Answer:
k = 5
Explanation:
The given polynomial is
5² + 13 +
Let one of the zeros be z. Given that one of the zero is the reciprocal of the other, the reciprocal of z is 1/z. The roots are z and 1/z
The standard form of a quadratic polynomial is
ax^2 + bx + c
By comparing the polynomial expressions,
a = 5, b = 13, c = k
The product of the roots of a quadratic polynomial is c/a = k/5
Thus,
1/z * z = k/5
1 = k/5
By cross multiplying,
k = 5
A vector has a magnitude of 50 and a direction of 30°. Another vector has a magnitude of 60 and a direction of 150°. What are the magnitude and direction of the resultant vector? Round the magnitude to the thousandths place and the direction to the nearest degree.
Step 1:
Draw the vector diagram
Step 2:
Write the angles to the horizontal axis.
30 degrees to the horizontal axis = 30
150 degrees to the horizontal axis = 180 - 150 = 30
Step 3:
Find the vertical component and the horizontal component of the magnitude.
[tex]\begin{gathered} \text{Horizontal component = Fcos}\theta \\ \text{Vertical component = Fsin}\theta \end{gathered}[/tex]Step 3:
[tex]\begin{gathered} \text{Sum of the vertical component V = 25 + 30 = 55} \\ \text{Sum of the horizontal component H = 43.3 - 51.96 = -8.66} \end{gathered}[/tex]Step 4:
Find the magnitude
[tex]\begin{gathered} \text{Magnitude = }\sqrt[]{V^2+H^2} \\ =\text{ }\sqrt[]{55^2+(-8.66)^2} \\ =\text{ }\sqrt[]{3025+74.9956} \\ =\text{ 56.678} \end{gathered}[/tex]Magnitude = 56.678
Step 5:
Find the direction
[tex]\begin{gathered} \text{Tan}\theta=\text{ }\frac{V}{H} \\ \theta=tan^{-1}(\frac{55}{8.66}) \\ \theta\text{ = 81} \end{gathered}[/tex]Direction = 81
solve the following equation, write the answer in reduced fraction form, if necessary. (x+5)(x-5)=0Separate multiple entries with commas.
what is the range of the giving relation {(9,1), (9,4) , (9,5) , (9,6)}
ANSWER
EXPLANATION
We are given the relation:
{(9, 1), (9, 4), (9, 5), (9, 6)}
The range of any set of points in
What is 4.73 x 3.4?
Please answer
Answer:
Explanation:
The product of 4.73 and 3.4 is calculated below:
A 150 lb individual weighs how many kg? Round to nearest kilogram.
Take into account that the relation between pounds and kilograms is:
1 kg = 2.204 lb
Then, you can use a conversion factor to determine how many kg are 150 lb, as follow:
[tex]150lb\cdot\frac{1\operatorname{kg}}{2.204lb}\approx68.05\operatorname{kg}[/tex]Hence, 150 lb are approximately 68.05 kg
If cosθ=3√2cosθ=32 then which of the following could be true?tan=−3√tangent is equal to negative square root of 3cscθ=12cosecant theta is equal to 1 halfsecθ=−2secant theta is equal to negative 2sinθ=2√2sine theta is equal to the fraction with numerator square root of 2 and denominator 2
Given that
[tex]\cos\theta=\frac{\sqrt{3}}{2}[/tex]we can determinate the sine of this angle using the following identity
[tex]\sin^2\theta+\cos^2\theta=1[/tex]If we substitute the value of the cosine on this identity, we're going to have:
[tex]\begin{gathered} \sin^2\theta+(\frac{\sqrt{3}}{2})^2=1 \\ \sin^2\theta+\frac{3}{4}=1 \\ \sin^2\theta=\frac{1}{4} \\ \sin\theta=\pm\frac{1}{2} \end{gathered}[/tex]The definitions of secant, tangent, and cosecant in terms of the sine and cosine are given by:
[tex]\begin{gathered} \tan\theta=\frac{\sin\theta}{\cos\theta} \\ \sec\theta=\frac{1}{\cos\theta} \\ \csc\theta=\frac{1}{\sin\theta} \end{gathered}[/tex]Using the known values for the sine and cosine functions on those definitions, we have:
[tex]\begin{gathered} \tan\theta=\frac{\pm\frac{1}{2}}{\frac{\sqrt{3}}{2}}=\pm\frac{1}{\sqrt{3}}=\pm\frac{\sqrt{3}}{3}\ne-\sqrt{3} \\ \\ \csc\theta=\frac{1}{\pm\frac{1}{2}}=\pm2\ne\frac{1}{2} \\ \\ \sec\theta=\frac{1}{\frac{\sqrt{3}}{2}}=\frac{2}{\sqrt{3}}=\frac{2\sqrt{3}}{3}\ne-2 \\ \\ \sin\theta=\pm\frac{1}{2}\ne\frac{\sqrt{2}}{2} \end{gathered}[/tex]All options are false.
(2,-1)(-3,5)1:2find the point that partitions the segment with the two given endpoints with the given ratio
We are given two points
A = (2, -1)
B = (-3, 5)
Ratio = 1:2
Let the ratio be P
Therefore, P is 1:2
Slope = Rise / Run
Rise = y2 - y1
Run = x2 - x1
x1 = 2, y1 = -1, x2 = -3 and y2 = 5
P = 1 / 1+ 3
P = 1/3
The horizontal distance is the same as run
Run = x2 - x1
=-3 - 2
Run = -5
Therefore we have
P x run
1/3 x -5
= -5/3
The distance between P and A on the x - axis is
-5/3 - 2
= -11/3
Rise = y2 - y1
5 - (-1)
= 5 + 1
Rise = 6
1/3 x 6
6/3 = 2
The distance between A and P on the y axis is
2 -(-1)
=2 + 1
= 3
The points are -11/3 and 3
The answer is (-11/3, 3)
What is the image (11,-5) after the Rx=0 • T(11,-5)(-22,-10)(0,-10)(22,10)(0,10)
The original point has coordinates (11,-5)
The transformation applied to this point are Rx=0 * T(11,-5)
First, you have to do the translation T(11,-5), this means that you have to make a horizontal translation 11 units to the right, and a vertical translation 5 units down, following the rule:
[tex](x,y)\to(x+11,y-5)[/tex]So, add 11 units to the x-coordinate and subtract 5 units to the y-coordinate of (11,-5)
[tex](11,-5)\to(11+11,-5-5)=(22,-10)[/tex]Once you've made the translation, you have to reflect the point (22,-10) over the vertical line x=0, this vertical line is the y-axis. This means that you have to reflect the point over the y-axis.
To do this reflection you have to invert the sign of the x-coordinate of the point and leave the y-coordinate the same:
[tex]R_{y-\text{axis}}=(x,y)\to(-x,y)[/tex][tex](22,-10)\to(-22,-10)[/tex]The coordinates of the point after the translation and reflection are (-22,-10), option 1
It costs $350 to repair a refrigerator compressor. Compute the QLF for losses incurred as a result of a deviation from a target setting with a nominal tolerance of 60 amps, where a 2-amp variation is acceptable. The mean squared deviation is 1/5
The Quality loss function QLF incurred as a result of a deviation from a target setting is $17.5
How to determine the QLF for the lossesQLF is acronym for quality loss function, this solved using the formula
= kv^2
where
k = constant
v = mean square deviation = 1/5
the constant k is solved by the formula
= c/T^2
where
c = cost of item = 350
T = variation acceptable = 2
= 350 / 2^2
= 87.5
QLF = kv^2\
= 87.5 * 1/5
= 17.5
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enclose the figure that occupies the position of the tens of thousand in each number. then write its value 573901 1926734 103485 2801345
ANSWER:
STEP-BY-STEP EXPLANATION:
The tens of thousand, would be the values of 10,000 in 10,000, therefore for each value it would be:
[tex]undefined[/tex]how many pounds is 19.2 kg
Let's begin by listing out the given information:
[tex]\begin{gathered} 19.2kg\rightarrow lb \\ \end{gathered}[/tex]From general acceptable law, we know that:
[tex]1kg=2.20462lb[/tex]Therefore, 19.2 kg will be converted to pounds using simple proportion as shown below:
[tex]undefined[/tex]wgat us 5he image of (0,-1) after a translation of left 5 units and down 1 unit
EXPLANATION
Given the point (0,-1), after a translation of left 5 units and down 1 unit the image would be:
Image: (-5,-2)
im completely lost on my review it says find the missing angle from these 2 congruent triangles.
We will reason to find the values of angles 1 through 6. To do so, we will use a key fact of triangles which is:
the sum of the angles of a triangle is 180°.
So, we will start by finding the value of angle 1. Note that angle 1 is in the triangle XYZ, whose other angles are 58° and 65°. Then, we have the following equation
[tex]\text{Angle 1 + 58\degree+65\degree=180\degree}[/tex]Since 58+65 = 123 then we have
[tex]\text{Angle 1 + 123 =180}[/tex]By subtracting 123 on both sides, we get that
[tex]\text{Angle 1 =180-123 = 57\degree}[/tex]So angle 1 measures 57°.
We can see that angles 1 and 2 are supplementary. That is, their measures add up to 180°. So, we have the following equation
[tex]\text{Angle 1 + Angle 2 =180}[/tex]Since angle 1 = 77° we have that
[tex]77\text{ + Angle 2 = 180}[/tex]which implies that angle 2 measures 123°. Using the same principle we can find the value of angle 5, since we have
[tex]\text{Angle 2 + Angle 5 = 180}[/tex]since angle 2 measures 123, we have that
[tex]123+\text{ Angle 5 = 180}[/tex]which implies that angle 5 measures 57°. Now, we see that angle 6 is in triangle VXW, so we can find the value of angle 6 as follows
[tex]\text{Angle 6 + Angle 5 + 67 = 180}[/tex]Then, since angle 5 measures 57° we have
[tex]\text{Angle 6 + 57\degree+67\degree=180\degree}[/tex]Since 57+67=124. Then , we have
[tex]\text{Angle 6 + 124 = 180 }[/tex]Subtracting 124 on both sides, we get
[tex]\text{Angle 6 = 180-124 = 56}[/tex]Now, we are missing to find the values of angles 3 and 4. To do so, first notice that
[tex]\text{Angle 2 + Angle 3 +Angle 4=180}[/tex]since these are the angles of triangle WXZ. We already know the measure of the angle 2 (123), so we have
[tex]\text{Angle 3 + Angle 4 =}180\text{ -123 = 57}[/tex]Unfortunately, the question doesn't give any more details on the triangles, so there are multiple solutions of values of angles 3 and 4 such that the equation holds
write word problem1- correct variable term for the left side2-correct constant term for the left side 3-correct operation between the terms of the left side 4-correct equal sign or inequality symbol 5-correct variable term for the right side6-correct constant term for the right side 7-correct operation between the terms of the right side58×+170>42×+320
For the equation
[tex]58x+170>42x+320[/tex]A word problem could be the following.
Suppose we have a coin whose value we do not know and let us call the value of this coin x. All we know that 58 of these coins plus $170 is greater than 42 of these coins plus $320. This information, when converted into a word problem, gives the above inequality.
Which of the following represents vector u = −3i + 8j in component form?
Solution
- The way to write vectors in component form is given below:
[tex]\begin{gathered} u=u_xi+u_yj \\ \text{ In Component form, we have:} \\ u=\langle u_x,u_y\rangle \end{gathered}[/tex]- Thus, we can apply the rule stated above to the question given to us.
- This is done below:
[tex]\begin{gathered} u=-3i+8j \\ \\ \therefore u=\langle-3,8\rangle \end{gathered}[/tex]Final Answer
The answer is
[tex]u=\langle-3,8\rangle\text{ (OPTION 2)}[/tex]Please help me with this ASAP!
The length of the side AB in triangle ΔABC is 12 centimeters
What is the length of a line or segment?The length of a line or segment is the distance between the endpoints.
The location at which the perpendicular bisector of segment [tex]\overline{AB}[/tex] in ΔABC intersects the side [tex]\overline{BC}[/tex] = Point D
The perimeter of ΔABC = 12 + The perimeter of ΔACD
Please find attached, the possible drawing of the figure in the question;
ΔADE is congruent to ΔBDE by Side-Angle-Side congruency postulate
[tex]\overline{AD}[/tex] is congruent to [tex]\overline{DB}[/tex] by Corresponding Parts of Congruent Triangles are Congruent.
The perimeter of ΔABC = AB + BC + AC
Perimeter of triangle ΔACD = AC + CD + AD
BC = CD + DB
The perimeter of ΔABC = AB + CD + DB + AC = 12 + AC + CD + AC
The substitution and subtraction property of equality indicates;
AB + CD + DB = 12 + CD + AD = 12 + CD + DB
AB = 12
Therefore, AB = 12
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5. Elena wanted to find the slope and y-intercept of the graph of 25x - 20y = 100.She decided to put the equation in slope-intercept form first. Here is her work-25x – 20y = 10020y = 100 – 25x5y = 5 --X-5. Describe Elena's mistake in her work above, and what the correct slopeand y-intercept of the line are.What are the x- and y-intercepts of the equation 4y + 9x = 18?
Given the equation:
25x - 20y = 100
Let' write the equation in slope-intercept form and find the mistaeke in Elena's worl.
Apply the slope intercept form of a linear equation:
y = mx + b
Rewrite the equation for y:
25x - 20y = 100
• Subtract 25x from both sides:
25x - 25x - 20y = 100 - 25x
-20y = 100 - 25x
• Divide all terms by -20:
[tex]undefined[/tex]please answer the question and please explain in simple way
The x intercepts are determide when you calculated the equation when y=0
To find the x-coordinate of the vertex you have to apply the next formula:
[tex]x=-\frac{b}{2a}[/tex]Where you follow the form of the equation:
[tex]y=ax^2+bx+c[/tex]X-intercep:
1. In this case if we have the equation in the form: x( x - 2) we can know that y=0 when one of the terms is 0:
y=0 when:
x=0x-2=0
x= - 22. y=0 when:
x-4=0
x=4x+5=0
x=-53. y=0 when:
x-1=0
x=1x-5=0
x=5x-coordinate of the vertex:To identify the coeficeints a and b we express the equation in a different form, we have to multiply. Then we can apply the formula to find the x coordinate of the vertex, as follow:
[tex]x=-\frac{b}{2a}[/tex]1.
[tex]y=x(x-2)=x^2-2x[/tex][tex]x=-\frac{(-2)}{2(1)}=\frac{2}{2}=1[/tex]2.
[tex]y=(x-4)(x+5)=x^2+5x-4x-20=x^2-x-20[/tex][tex]x=-\frac{(-1)}{2(1)}=\frac{1}{2}[/tex]3.
[tex]y=(x-1)(x-5)=x^2-5x-x+5=x^2-6x+5[/tex][tex]x=-\frac{(-6)}{2(1)}=\frac{6}{2}=3[/tex]The data for the control group has a a. first common differenceb. second common difference c. common ratioTherefore the data is being generated by a a. linear functionb. quadratic function c. exponential functionThe data for the original formula has aa. first common difference b. second common differencec. common ratioTherefore the data is being generated by a a. linear functionb. quadratic functionc. exponential function The data for the improved formula has a a. first common difference b. second common difference c. common ratio Therefore the data is being generated by a a. linear functionb. quadratic functionc. exponential function
Answer:
The data for the control group has a first common difference, therefore the data is being generated by a linear function
The data for the original group has a second common difference, therefore the data is being generated by a quadratic function
The data for the Improved group has a common ratio, therefore the data is being generated by an exponential function
Explanation:
Given the table in the attached image.
The data for the control group has a common difference, that is the difference between consecutive values are the same.
[tex]d=13-6=20-13=27-20=34-27=41-34=7[/tex]Since the values have a common difference then it is a linear function.
The original formula has a second common difference, therefore the data is being generated by a quadratic function.
The improved formula has a common ratio;
[tex]r=\frac{18}{9}=\frac{36}{18}=\frac{72}{36}=\frac{144}{72}=\frac{288}{144}=2[/tex]Therefore, the data is being generated by an exponential function.
subtract.(9r + 9) - (9r + 3)
Consider the given expression,
[tex](9r+9)-(9r+3)[/tex]Eliminate the parenthesis,
[tex]9r+9-9r-3[/tex]Take the like terms together,
[tex]\begin{gathered} (9r-9r)+(9-3) \\ 0+6 \\ 6 \end{gathered}[/tex]Thus, the value of the expression is 6.
Find the axis of symmetry of the graph y = x2 + 8x + 16.
The axis of simetry of a parabola is the vertical line that cross the vertex of the parabola.
So, we need to find the x-value of the vertex:
[tex]\begin{gathered} \text{The general equation of a parabola is:} \\ y=ax^2+bx+c \\ \text{The x-value of the vertex is:} \\ x_v=-\frac{b}{2a} \end{gathered}[/tex]So, in this case a=1 and b=8:
[tex]x_v=-\frac{8}{2\cdot1}=-4_{}[/tex]The axis of simetry is x=-4.
The Homecoming committee wants to raise between $1500 and $2000 at the dance.They have already saved $800 to put towards the dance. If tickets are $20 each, howmany tickets must they sell? Variable Represents:Inequality:Solve:Sentence:
Answer:
35≤t≤60
Explanation:
Let the variable t represents the number of tickets they must sell.
Cost of a ticket =$20
• Cost of t tickets =$20t
Since they have already saved $800
Total balance = 800+20t
The committee wants to raise between $1500 and $2000 at the dance.
Therefore, the inequality representing this situation is:
[tex]1500\leqslant800+20t\leqslant2000[/tex]We solve for t.
[tex]\begin{gathered} 1500\leqslant800+20t\leqslant2000\text{ (Subtract 800 from all sides)} \\ 1500-800\leqslant800-800+20t\leqslant2000-800 \\ 700\leqslant20t\leqslant1200\text{ (Divide all through by 20)} \\ \frac{700}{20}\leqslant\frac{20t}{20}\leqslant\frac{1200}{20} \\ 35\leqslant t\leqslant60 \end{gathered}[/tex]The homecoming committee must sell between 35 and 60 tickets to meet their goal.
Noah bought 15 baseball cards for $9 assuming each baseball card cost the same amount answer the following questions one at this rate how much will the third 30 baseball cards cost explain your reasoning. At this rate how much will 12 baseball cards cost explain your reasoning. Do you think this information will be better represented using a table or a double number line explain your reasoning.
We know that 15 baseball costs $9.
We have to divide to find the unit cost.
[tex]\frac{9}{15}=0.6[/tex]Each baseball card cost 60 cents.
So, for 30 cards, it would cost
[tex]\begin{gathered} 0.6\cdot30=18 \\ 0.6\cdot12=7.2 \end{gathered}[/tex]Hence, 30 baseball cards cost $18, at the same unit price. And 12 baseball cards would cost $7.20.Observe that to get the answers, we just had to multiply the number of cards by the unit price.
There's no need for a table or a number double line because they are used when the amount of data is big enough. It is better to keep it simple.
2The points A(2,5), B(6,5), C(5,2) and D(1, 2) are the vertices of a parallelogram.If the parallelogram is translated down two units and right three units, what will bethe coordinates of the final image of point B?
To answer this question, we need to apply the rule of translation to each of the points of the parallelogram. This rule can be expressed as: (x + 3, y -2), that is, the parallelogram is translated down two units and right three units.
Then, we have:
A (2, 5) ---> A'(2 + 3, 5 - 2) ---> A' (5, 3)
B (6, 5) ---> B' (6 + 3, 5 -2 ) ---> B' (9, 3)
C (5, 2) ---> C' (5 + 3, 2 - 2) ---> C' (8, 0)
D (1, 2) ---> D' (1 + 3, 2 -2) ---> D' (4, 0)
Therefore, the coordinates of the final image of point B are B' (9, 3).
Juanita is eight years older than her brother hector. If Juanita is nineteen years old this year, how old is hector
juanita: 19
hector:?
[tex]h+9=j[/tex][tex]h+9=19[/tex][tex]h=19-9=10[/tex]Hector is 10 years
A laboratory tested 82 chicken eggs and found that the mean amount of cholesterol was 228 milligrams with sigma equals 19.0 milligrams. Construct a 95% confidence interval for the true mean cholesterol content u of all such eggs.
ANSWER
[tex]223.88,232.11[/tex]EXPLANATION
Given;
[tex]\begin{gathered} n=82 \\ \bar{x}=228 \\ \sigma=19.0 \\ \end{gathered}[/tex]At 95% confidence level;
[tex]\begin{gathered} \propto=1-95\% \\ =1-0.95 \\ =0.05 \\ \frac{\propto}{2}=0.025 \\ Z_{\frac{\operatorname{\propto}}{2}}=Z_{0.025}=1.96 \\ \end{gathered}[/tex]At 95% confidence interval for true mean;
[tex]\begin{gathered} \bar{x}\pm Z_{\frac{\operatorname{\propto}}{2}}\frac{\sigma}{\sqrt{n}} \\ =228\operatorname{\pm}1.96\times\frac{19}{\sqrt{82}} \\ =228+1.96\times\frac{19}{\sqrt{82}}<228-1.96\times\frac{19}{\sqrt{82}} \\ =228-4.1124<228+4.1124 \\ =223.88<\mu<232.11 \end{gathered}[/tex]Therefore, 95% confidence interval for the true mean cholesterol content
(223.88,232.11)
Write the phrase as an algebraic expression8. the quotient of eight and a number h
the quotient of eight and a number h
we have that
quotient is a division
where
eight is the numerator and h is the denominator
so
8/h
the answer is 8/h
Find the height of the trapezoid.Base1: 100Base2: 56Leg1: 31Leg2: 31 Please help!!
To find the area of a trapezoid we can use this equation:
[tex]A=A_r+A_{t1}+A_{t2}[/tex]so we have to find the missing sides so:
So the area is:
[tex]undefined[/tex]What definition would justify the following statement?If T is the midpoint of segment RS then, Segment RT is congruent to segment TS.Options:Definition of Angle BisectorDefinition of CongruenceDefinition of MidpointDefinition of Segment Bisector
ANSWER
Definition of Segment Bisector
EXPLANATION
The statement given is:
If T is the midpoint of segment RS then, Segment RT is congruent to segment TS.
The very first portion of that statement gives us the context of this statement.
We see two key words there:
- Midpoint
- Segment
The statement is talking about a segment and so it cannot be about an Angle Bisector.
Also, we see T acting as a means of bisecting the segment RS into equal parts.
How do we know? We have that Segment RTis congruent (or equal/identical) to segment TS.
This tells us that T acts as a bisector for that segment RS.
We can therefore say that the statement justifies the Definition of a Segment Bisector.
What is the probability that Erika will get to move ahead on this spin.
total outcomes=8
move ahead outcome=4
probabilty of move ahead =4/8=1/2
Thus the answer is 1/2.