Answer:
y = 30
z = 115
Step-by-step explanation:
z° + 65° = 180°
(Exterior Angles on the same side of transversal)
z° = 180° - 65°
z° = 115°
z = 115
(5y - 85)° + z° = 180°
(Linear pair angles)
(5y - 85)° + 115° = 180°
(5y - 85)° = 180° - 115°
(5y - 85)° = 65°
5y - 85 = 65
5y = 65 + 85
5y = 150
y = 150/5
y = 30
an acute isosceles triangle, , is inscribed in a circle. through and , tangents to the circle are drawn, meeting at point . if and in radians, then find .
\(\angle AQO + \angle OQB = 120^\circ$, so $\boxed{\theta = 60^\circ}$\) is the solution.
Let's first draw a diagram to visualize the problem:
Since \($\triangle ABC$\) is isosceles, we have \($\angle BAC = \angle BCA = \theta$\) and \($\angle ABC = 180^\circ - 2\theta$\). Let O be the center of the circle, and let D and E be the points of tangency of the tangents through A and C, respectively.
Since \($AD$\) and \($CE$\) are tangents to the circle, we have \($OD \perp AD$\) and \($OE \perp CE$\). Since \($AO$\) and \($CO$\) are radii of the circle, we have \($AO \perp BC$\) and \($CO \perp AB$\).
Therefore, \($OD \parallel CO$\) and \($OE \parallel AO$\). It follows that \($\angle DOB = \angle COB = \theta$\), and \($\angle EOA = \angle AOB = \theta$\).
Thus, \($\angle DOA = \angle EOC = \theta$\), and \($\angle AOE = \angle DOC = \theta$\).
Now, consider the quadrilateral \($AODE$\). Since \($\angle AOE = \angle DOA = \theta$\), we have \($\angle OAE = \angle ODE = 90^\circ - \theta$\). Similarly, \($\angle OCE = \angle OED = 90^\circ - \theta$\). Since \($\triangle ABC$\) is isosceles, we have \($AB = BC$\), so \($AD = EC$\).
It follows that \($\triangle AOD \cong \triangle CEO$\) by SAS congruence.
Therefore, \($AO = CO$\), so \($\triangle AOB$\) and \($\triangle COB$\) are congruent by SAS congruence.
Thus, \($AB = BC$\), so \($\triangle ABC$\) is equilateral.
Therefore, \($\theta = 60^\circ$\).
Finally, since \($\angle AOB = \theta = 60^\circ$\), we have \($\frac{1}{2}\angle APB = \theta = 60^\circ$\), so \($\angle APB = 120^\circ$\).
Therefore, \($\angle APQ = \angle BPQ = \frac{1}{2}(180^\circ - \angle APB) = 30^\circ$\). Since \($\triangle APQ$\) is isosceles, we have \($\angle QAP = \angle QPA = \frac{1}{2}(180^\circ - \angle APQ) = 75^\circ$\).
Therefore, \($\angle AQP = \angle BQP = 105^\circ$\), so \($\angle AQB = 2\angle BQP = 210^\circ$\).
Thus, \($\angle AQO = \frac{1}{2}(360^\circ - \angle AQB) = 75^\circ$\), and \($\angle OQB = \frac{1}{2}(180^\circ - \angle AQB) = 45^\circ$\).
Therefore, \(\angle AQO + \angle OQB = 120^\circ$, so $\boxed{\theta = 60^\circ}$\) is the solution.
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complete the following sentence: an endomorphism is injective if and only if is not an eigenvalue
The statement "an endomorphism is injective if and only if it is not an eigenvalue" is not true in general.
An endomorphism is a linear map from a vector space to itself. An endomorphism is said to be injective if it preserves distinctness of elements, i.e., if it maps different vectors to different vectors. On the other hand, an eigenvalue of an endomorphism is a scalar that satisfies a certain equation involving the endomorphism and a non-zero vector called an eigenvector.
Now, the statement "an endomorphism is injective if and only if it is not an eigenvalue" is not true in general. In fact, the two concepts are not directly related. It is possible for an endomorphism to be injective and have eigenvalues, and it is possible for an endomorphism to not have eigenvalues and not be injective.
However, if we consider a specific case where the endomorphism is a linear transformation on a finite-dimensional vector space, then we can make the following statement: "an endomorphism is injective if and only if it does not have 0 as an eigenvalue." This statement is true because an endomorphism is injective if and only if its kernel (the set of vectors it maps to 0) is trivial (only the zero vector). This happens if and only if 0 is not an eigenvalue, since an eigenvalue of 0 means that there exists a non-zero vector that is mapped to 0.
In summary, the statement "an endomorphism is injective if and only if it is not an eigenvalue" is not true in general, but it is true in the specific case of a linear transformation on a finite-dimensional vector space: "an endomorphism is injective if and only if it does not have 0 as an eigenvalue."
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help with this question
Answer:
b
Step-by-step explanation:
i really need this answer
I need help ASAP this is really hard
Answer:
x = -13
Step-by-step explanation:
Isolate the variable (x)
9 - 2x = 35
Subtract 9 from both sides
This action cancels out the 9 on the side of the variable
- 2x = 35 - 9
- 2x = 26
Divide by -2 on both sides
x = 26 ÷ -2
x = -13
Please help! Will mark brainliest
Answer:
Two angles whose sum in 90 degrees
Step-by-step explanation:
Charlene wants to earn at least $600 this month in commission. What is the minimum amount she needs to sell to earn $600 if she earns a 4.5% commission on everything she sells? Round to the nearest dollar.
Answer:
She will need to earn a little more than $1333 that week.
Step-by-step explanation:
600/0.45 = 1333.333(repeating) rounded to nearest dollar is 1333
Check by doing 1333 x 0.45 (comes out to be 599.85)
The minimum amount she needs to sell to earn $600 if she earns a 4.5% commission on everything she sells is 1333 dollars that week.
What is the fundamental principle of multiplication?Multiplication is the mathematical operation that is used to determine the product of two or more numbers. If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.
Given that Charlene wants to earn at least $600 this month in the commission.
600/0.45 = 1333.333 rounded to nearest dollar
= 1333
Therefore, the minimum amount she needs to sell to earn $600 if she earns a 4.5% commission on everything she sells is 1333 dollars.
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The grid above shows the graph of the parent function f(x)= land a translated functions graph.
Write the equation for the translated graph.
The blue graph is a translation of 2 units to the left and 1 unit up of the parent function, thus, the equation is:
g(x) = |x + 2| + 1
How to find the translated function?We know that the red graph is an absolute value function, so we have:
f(x) = |x|
And we want to find the equation of the blue absolute value function, which is a translation of the above one.
Notice that the vertex of the blue one is at (-2, 1), so we have a translation of 2 units to the left and one unit up, it is just written as:
y = |x + 2| + 1
We conclude that the translated function is:
g(x) = |x + 2| + 1
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What does the denominator of the fraction \dfrac23 3 2 start fraction, 2, divided by, 3, end fraction mean?
Answer: It represents that 2 will be divided into 3 equal parts.
Step-by-step explanation:
Numerator is the top number in a fraction. It represents the total item it has to divide.Denominator is the bottom number in a fraction. it represents the number of equal parts the item is divided into.The given fraction : \(\dfrac{2}{3}\)
here, Numerator = 2
Denominator = 3
It represents that 2 will be divided into 3 equal parts.
The following pedigree shows the inheritance of a mild, but very rare condition in Siberian Husky dogs. If individuals 1 and 2 are crossed, what is the probability that they will produce an affected pup?
The probability of producing an affected pup from the cross between individuals 1 and 2 is 25%.
The pedigree shows that the mild, but rare condition in Siberian Husky dogs is inherited in an autosomal recessive manner, meaning that an individual must inherit two copies of the mutated gene (one from each parent) to express the condition.
In this pedigree, individual 1 is unaffected, but a carrier of the mutated gene, as indicated by the half-filled circle. Individual 2 is also a carrier, but it is unclear whether or not they are affected, as indicated by the half-filled square.
If individuals 1 and 2 are crossed, we can use a Punnett square to determine the probability of producing an affected pup.
The Punnett square would have two columns and two rows, representing the two alleles each parent can contribute to their offspring. The probabilities for each possible outcome are:
25% chance of producing an affected pup (homozygous recessive)50% chance of producing a carrier pup (heterozygous)25% chance of producing an unaffected pup (homozygous dominant)Therefore, the probability of producing an affected pup from the cross between individuals 1 and 2 is 25%.
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The graph of g(x) resembles the graph of f(x)=x^2, but it has been changed. Which of these is the equation of g(x)?
Answer:
A.
Step-by-step explanation:
Anwer A has the following equation:
\(g(x)=\frac{3}{5}x^2-3\)
In this equation, we can calculated the intercept replacing x by 0, as:
\(g(x)=\frac{3}{5}0^2-3=-3\)
if this is the answer, the graph of g(x) should be through the point (0,-3) and that happens.
Additionally, the roots of the equations are calculated replacing g(x) by 0 and solving for x, so:
\(0=\frac{3}{5}x^2-3\\x_1=\sqrt{5}=2.236\\x_2=-\sqrt{5}=-2.236\)
It means that the graph of g(x) should be through the points (2.236,0) and (-2.236,0) and that happens too.
So, the answer is A, \(g(x)=\frac{3}{5}x^2-3\)
2) If x+y=6 and xy=5 find x-y?
Answer:
x - y = ± 4Step-by-step explanation:
Given
x + y = 6 and xy = 5To find
x - ySolution
(x - y)² = (x + y)² - 4xy = 6² - 4*5 = 36 - 20 = 16 = 4²(x - y)² = 4²x - y = ± 41. When drawn in standard position, which of the following angles is coterminal with 125?
(1) -275
(3) 235
(2) 485
(4) 415
The angle which is coterminal with the angle 125 degree when drawn in standard position is -235 degrees. Option A is correct.
What is the coterminal or terminal side of an angle?The terminal side of an angle is the rotated side of the initial side around a point to form an angle. This rotation can be clockwise or counter clock wise.
The angle given in the problem is,
θ=125°
The angle which is coterminal of this angle is,
θ=125°-360°
θ=-235°
Thus, the angle which is coterminal with the angle 125 degree when drawn in standard position is -235 degrees. Option A is correct.
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please help, will be grateful and give brainliest!
Answer:
x=216°
Step-by-step explanation:
100%=360°
To find 10% divide by 10
10%=36°
x4
40%=144°
in a full circle thered 360°
360-144=216°
x=216°
Find value of x.
A. 110
B. 47
C. 68
D. 112
Answer:
B
Step-by-step explanation:
The sum of the inner angles of a quadrilateral is 360 degrees
135 + 110 + 68 + x = 360
313 + x = 360
x = 47 degrees
Answer:
47
Step-by-step explanation:
whole thing is 360 degrees
68 + 110 + 135 = 313
360 - 313 = 47
x looks small too (if you had to guess in a multiple choice question)
What is the approximate circumference of the circle that has a center at (2, 1) and passes through the point (7, 1)? A 10 units B. 16 units С 31 units D 79 units
Answer:
C. 31 units
Step-by-step explanation:
Circumference of a circle is the distance around the circle and is given by C = pi•d
Your circle with a point and center given has a radius of 5 because from (2,1) to (7,1) is 5 units. Radius 5 means the diameter is 10.
C = pi•10
= 3.14•10
= 31.4 using 3.14 as an approximation for pi.
Circumference is approximately 31 units.
JK Corp Reported The Following Inventory Transactions (In Chronological Order) For The Year: Purchase Sales 50 Units At $30 13 Units At $35 30 Units At $40 35 Units At $45 100 Units At $50 60 Units At $60 Assuming Inventory At The Beginning Of The Year Was Zero, Calculate The Year-End Inventory Using FIFO And LIFO FIFO: $2,960; LIFO: $2,380 FIFO: $3,600 And
The year-end inventory using FIFO and LIFO is as follows:
FIFO = $3,600LIFO = $2,380.What is the difference between FIFO and LIFO?FIFO and LIFO are assumptions made to evaluate the cost of goods sold and the ending inventory.
FIFO, which stands for First-in, First-out, assumes that goods are sold chronologicall as they are bought.
LIFO (Last-in, First-out) is a costing method that assumes that goods are sold in reverse order.
Purchase Sales
50 Units At $30 13 Units At $35
30 Units At $40 35 Units At $45
100 Units At $50 60 Units At $60
FIFO:
Ending inventory = 72 units at $50 = $3,600 (72 x $50)
LIFO:
Ending inventory = 72 units
50 Units at $30 = $1,500 ($30 x 50)
22 units at $40 = $880 ($40 x 22)
Ending inventor = $2,380
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what is 76683932992840842842774839498289294929x91983918938019308926753234793357888890878676932 eqaul to
Answer:
76683932992840842842774839498289294929x91983918938019308926753234793357888890878676932 is a very large number and its exact value is not possible to calculate by hand or with common calculators. However, it can be calculated using a computer with advanced mathematical software.
Step-by-step explanation:
We've seen that as the sailboat logo is resized by dilation, the line segments that make up the logo may be mapped onto
parallel lines or stay on the same line. The lengths of the image are the lengths of the preimage multiplied by the scale factor
Now we will use GeoGebra to compare the angles of a dilated figure to the angles of the original figure. Open dilations
again. Then complete each step below. For help, watch this video to learn more about measurement tools in GeoGebra.
Part A
Measure and record the measures of these angles in the original logo. Then set n = 0.5 and n = 2, and record the
measures of the corresponding angles in each resulting image.
BIUX² X₂ 14pt
A
Angle Original Measure Measure After Dilation
n = 0.5
n = 2
ZFGB
ZGBC
ZLKJ
B
The angle measures of the triangles before and after dilation are the same
Calculating the angle measures before and after dilationGiven that, we have a triangle that is dilated to form another triangle by a scale factor of n
The dilation transformation is a rigid transformation
This means that it changes the size of a shape after it is applied
However, the shape and the image would be similar shapes and as such would have their angles unchanged
This means that irrespective of the value of the scale factor n, the angle measures would remain the same
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PPLEASE HELP FOR 10 POINTS!!!!!
Write an equation to represent the verbal description.
In a computer game, Nikolai started with x points. After losing 50 points, Nikolai then tripled his score for a total of y points.
Answer:
\(y=3(x-50)\)
Hope This Helps! :)Please Give Brainliest if this is correct!
(Which I am pretty confident in...)
A wildlife biologist is tracking the return of free-tailed bats (Tadarida brasiliensis) to their cave in the early morning. His measurements indicate that the bats return at a rate of 2.0 per second. What is the probability of 3 bats arriving in the next second?
The probability of 3 bats arriving in the next second is approximately 0.18045, or 18.05%.
To calculate the probability of 3 bats arriving in the next second, we can use the Poisson distribution formula.
In this case, the average rate of bats arriving per second is λ = 2.0, and we want to find the probability of 3 bats arriving (k = 3).
Let's calculate the probability using the formula:
P(X = 3) = \((e^{(-2.0) }* 2.0^{3})\) / 3!
Calculating further:
P(X = 3) = (0.13534 * 8) / 6
P(X = 3) ≈ 0.18045
So, the probability of 3 bats arriving in the next second is approximately 0.18045, or 18.05%.
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Use the leading coefficient and degree of the polynomial function f(x) = x3 – 7x2 + 10x to determine the end behavior of its graph. Select all the correct statements. A. As x → ∞, y → ∞. B. As x → ∞, y → −∞. C. As x → −∞, y → ∞. D. As x → −∞, y → −∞. E. As x → ∞, y → 0.
Given:
The function is
\(f(x)=x^3-7x^2+10x\)
To find:
The end behavior of its graph.
Solution:
We have,
\(f(x)=x^3-7x^2+10x\)
Here, leading coefficient is 1 which is positive and degree of function is 3 which is odd.
For odd degree and positive leading coefficient, the end behavior is
\(f(x)\to \infty\text{ as }x\to \infty\)
\(f(x)\to -\infty\text{ as }x\to -\infty\)
Using this, we get
\(\text{As }x\to \infty, y\to \infty\)
\(\text{As }x\to -\infty, y\to -\infty\)
Therefore, the correct statements are A and D.
We want to study the end behavior of the given polynomial.
The two correct statements are A and D.
As x → ∞, y → ∞As x → −∞, y → −∞The polynomial is:
f(x) = x^3 - 7*x^2 + 10*x.
We can see that the degree of this polynomial is odd, this means that the behavior on the negative side is opposite to the one in the positive side.
In this case, the leading coefficient is one, so it is positive. This will mean that, for large positive values of x, f(x) will be positive.
For large (in absolute value) negative values of x, f(x) will be negative.
Then the end behavior is given by:
As x → ∞, y → ∞As x → −∞, y → −∞So the two correct statements are A and D.
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3x+7+56=90 what is this
Answer:
X=9
Hope this helps! :)
3 t-shirts and 2 hats costs £14.
2 t-shirts and 7 hats costs £15.
Find the cost of a t-shirt.
Find the cost of a hat.
t-shirt: £
o
hat: £
A car rental agency charges a fee of $35 per day plus $.20 for each mile driven. How much will it cost to rent the car for 4 days and drive 730 miles? Your answer should include a $ and two decimal places, in the format $10.00
Answer:
$271.00. Remember to put it in the right format
Step-by-step explanation:
So since its 35 dollars per day, we can first do 35*4 to get 140. So just for having the car, it costs 125 dollars.
Now to find the amount of money for the miles, we can do 730*0.20=146
Now we add those two amounts so we do 125+146=271.
So $271.00
It costs $3.50 for 5 pounds of bananas. If the price per pound stays the
same, how much would 4 pounds of
bananas cost?
Answer:
$14.00
Step-by-step explanation:
Here's why. So, if 5 pounds of bananas is $3.50 per pound. All you need to do is do 3.50 * 4 and you'll get your answer, which is $14.00 .
It's pretty easy. If you have a problem like this just multiple the price with the number that they provide you with. :D
Find a sinusoidal function with the following four attributes: (1) amplitude is 10, (2) period is 5, (3) midline is y = 31, and (4) ƒ(3) = 41. f(x) = =
The sinusoidal function that satisfies the given attributes is f(x) = 10 * sin(2π/5 * x - π/5) + 31.
To find a sinusoidal function with the given attributes, we can use the general form of a sinusoidal function:
f(x) = A * sin(Bx + C) + D
where A represents the amplitude, B represents the frequency (related to the period), C represents the phase shift, and D represents the vertical shift.
Amplitude: The given amplitude is 10. So, A = 10.
Period: The given period is 5. The formula for period is P = 2π/B, where P is the period and B is the coefficient of x in the argument of sin. By rearranging the equation, we have B = 2π/P = 2π/5.
Midline: The given midline is y = 31, which represents the vertical shift. So, D = 31.
f(3) = 41: We are given that the function evaluated at x = 3 is 41. Substituting these values into the general form, we have:
41 = 10 * sin(2π/5 * 3 + C) + 31
10 * sin(2π/5 * 3 + C) = 41 - 31
10 * sin(2π/5 * 3 + C) = 10
sin(2π/5 * 3 + C) = 1
To solve for C, we need to find the angle whose sine value is 1. This angle is π/2. So, 2π/5 * 3 + C = π/2.
2π/5 * 3 = π/2 - C
6π/5 = π/2 - C
C = π/2 - 6π/5
Now we have all the values to construct the sinusoidal function:
f(x) = 10 * sin(2π/5 * x + (π/2 - 6π/5)) + 31
Simplifying further:
f(x) = 10 * sin(2π/5 * x - 2π/10) + 31
f(x) = 10 * sin(2π/5 * x - π/5) + 31
Therefore, the sinusoidal function that satisfies the given attributes is f(x) = 10 * sin(2π/5 * x - π/5) + 31.
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If a student completes 5 problems out of a total of 8 on a pop quiz, what percentage of the quiz was completed?
Answer:
\(\huge\boxed{\sf 62.5 \%}\)
Step-by-step explanation:
Given that,
Completed problems = 5
Total = 8
Percentage:\(\displaystyle = \frac{completed}{total} \times 100 \%\\\\= \frac{5}{8} \times 100\%\\\\= 0.625 \times 100 \%\\\\= 62.5 \%\\\\\rule[225]{225}{2}\)
A sign is 4 1/2 feet wide and 5 1/4 feet long. Find the area of the surface of the sign
Answer:
the answer is 5 5/8
i think it's this
In ΔHIJ, i = 550 inches, j = 150 inches and ∠H=92°. Find the length of h, to the nearest inch.
Answer:575
Step-by-step explanation: deltamath