, -12)
use the trigonometric ratio to find the measure of θ in the triangle. Give your answer to the nearest degree
Answers
θ = 64°
Explanation:
Trigonometric ratio SOHCAHTOA
hypotenuse = 10cm
angle = θ
opposite = side opposite the angle = 9cm
adjacent = not given
Since we know the opposite and the hypotenuse, we would apply sine ratio (SOH)
[tex]\begin{gathered} \sin \text{ }\theta\text{ = }\frac{opposite}{\text{hypotenuse}} \\ \sin \text{ }\theta\text{ = }\frac{9}{10} \end{gathered}[/tex][tex]\begin{gathered} \sin \theta\text{ = 0.9} \\ \theta=sin^{-1}(0.9) \\ \theta=\text{ 64.16}\degree \\ To\text{ the nearest degr}ee,\text{ }\theta=\text{ 64}\degree \end{gathered}[/tex]