The measure of the angle between the shorter leg and the hypotenuse, [tex]\theta[/tex] = 70.53 °
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between the sides and angles of triangles.
Given that:
Let us consider the shorter leg be 'x'.
and, the Hypotenuse be '3x '.
Using trigonometric functions,
[tex]cos \theta= \frac{Base}{Hypotenuse}[/tex]
cos [tex]\theta[/tex] = x /3x
cos [tex]\theta[/tex] = 1/3
[tex]\theta[/tex] = [tex]cos^{-1}[/tex] (1/3)
[tex]\theta[/tex] = 70.53 °
Hence, the measure of the angle between the shorter leg and the hypotenuse 70.53 °
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The perimeter of a rectangle is 276 centimeters. It's length is five times its width. What are the dimensions?
Solve 152x = 36. Round to the nearest ten-thousandth.
A. 0.6616
B. 2.6466
C. 1.7509
D. 1.9091
Since no one was getting the the answer that is on the assignment I plugged the problem into an algebra calculator, and got A 0.6616
Which of the following equations describes the graph shown?
A.) y = x+2
B.) y = -x - 2
C.) y = x - 2
D.) y = -x + 2
Answer: The correct option is (D) y = -x + 2.
Step-by-step explanation: We are to select the correct equation that describes the given graph.
We can see that the graph is a straight line passing through the points (0, 2) and (1, 1).
So, the slope of the line will be
[tex]m=\dfrac{2-1}{0-1}=-1.[/tex]
Therefore, the equation of the line with slope m = -1 and passing through the point (0, 2) is given by
[tex]y-2=m(x-0)\\\\\Rightarrow y-2=-1\times x\\\\\Rightarrow y-2=-x\\\\\Rightarrow y=-x+2.[/tex]
Hence, the equation that describes the graph is y = -x + 2.
Thus, (D) is the correct option.
Match the pairs of values of f(x) and g(x) with the corresponding values of h(x) if h(x) = f(x) ÷ g(x).
Screenshot of the tiles below
(Please help)
The We have given that the pairs of values of f(x) and g(x) with the corresponding values of h(x) s given below.
(x^2-9)/(x-3)
x^2-4x+3/x-3
x^2+4x-5/x-1
x^2-16/x-4
We have to match the pairs of values of f(x) and g(x) with the corresponding values of h(x) if h(x) = f(x) ÷ g(x).
What is the function?A function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function. Functions were originally the idealization of how a varying quantity depends on another quantity.
1)f(x)/g(x)=(x^2-9)/(x-3)=x+3
2)f(x)/g(x)=x^2-4x+3/x-3=x+1
3)f(x)/g(x)=x^2+4x-5/x-1=x+5
4)f(x)/g(x)=x^2-16/x-4=x+4
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What is the equation of the line that is parallel to the line y = x + 4 and passes through the point (6, 5)?
Help Please!!!!!!
f(x)=5x^2+9x−4
g(x)=−8x^2−3x−4
Find (f+g)(x)
My Options Are...:
a. 3x^2+6x−8
b. −3x^3+6x^2−8x
c. −3x^4+6x^2−8
d. −3x^2+6x−8
What is -11-8-13(-10)? And how did you get you're answer
Driving on the North West Express-way, Debbie averaged 62 miles per hour for 3 & one fourth hours. How far did she drive?
1/4 = 0.25
s0 3 1/4 = 3.25
62x3.25 = 201.50 miles = 201 1/2 if you need it in fraction form
In 45-45-90 right triangle, what is the ratio of the length of one leg to the length of the other leg
Answer: it’s 1:1
Step-by-step explanation:
I have 3 questions here , one of them I just need my answer checked on and the other two I really need help with. Thank you!!
The figure shows secant GC and tangent GB intersecting to form an angle. Find x and y If necessary, round to the tenths place.
The value of y, calculated using the difference between the intercepted arcs, is 69.5° when rounded to the tenths place.
The figure provided depicts a circle with a secant (line GC) and a tangent (line GB) intersecting at point G, forming an angle. There are several angle measures given in the figure: angle ECA is 30°, angle ADB is 58°, and angle EAB is 161°. The angles x° and y° are what we need to find.
Here's how to find x and y:
1. To find x:
- The angle formed by a tangent and a chord (GB and BA in this case) is equal to the angle in the alternate segment of the circle. Therefore, x is equal to the angle in the alternate segment, which is angle ADB (58°). So, x = 58°.
2. To find y:
- The angle formed by a tangent and a secant (GB and GC in this case) from the external point G is equal to the difference between the measure of the intercepted arc (the large arc EAC) and the measure of the adjacent arc (the small arc EC). This can be calculated by the formula [tex]\( y = \frac{1}{2}(\text{large arc} - \text{small arc}) \).[/tex]
- The large arc EAC is the full circle (360°) minus the small arc EBC (161°), so the measure of arc EAC is 360° - 161° = 199°.
- The small arc EC is twice the angle ECA (which is an inscribed angle) because the measure of an arc is twice the measure of an inscribed angle that subtends it. So, the measure of arc EC is 2 * 30° = 60°.
- Now we can calculate y using the formula: [tex]\( y = \frac{1}{2}(199 - 60) \).[/tex]
Let's calculate the exact values for x and y.
The value of x is equal to the angle ADB, which is 58°.
The value of y, calculated using the difference between the intercepted arcs, is 69.5° when rounded to the tenths place.
Therefore, [tex]\( x = 58 \) and \( y = 69.5 \).[/tex]
Which algebraic expression represents “the difference of 54 and a number”?
For this case, the first thing we should do is define a variable.
We have then:
x: unknown number
Then, we write the algebraic expression that models the following problem:
the difference of 54 and a number.
We have then:
[tex]54-x[/tex]
Answer:
An algebraic expression that represents "the difference of 54 and a number" is:
[tex]54-x[/tex]
Answer:
A
Step-by-step explanation:
A baseball team has won 13 out of 18 games they played this session. How many additional games must the team win in a row to raise its winning percentage to 80%?
A) 7
B) 14
C) 5
D) 24
True or false the center of the circumscribed circle about a triangle is equidistant to the vertices of the inscribed triangle
Answer:
True
Step-by-step explanation:
Consider triangle ABC inscribed in the circle with center at point O. Point O is a point of intersection of perpendicular bisectors of sides AC, AB and BC. According to the attached diagram, points E, F and G are midpoints of sides BC, AC and AB, respectively.
Then
EB=EC;FC=FA;GA=GB.Since segments OE, OF and OG are perpendicular bisectors of sides BC, AC and AB, then
m∠OBE=m∠OCE=90°;m∠OCF=m∠OAF=90°;m∠OBG=m∠OAG=90°.You get three pairs of congruent triangles:
ΔOBE≅ΔOCE;ΔOCF≅ΔOAF;ΔOBG≅ΔOAG.This gives you that
[tex]OB=OC=OA.[/tex]
Each of these segments is a radius of the circumscribed circle about a triangle ABC, then the center of the circumscribed circle about a triangle is equidistant to the vertices of the inscribed triangle.
Which is heavier 9 5/8 pounds or 9 3/4 pounds
Find the area of the larger regular pentagon if the smaller pentagon has an area of 43.01 inches^2. The side length of the small pentagon is 5 and the side length of the large pentagon is 8.
Bryce is testing whether school is more enjoyable when students are making high grades. He asked 100 students if they enjoyed school and whether their GPA was above or below 3.0. He found that 33 of the 40 students with a GPA above 3.0 reported that they enjoyed school, and 5 of the 60 students with a GPA below 3.0 reported that they enjoyed school. What is the probability that a student with a GPA below 3.0 does not enjoy school?
85%
92%
65%
75%
Answer:
The answer is 92%.
Step-by-step explanation:
5 of the 60 students reported that they like school. This means that the other 55 don't like school. You then divide 55/60 and you get 92%. So, therefore, your answer is 52%.
Find the area of a sector that has a central angle of 40 and a radius of 2 cm. Round your answer to the nearest 100th. Use 3.14=
In the triangle below, determine the value of a.
A hyperbola centered at the origin has a vertex at (3, 0) and a focus of the hyperbola is located at (9, 0). What are the equations of the directrices?
x = ±
To find the equations of the directrices for a hyperbola centered at the origin with a vertex at (3, 0) and a focus at (9, 0), we use the formula x = ±a/e. The hyperbola's directrices are x = ± 1.
Explanation:The student asked about the equations of the directrices for a hyperbola that is centered at the origin, with a vertex at (3, 0) and a focus at (9, 0). A hyperbola has two directrices, and each is a line that is perpendicular to the transverse axis and equidistant from the center as the foci are, but on the opposite side. The equation of a directrix can be found using the formula x = ±a/e, where 'a' is the distance from the center to the vertex and 'e' is the eccentricity, which is the ratio of the distance from the center to a focus (c) over 'a'.
In this case, the hyperbola is aligned along the x-axis. Given a vertex at (3, 0), it implies that 'a' is equal to 3. Since the focus is at (9, 0), it suggests 'c' is equal to 9. The eccentricity 'e' can be found by e = c/a, which is 9/3 = 3. Using the directrix formula x = ±a/e, the two directrices of the hyperbola would be x = ±(3/3), which simplifies to x = ± 1.
Applying the distributive property, the expression becomes (3x)(–x) + (3x)(4) + (–5)(–x) + (–5)(4). What is the simplified product in standard form?
The volume of a cube depends on the length of its sides. This can be written in function notation as v(s). What is the best interpretation of v(4)=64
the square has a radius of 3 square root 2 what is the apothem?
The apothem of the square is equal to half the length of a side of the square, which can be calculated by doubling the radius. In this case, the apothem is 3√2.
Explanation:The apothem of a square is a line segment drawn from the center of the square to any side of the square, perpendicular to that side. The apothem is equal to half the length of a side of the square.
Given that the square has a radius of 3√2, we can determine the length of a side of the square by doubling the radius. So, the length of a side is 2 * 3√2 = 6√2.
Therefore, the apothem of the square is half the length of a side, which is (6√2)/2 = 3√2.
The cells of a certain culture of bacteria triple every 2 minutes. If there are 40 cells in the beginning, in how many minutes will there be more than 9500 cells?
A) 4 min
B) 5 min
C) 11 min
D) 10 min
Answer: 10 min
Step-by-step explanation:
Final answer:
The bacterial culture that triples every 2 minutes will surpass 9500 cells just after 10 minutes. Since we cannot have a fraction of a minute in this context, the answer is 11 minutes (Option C).
Explanation:
The student is asking about exponential growth, specifically in a bacterial culture that triples every 2 minutes. To find out how many minutes it will take for the initial 40 cells to grow to more than 9500, we can use the formula for exponential growth:
N = N0 × 3t/2
Where N is the final number of cells, N0 is the initial number of cells (40 in this case), and t is the time in minutes.
We want N to be greater than 9500, so we solve the inequality:
9500 < 40 × 3t/2
Dividing both sides by 40 gives:
237.5 < 3t/2
Next, we find the smallest t for which the inequality holds by applying logarithms and solving:
t > 2 × (log3(237.5))
Calculating the right side, we get:
t > 10.096
So, the culture will have more than 9500 cells just after 10 minutes. The smallest whole number of minutes greater than 10.096 is 11, hence the answer is: C) 11 min
Julio checked the temperature of a bag of frozen peas and found it was at −13°C. After he left the bag out of the freezer for an hour, its temperature rose to 8°C. What was the change in temperature in an hour?
a)−21°C
b)21°C
c)5°C
d)−5°C
At the middle school graduation dance, the DJ played 12 slow dances, which was equal to the quotient of the number of fast dances and two.
quotient means divide
so 12 = x/2
x = 12*2 = 24
x =24 fast songs
(05.05)What is the rate of change of the linear relationship modeled in the table?
x y
1 2
3 5
5 8
7 11
negative three over two
two over three
one
1 three over two
Answer: three over two
Step-by-step explanation:
We know that the rate of change of a function [tex]y=f(x)[/tex] is given by :-
[tex]k=\dfrac{\text{change in y}}{\text{change in x}}[/tex]
From the consecutive values in the table, the change in x = [tex]3-1=2[/tex]
Change in y = [tex]5-2=3[/tex]
Now, the rate of change of the linear relationship modeled in the table will be ;-
[tex]k=\dfrac{3}{\text{2}}[/tex]
PLEASE HELP!!! Evaluate Show your work.
Answer:
[tex]\sqrt{7x}(\sqrt{x}-7\sqrt{7})\Rightarrow x\sqrt{7}-49\sqrt{x}[/tex]
Step-by-step explanation:
Given: [tex]\sqrt{7x}(\sqrt{x}-7\sqrt{7})[/tex]
Simplify the expression.
[tex]\Rightarrow \sqrt{7x}(\sqrt{x}-7\sqrt{7})[/tex]
Distribute [tex]\sqrt{7x}[/tex] over parentheses
[tex]\Rightarrow \sqrt{7x}\cdot\sqrt{x}-\sqrt{7x}\cdot7\sqrt{7}[/tex]
[tex]\Rightarrow \sqrt{7x^2}-7\sqrt{7^2x}[/tex]
square term take out from square root
[tex]\Rightarrow x\sqrt{7}-7\cdot 7\sqrt{x}[/tex]
[tex]\Rightarrow x\sqrt{7}-49\sqrt{x}[/tex]
[tex]\sqrt{7x}(\sqrt{x}-7\sqrt{7})\Rightarrow x\sqrt{7}-49\sqrt{x}[/tex]
The cells of a certain culture of bacteria double every 6 minutes. If the culture contains 100 cells in the beginning, then the total number of cells P in this culture after t minutes is given by the exponential equation P = 100(2)t/6. Identify the number of minutes it will take for the number of cells to exceed 50,000.
A) 53 min
B) 49 min
C) 48 min
D) 54 min
Since the growth is exponential, therefore I believe the correct form of the equation is:
P = 100 (2)^(t / 6)
Where t / 6 is the exponent of 2
So to find for the amount of time needed to exceed the population of 50,000, all we have to do is to plug in that value in the equation and find for t. Therefore:
P = 100 (2)^(t / 6)
50000 = 100 (2)^(t / 6)
500 = 2^(t / 6)
log 500 = (t / 6) log 2
t / 6 = log 500 / log 2
t = 6 * 8.96578
t = 53.8 mins = 54 mins
Answer:
D. 54 min
if a radius of a circle is perpendicular to a chord, then it _____ that chord.
a. is equal in length to
b. bisects
c. is congruent to
d. parallels
If a radius of a circle is perpendicular to a chord, then it _bisects____ that chord.
What is radius of circle?
In classical geometry, a radius of a circle or sphere is any of the line segments from its center to its perimeter, and in more modern usage, it is also their length. The name comes from the latin radius, meaning ray but also the spoke of a chariot wheel.
What is chord?
A chord of a circle is a straight line segment whose endpoints both lie on a circular arc. The infinite line extension of a chord is a secant line, or just secant. More generally, a chord is a line segment joining two points on any curve, for instance, an ellipse.
According to question, we have to fill in the blank.
The property of the circle is that if a radius of a circle is perpendicular to a chord, then it bisects that chord.
Hence we can conclude that Option(B) is correct.
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Final answer:
A radius of a circle that is perpendicular to a chord bisects the chord, dividing it into two equal segments.(Option b)
Explanation:
If a radius of a circle is perpendicular to a chord, then it bisects that chord. This statement is supported by a theorem in geometry which states that, in a circle, the radius bisecting an angle at the centre is perpendicular to the chord which subtends the angle and also bisects this chord. Therefore, by drawing a radius from the center of a circle to the midpoint of a chord, you create two equal segments, effectively bisecting the chord.
Thus, a perpendicular radius drawn from the center of a circle to a chord's midpoint ensures that the chord is bisected into two equal segments. This geometric principle facilitates chord division and enhances the understanding of circle properties.