Given the parallelogram in the attached image.
Recall that two adjacent angles in a parallelogram add up to 180 degrees.
So;
[tex]m\angle\text{PQR}+m\angle QRS=180^{\circ}[/tex]Given;
[tex]undefined[/tex]I'm behind in geometry if you could teach me this I would highly appreciate it
We know that AC and BD bisect each other, but AC is not equal to BD.
Basically, the problem is saying that these segments are bisectors of each other, that can be represented as the image below shows
As you can see in the image, AC and BD bisect each other, but their lengths are not equal.
How long is the control line? I couldn’t figure this out
Solution:
Given the circle with center A as shown below:
The plane travels 120 feet counterclockwise from B to C, thus forming an arc AC.
The length of the arc AC is expressed as
[tex]\begin{gathered} L=\frac{\theta}{360}\times2\pi r \\ \text{where} \\ \theta\Rightarrow angle\text{ (in degre}e)\text{subtended at the center of the circle} \\ r\Rightarrow radius\text{ of the circle, which is the }length\text{ of the control line} \\ L\Rightarrow length\text{ of the arc AC} \end{gathered}[/tex]Given that
[tex]\begin{gathered} L=120\text{ f}eet \\ \theta=80\degree \\ \end{gathered}[/tex]we have
[tex]\begin{gathered} L=\frac{\theta}{360}\times2\pi r \\ 120=\frac{80}{360}\times2\times\pi\times r \\ cross\text{ multiply} \\ 120\times360=80\times2\times\pi\times r \\ \text{make r the subject of the equation} \\ \Rightarrow r=\frac{120\times360}{2\times\pi\times80} \\ r=85.94366927\text{ fe}et \end{gathered}[/tex]Hence, the length of the control line is 85.94366927 feet.
someone please help…
Q.12 The polynomials are 2 and 3
What is polynomial ?
A polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables. An example of a polynomial of a single indeterminate x is x² − 4x + 7.
Given, p(x) = -x² + x + 2
p has a degree 2
Let, a = 1 + i√2
b = 1 - i√2
a + b = 1 + i√2 + 1 - i√2
= 2
a * b = (1 + i√2) * (1 - i√2 )
= 1 - (i√2)²
= 1 - i²*2 (where, i² = -1)
= 1 + 2
= 3
Therefore, the polynomial are 2 and 3
Q.13 The polynomial is x³ + x
Given, Q(x) = x³ - 2x² - 1
Q has a degree of 3
=>(x - 0) (x - i) (x + i)
=>(x² - ix) (x + i)
=>x³ + x²i - ix² - i²x (where i² = -1)
=>x³ + x
Therefore, the polynomial is x³ + x
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A football team was able to run the ball for 8 yards on their first play. On the second play they lost 12 yards. The third play they lost another 11 yards. What was their total yards they gained?
The total yards gained or lost is the algebraic sum so the resultant yards is -15 yards thus they lose 15 yards.
What is the arithmetic operator?Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,
Subtraction = Minus of any two or more numbers.
Summation = addition of two or more numbers or variable
Let's consider all gained yards by positive (+) and all lost yards by negative (-).
Given that,
In the first play = +8 yards (gain)
In second play = -12 yards (lost)
In the third play = 11 yards (Lost)
So total yards = +8 - 12 - 11 = -15 (Lost)
Therefore, the football team lost 15 yards.
Hence "The total yards gained or lost is the algebraic sum so the resultant yards is -15 yards thus they lose 15 yards".
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How do you find the square root of 18? Needs to be in decimal form and we cannot use calculators
Given:
[tex]\sqrt{18}[/tex]To find:
The root of 18 without using a calculator
There is a formula that gives an approximation of a square root without a calculator. This is given as:
[tex]\begin{gathered} \sqrt{N}\text{ = }\frac{N\text{ + M}}{2\sqrt{M}} \\ where\text{ N = is the number we want to find its root} \\ M\text{ = is a perfect square close the number we are to find} \\ That\text{ is a number we can find its root } \end{gathered}[/tex][tex]\begin{gathered} \text{N = 18} \\ M\text{ = 16 is the closest number to 18 we can find its root} \\ \\ substitute\text{ the values into the formula:} \\ \sqrt{18}\text{ = }\frac{18\text{ + 16}}{2\times\sqrt{16}} \\ \\ \sqrt{18}\text{ = }\frac{34}{2(4)} \end{gathered}[/tex][tex]\begin{gathered} \sqrt{18}\text{ = }\frac{34}{8} \\ \\ \sqrt{18}\text{ = 4.25} \end{gathered}[/tex]The side of a square is represented by (s - 4);1. Write an expression that could represent the perimeter of the square.2. If the perimeter of the square is no more than 80 ft, what is the maximum value of s?
We have a square with sides (s-4).
The perimeter of a square is 4 times the length of the side, so we can write:
[tex]P=4\cdot(s-4)=4s-16[/tex]If P is no more than 80 ft, we can find the maximum value for s as:
[tex]\begin{gathered} P<80 \\ 4s-16<80 \\ 4s<80+16 \\ 4s<96 \\ s<\frac{96}{4} \\ s<24 \end{gathered}[/tex]Answer:
1) The perimeter is P = 4s-16
2) The maximum value for s, if the perimeter is no more than 80 ft, is 24 ft.
Evaluate. 12⋅(1/4+1/3)to the power of2+2/3 Enter your answer as a mixed number in simplest form by filling in the boxes.
12×(1/4+1/3)to the power of2+2/3 using PEDMASand INDICIES rule gives 7^8/3
What is Indices? lndicies is expressed as Ax^n. Where A is the coefficient, x is the base and n is the power or index.
12×(1/4+1/3)to the power of2+2/3
Evaluating the expression
= (12×( 1/4+1/3))^2+2/3
using PEDMAS
= (12× 7/12)^8/3
opening the bracket, we therefore have
= 7^8/3
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Function A gives the audience in millions
Using function concepts, it is found that:
a) The meaning of each expression is given as follows:
A(4) = audience after four hours.A(0.5) = 1.5 = the audience after 0.5 hours is of 1.5 million peopleb) The expression is: A(4) = 1.3.
c) The expression is: A(2) = A(2.5).
FunctionIn the context of this problem, the format of the function is:
A(t).
In which the meaning of each variable is given as follows:
t is the time in hours after the beginning of the show.A(t) is the audience, in millions of hours.Which gives the meaning of each expression in item a.
For item b, the expression is given as follows:
A(4) = 1.3.
As 4 hours after the episode premiered, the audience was of 1.3 million people.
For item c, the expression is given as follows:
A(2) = A(2.5).
As the audience after 2 hours = 120 minutes is the same as the audience half an hour = 30 minutes later.
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0.04 divided by 0.628
Answer:
0.1 also 0.0636942675
A composite figure is created using asquare and a semicircle. What is the area ofthe figure?12 in200.52202.52204.52206.52
The area of the composite figure will be the sum of the area of the square and the area of the semicircle. The formula for determining the area of a square is expressed as
Area = length^2
From the diagram,
length = 12
Area of square = 12^2 = 144
The formula for determining the area of a semicircle is expressed as
Area = 1/2 * pi * radius^2
Radius = diameter/2
The diameter of the semicircle is 12. Thus,
radius = 12/2 = 6
pi = 3.14
Area of semicircle = 1/2 * 3.14 * 6^2 = 56.52
Area of composite figure = 144 + 56.52 = 200.52 in^2
The first option is the correct answer
I'll give brainliest!
Answer:
24
Step-by-step explanation:
8y^0 + 2y^2 * x^-1
8(4)^0 + 2(4)^2 * 2^-1
8 + 2 * 16 * 2^-1
8 + 2 * 2^-1 * 16
8 + 2^1 - 1 * 16
8 + 16
24
Hope this helps! :)
If XD = 2X – 6 and XV = 3x – 6 and WY and XV bisect at D, what is XV?
The diagonal WY bisects the diagonal XV at point D, which means that XV is divided into two equal line segments XD and XV.
[tex]XD=XV[/tex]Replace the equation above with the given expressions for both line segments:
XD= 2x-6
XV= 3x-6
[tex]2x-6=3x-6[/tex][tex]undefined[/tex]please di it quickly I just need to confirm answer
The Solution:
Given:
[tex]\begin{gathered} V=(-5,3) \\ \\ W=(\frac{3}{2},-\frac{1}{2}) \end{gathered}[/tex]Required:
To find the value of V - W
[tex]V-W=\lbrace(-5-\frac{3}{2}),(3--\frac{1}{2})\rbrace=(-6\frac{1}{2},3\frac{1}{2})=(-\frac{13}{2},\frac{7}{2})[/tex]
Therefore, the correct answer is [option 3]
the bearing of L from Q is 90° what is the bearing of Q for L
Given:
the bearing of L from Q is 90°
Required:
what is the bearing of Q for L
Explanation:
There is a 180 degree difference in bearing between two location(L from Q, Q from L)
If L from Q is 90 degree then
Q from L is
180-90=90degree
Required answer:
90 degree
What is x2 + 6x complete the square
You have the following expression:
x² + 6x
In order to complete the square, take into account that 6 is two times the product of the first coeffcient by the second one in the binomial (a+ b)², then, you have:
6 = 2ab
a=1 because is the coeffcient of the term with x², then for b you obtain:
b = 6/2(1) = 3
the third term of the trynomial is the squared of b.
rThe number of dogs per household in a neighborhood is given in the probabilitydistribution. Find the mean and the standard deviation. Round to 1 decimal.# of Dogs012.34P(x)0.640.250.060.03.02a) What is the mean rounded to 2 decimal place?b) What is the standard deviation rounded to 2 decimal place?
N = Number of data
x1...xn = Samples
[tex]s=\sqrt[]{\frac{\sum ^n_{n\mathop=1}(y-\mu)^2}{n-1}}[/tex]Let's calculate first:
[tex]\sum ^n_{n\mathop=1}yn=0.64+0.25+0.06+0.03+0.02=1[/tex]Now:
[tex]\sum ^n_{n\mathop=1}yn^2=(0.64)^2+(0.25)^2+(0.06)^2+(0.03)^2+(0.02)^2=0.477[/tex]So:
[tex]s=\sqrt[]{\frac{0.477-\frac{(1)^2}{5}}{5-1}}=0.2631539473\approx0.3[/tex]Which equation is true when A.n = 1.2 B.
1.2n=10 n+1=1.2 C. 5+n=6.2 D. 10n=1.2
The true equation is 5 + n = 6.2.
Here we have to find the equation for which n = 1.2.
So the first equation is
10n = 1.2
So for this, we get the value of n as:
n = 1.2/10
= 0.12
which is not equal to 1.2.
So it is not correct
The second equation is:
n + 1 = 1.2
n = 0.2
which is not equal to 1.2
So it is also not correct.
The third equation is:
5 + n = 6.2
n = 6.2 - 5
= 1.2
So it is correct.
The fourth equation is:
1.2n = 10
n = 10/1.2
= 8.33
Here n is not equal to 1.2
So it is also correct.
Therefore the correct equation is 5 + n = 6.2.
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Out of 450 applicants for a job, 249 are female and 59 are female and have a graduate degree. Step 1 of 2 : What is the probability that a randomly chosen applicant has a graduate degree, given that they are female? Express your answer as a fraction or a decimal rounded to four decimal places.
The probability that a randomly chosen applicant has a graduate degree, given that they are female is 0.236.
What is the probability?Probability refers to a possibility that deals with the occurrence of random events. The probability of all the events occurring need to be 1.
P(E) = Number of favorable outcomes / total number of outcomes
Given that 249 are female and 59 are female and have a graduate degree out of 450 applicants.
We are given following in the question;
M: Applicant is male.
G: Applicant have a graduate degree
F : Applicant is female.
The Total number of applicants = 450
Number of female applicants = 249
Number of female applicants have a graduate degree = 59
Therefore,
P(G/F) = P([tex]G^F[/tex])/P(F)
= 59/207 or 0.236
Hence, the probability that a randomly chosen applicant has a graduate degree, given that they are female is 0.236.
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Luther made $9,000 in interest by placing $60,000 in a savings account with simple interest for 3 years. What was the interest rate?
Answer:
[tex]5\%\text{ or }0.05[/tex]
Step-by-step explanation:
Simple interest rate means if I have "P" amount that I initially deposited, then every year this amount increases by "x% of P" or the original amount I deposited. So it's increasing by the same amount each year, unlike compound interest.
The formula for calculating the amount of interest is: [tex]I=P*r*t[/tex]
Where, r is the interest rate, t is the time unit, and P is the initial amount.
In most cases the t will be expressed in years, and one thing to note is the r is the interest rate in decimal form, so [tex]30\%=0.30[/tex], we want to convert it to decimal form by dividing by 100
We know the amount of interest, as it's given to us as 9,000, and the principle amount or initial amount, given to us as 60,000, and also the time which is given to us as 3 years.
So we know that:
[tex]I=9,000\\P=60,000\\t=3\\[/tex]
Plugging all these values into the equation we get:
[tex]9,000=60,000*3*r\\\\9,000=180,000*r\\\\\frac{9,000}{180,000}=r\\\\0.05=r[/tex]
as noted above, this interest rate, "r" is expressed in decimal form. Since we have to divide by 100 to convert from percentage to decimal, we have to multiply by 100 to convert from decimal to percentage.
this gives us: [tex]r=5\%[/tex]
Hello me with part B pleaseeee
Answer:
0, 0, 0
Step-by-step explanation:
You want the sum of a number and its opposite for the numbers ...
3, 7.5, and -2 2/3
Additive inverseThe definition of the additive inverse (opposite) of a number is that it is the number that produces 0 when summed with the original number.
Any number summed with its opposite will give zero.
The sums are ...
3 + (-3) = 07.5 + (-7.5) = 0-2 2/3 + (2 2/3) = 0Consider the following equation of the circle. Graph the circle
Explanation
Given the equation;
[tex](x+6)^2+(y+7)^2=4[/tex]Using a graphing calculator, the graph of the circle becomes;
Answer:
Solve the problems.
Prove: BD = CD
The Angle-Side-Angle (ASA) criterion states that any two angles and the side included between them of one triangle are identical to the corresponding angles and the included side of the other triangle if two triangles are congruent. One of the requirements for two triangles to be congruent is angle side angle.
When two parallel lines are intersected by another line, comparable angles are the angles that are created in matching corners or corresponding corners with the transversal.
If the three sides and the three angles of both angles are equal in any orientation, two triangles are said to be congruent.
Given,
M∠1 = M∠2
(On joining BD and CD)
M∠ADB = M∠ADC
In ΔABD and ΔADC
M∠ADB = M∠ADC (Given)
M∠BAD = M∠DAC (Given)
AD = AD (Common Sides)
⇒ ΔABD ≅ ΔADC (Angle Side Angle Property)
So, BD = CD (Corresponding sides are equal to a Congruent Triangle)
Hence, proved that BD = CD.
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There is a 5% chance that the mean reading speed of a random sample of 21
second grade students will exceed what value?
There is a 5% chance that second graders will be faster than 94.597 wpm.
Sample size = 21
standard deviation = 10 wpm
SE = 10/sqrt(21) = 2.18 as a consequence.
Let X be the average reading speed of 21 second-grade students. z = (X - 91)/2.18 Normal(91,2.18) (91,2.18).
If the 95th percentile of a standard normal variable z is 1.65 [5% probability], the outcome is 91 + 1.65 x 2.18 = 94.597.
So there's a 5% chance that the average reading speed of a random sample of 21 second-graders will be faster than 94.597 wpm.
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Simplify the trigonometric expression. cos(theta+pi/2)
We have to simplify the expression:
[tex]\cos (\theta+\frac{\pi}{2})[/tex]We could see it graphically:
We see that for any angle theta, the cosine of theta + pi/2 is equal to negative sin of theta.
Then we can write:
[tex]\cos (\theta+\frac{\pi}{2})=-\sin (\theta)[/tex]The answer is -sin(theta).
The equation for a line that has a y-intercept of -8 and passes through (-4,2) is y=-5/2x-8 True False
1) Let's verify whether that's true or not, plugging in that point into the equa
(-4,2)
[tex]\begin{gathered} 2=\frac{-5}{2}(-4)\text{ -8} \\ 2=10-8 \\ 2=2 \end{gathered}[/tex]Since this is an identity, in other words, the left side is equal to the right side then we can say that's true.
So that's true y=-5/2x-8 is the equation of the line that has in one of its points the y-coordinate y=-8
16. The height, h, in feet of an object above the ground is given by h = -16t² +64t+190, t≥0, where t is the time in seconds. a) b) c) d) When will the object be 218 feet above the ground? When will it strike the ground? Will the object reach a height of 300 feet above the ground? Find the maximum height of the object and the time it will take.
the maximum height is 254 feet.
Answer:
a) 0.5 seconds and 3.5 seconds.
b) 5.98 seconds (2 d.p.)
c) No.
d) 254 feet at 2 seconds.
Step-by-step explanation:
Given equation:
[tex]h=-16t^2+64t+190, \quad t \geq 0[/tex]
where:
h is the height (in feet).t is the time (in seconds).Part aTo calculate when the object will be 218 feet above the ground, substitute h = 218 into the equation and solve for t:
[tex]\begin{aligned}\implies -16t^2+64t+190 & = 218\\-16t^2+64t+190-218& = 0\\-16t^2+64t-28 & = 0\\-4(4t^2-16t+7) & = 0\\4t^2-16t+7 & = 0\\4t^2-14t-2t+7 &=0\\2t(2t-7)-1(2t-7)&=0\\(2t-1)(2t-7)&=0\\\implies 2t-1&=0\implies t=\dfrac{1}{2}\\\implies 2t-7&=0 \implies t=\dfrac{7}{2}\end{aligned}[/tex]
Therefore, the object will be 218 feet about the ground at 0.5 seconds and 3.5 seconds.
Part bThe object strikes the ground when h is zero. Therefore, substitute h = 0 into the equation and solve for t:
[tex]\begin{aligned}\implies -16t^2+64t+190 & = 0\\-2(8t^2-32t-95) & = 0\\8t^2-32t-95 & = 0\end{aligned}[/tex]
Use the quadratic formula to solve for t:
[tex]\implies t=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}[/tex]
[tex]\implies t=\dfrac{-(-32) \pm \sqrt{(-32)^2-4(8)(-95)} }{2(8)}[/tex]
[tex]\implies t=\dfrac{32 \pm \sqrt{1024+3040} }{16}[/tex]
[tex]\implies t=\dfrac{32 \pm \sqrt{4064} }{16}[/tex]
[tex]\implies t=\dfrac{32 \pm \sqrt{16 \cdot 254} }{16}[/tex]
[tex]\implies t=\dfrac{32 \pm \sqrt{16} \sqrt{254} }{16}[/tex]
[tex]\implies t=\dfrac{32 \pm 4 \sqrt{254} }{16}[/tex]
[tex]\implies t=\dfrac{8\pm \sqrt{254} }{4}[/tex]
As t ≥ 0,
[tex]\implies t=\dfrac{8+ \sqrt{254} }{4}\quad \sf only.[/tex]
[tex]\implies t=5.98 \sf \; s \; (2 d.p.)[/tex]
Therefore, the object strikes the ground at 5.98 seconds (2 d.p.).
Part c
To find if the object will reach a height of 300 feet above the ground, substitute h = 300 into the equation and solve for t:
[tex]\begin{aligned}\implies -16t^2+64t+190 & = 300\\-16t^2+64t+190-300 & =0\\-16t^2+64t-110 & =0\\-2(8t^2-32t+55) & =0\\8t^2-32t+55& =0\end{aligned}[/tex]
Use the quadratic formula to solve for t:
[tex]\implies t=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}[/tex]
[tex]\implies t=\dfrac{-(-32) \pm \sqrt{(-32)^2-4(8)(55)} }{2(8)}[/tex]
[tex]\implies t=\dfrac{32 \pm \sqrt{1024-1760} }{16}[/tex]
[tex]\implies t=\dfrac{32 \pm \sqrt{-736} }{16}[/tex]
[tex]\implies t=\dfrac{32 \pm \sqrt{16 \cdot -1 \cdot 46} }{16}[/tex]
[tex]\implies t=\dfrac{32 \pm \sqrt{16} \sqrt{-1} \sqrt{ 46}}{16}[/tex]
[tex]\implies t=\dfrac{32 \pm 4i\sqrt{ 46} }{16}[/tex]
[tex]\implies t=\dfrac{8\pm \sqrt{ 46} \;i}{4}[/tex]
Therefore, as t is a complex number, the object will not reach a height of 300 feet.
Part dThe maximum height the object can reach is the y-coordinate of the vertex.
Find the x-coordinate of the vertex and substitute this into the equation to find the maximum height.
[tex]\textsf{$x$-coordinate of the vertex}: \quad x=-\dfrac{b}{2a}[/tex]
[tex]\implies \textsf{$x$-coordinate of the vertex}=-\dfrac{64}{2(-16)}=-\dfrac{64}{-32}=2[/tex]
Substitute t = 2 into the equation:
[tex]\begin{aligned}t=2 \implies h(2)&=-16(2)^2+64(2)+190\\&=-16(4)+128+190\\&=-64+128+190\\&=64+190\\&=254\end{aligned}[/tex]
Therefore, the maximum height of the object is 254 feet.
It takes 2 seconds for the object to reach its maximum height.
Select True or False for each statement.
A right triangle always has obtuse exterior angles at two vertices.
Answer:
true
Step-by-step explanation:
it is true ........
Explanation:
A right triangle has exactly one angle that is 90 degrees. This is called a right angle.
The other two angles are acute, which means they are less than 90 degrees. An example would be 30 degrees and 60 degrees.
If 30 degrees is an interior acute angle, then 180-30 = 150 degrees is the exterior obtuse angle. Similarly, the adjacent angle to the 60 is 180-60 = 120 degrees.
This example shows we have two obtuse exterior angles. This applies to any right triangle, and not just this particular one.
helppppppppppppp meeeeeeeeeeeeeeeeeeeeeeeeeee
Answer:
55.17
Step-by-step explanation:
[tex]P(0)=0.023(0)^3-0.289(0)^2+3.068(0)+55.170=55.17[/tex]
The radius, R, of a sphere is 4.8 cm. Calculate the sphere's volume, V. Use the value 3.14 for it, and round your answer to the nearest tenth. (Do not round any intermediate computations.) --0- V = 3 em Х 5 ?
The formula to calculate the volume of a sphere is given to be:
[tex]V=\frac{4}{3}\pi r^3[/tex]where r is the radius.
From the question, we have the following parameters:
[tex]\begin{gathered} \pi=3.14 \\ r=4.8 \end{gathered}[/tex]Therefore, the volume is calculated to be:
[tex]\begin{gathered} V=\frac{4}{3}\times3.14\times4.8^3 \\ V=463.0 \end{gathered}[/tex]The volume is 463.0 cm³.
please help! I do not understand and it is due tonight!!!!!!!
Consider that there are, generally, the following types of angles pairs,
1. Adjacent Angles: Angles that share a common side and are formed on the same vertex.
2. Complementary Angles: Angles that are adjacent and together form a right angle.
3. Supplementary Angles: Angles that are adjacent and whose sum of degree measures is 180 degrees.
a.
The adjacent angles to angle 4 are angles 1 and 3.
There are no complementary angles associated with angle 4.
The supplementary angles to angle 4, are angles 1 and 3.
Thus, the angle pairs that include angle 4 are,
[tex](\angle4\text{ and }\angle1),\text{ }(\angle4\text{ and }\angle3)[/tex]b.
The adjacent angles to angle 5 are angles 6 and 7.
There are no complementary angles associated with angle 5.
The supplementary angles to angle 5, are angles 6 and 7.
Thus, the angle pairs involving angle 5 are,
[tex](\angle5\text{ and }\angle6),\text{ }(\angle5\text{ and }\angle7)[/tex]