The inverse of function f(x) when f(x) = -2 is f¯¹(x) = 2x + 3.So, the correct option is D.
To find the inverse of a function, we switch the x and y variables and solve for y. So, if f(x) = -2, we have:
x = -2
y = f(x) = -2
Switching x and y, we get:
x = f¯¹(y)
y = -2
Solving for f¯¹(y), we get:
f¯¹(y) = 2y + 3
Therefore, the inverse of f(x) when f(x) = -2 is f¯¹(x) = 2x + 3.
To find the inverse of a function, we need to swap the input (x) and output (f(x)), and then solve for the new input. Given f(x) = -2, let's find the inverse:
1. Swap the input and output: x = -2
2. Solve for the new input: Since the function f(x) is a constant function and doesn't involve x, the inverse of f(x) when f(x) = -2 is f¯¹(x) = 2x + 3.
Therefore, Option D is the correct inverse of f(x).
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What is the volume of the prism? 3ft. 1 1/2 ft. 6ft. Use the formula V=Bh to calculate the volume of the prism.
Answer:
18 ft.
Step-by-step explanation:
Name the acute angle in the shape
Answer:
∠ADB
Step-by-step explanation:
Acute angles measure less than 90°.
So, here ∠ADB is acute angle,
Consider the quadratic function f(x) = x2 – 5x + 12. Which statements are true about the function and its graph? Select three options. The value of f(–10) = 82 The graph of the function is a parabola. The graph of the function opens down. The graph contains the point (20, –8). The graph contains the point (0, 0).
The three true statements about the function and its graph are The graph of the function is a parabola, The graph does not open down (it opens upwards). and None of the given points, (20, -8) or (0, 0), lie on the graph.
Based on the quadratic function f(x) = x^2 – 5x + 12:
The value of f(-10) = 82 is not true.
To find the value of f(-10), substitute x = -10 into the function: f(-10) = (-10)^2 - 5(-10) + 12 = 100 + 50 + 12 = 162.
The graph of the function is a parabola.
This statement is true. The quadratic function has a degree of 2, which means its graph will be a parabola.
The graph of the function opens down.
This statement is not true. The coefficient of the x^2 term in the quadratic function is positive (1), so the parabola opens upwards.
The graph contains the point (20, -8).
This statement is not true. To verify if the point (20, -8) is on the graph, substitute x = 20 into the function: f(20) = (20)^2 - 5(20) + 12 = 400 - 100 + 12 = 312. Therefore, the point (20, -8) does not lie on the graph.
The graph contains the point (0, 0).
This statement is not true. To verify if the point (0, 0) is on the graph, substitute x = 0 into the function: f(0) = (0)^2 - 5(0) + 12 = 0 - 0 + 12 = 12. Therefore, the point (0, 0) does not lie on the graph.
Therefore, the three true statements about the function and its graph are:
The graph of the function is a parabola.
The graph does not open down (it opens upwards).
None of the given points, (20, -8) or (0, 0), lie on the graph.
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Help please I have to answer these questions using the graph.
The answers to all parts is shown below.
a. According to the graph, the concentration after 8 hours is approximately 22 mg/L.
b. The concentration increases from 0 to approximately 30 mg/L over the first 4 hours, and then decreases from approximately 30 mg/L to 16 mg/L between 4 and 20 hours.
c. The drug is at its maximum concentration after approximately 4 hours, with a maximum concentration of approximately 30 mg/L.
d. According to the graph, it takes approximately 12 hours for the concentration to decrease from the maximum concentration of approximately 30 mg/L to 16 mg/L.
e. After 1 week, the graph predicts that the concentration will be very close to 0 mg/L. After 1 month, the concentration is predicted to be essentially 0 mg/L.
f. During the first 4 hours, the concentration increases from 0 to approximately 30 mg/L.
Between 4 and 8 hours, the concentration decreases slightly from approximately 30 mg/L to 28 mg/L.
Between 8 and 12 hours, the concentration decreases more rapidly from 28 mg/L to approximately 22 mg/L.
Between 12 and 20 hours, the concentration decreases gradually from 22 mg/L to 16 mg/L.
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Help please answer the number 3 only thanyou
i will give brainliest
Answer:If cos(\theta) = \sqrt(3)/2, then we can use the Pythagorean identity sin^2(\theta) + cos^2(\theta) = 1 to find sin(\theta):
sin^2(\theta) + (\sqrt(3)/2)^2 = 1
sin^2(\theta) + 3/4 = 1
sin^2(\theta) = 1 - 3/4
sin^2(\theta) = 1/4
sin(\theta) = +/- 1/2
Since \theta is an acute angle, sin(\theta) must be positive. Therefore, sin(\theta) = 1/2.
We can then use the identity tan(\theta) = sin(\theta)/cos(\theta) to find tan(\theta):
tan(\theta) = sin(\theta)/cos(\theta)
tan(\theta) = (1/2)/(\sqrt(3)/2)
tan(\theta) = 1/\sqrt(3)
Finally, we can use the reciprocal and quotient identities to find the values of sec(\theta) and csc(\theta):
sec(\theta) = 1/cos(\theta)
sec(\theta) = 2/\sqrt(3)
csc(\theta) = 1/sin(\theta)
csc(\theta) = 2
Step-by-step explanation:
Answer:
[tex]\sin\theta=\dfrac{1}{2}[/tex]
[tex]\tan\theta=\dfrac{\sqrt{3}}{3}[/tex]
[tex]\csc\theta=2[/tex]
[tex]\sec\theta=\dfrac{2\sqrt{3}}{3}[/tex]
[tex]\cot\theta=\sqrt{3}[/tex]
Step-by-step explanation:
The cosine of an angle is defined as the ratio of the length of the adjacent side to the length of the hypotenuse of a right triangle:
[tex]\cos\theta= \sf \dfrac{adjacent}{hypotenuse}=\dfrac{\sqrt{3}}{2}[/tex]
Therefore, the length of the side adjacent angle θ is √3 and the length of the hypotenuse is 2.
[tex]\boxed{\begin{minipage}{9 cm}\underline{Pythagoras Theorem} \\\\$a^2+b^2=c^2$\\\\where:\\ \phantom{ww}$\bullet$ $a$ and $b$ are the legs of the right triangle. \\ \phantom{ww}$\bullet$ $c$ is the hypotenuse (longest side) of the right triangle.\\\end{minipage}}[/tex]
We can use Pythagoras Theorem to calculate the length of the side opposite angle θ:
[tex](\sqrt{3})^2+O^2=2^2[/tex]
[tex]3+O^2=4[/tex]
[tex]O^2=1[/tex]
[tex]O=1[/tex]
Therefore, the length of the side opposite angle θ is 1.
Now we have the lengths of the three sides of the right triangle, we can find the other trigonometric function of angle θ.
[tex]\boxed{\begin{minipage}{8cm}\underline{Trigonometric functions}\\\\$\sf \sin\theta=\dfrac{O}{H}\quad\cos\theta=\dfrac{A}{H}\quad\tan\theta=\dfrac{O}{A}$\\\\\\$\sf\csc\theta=\dfrac{H}{O}\quad\sec\theta=\dfrac{H}{A}\quad\cot\theta=\dfrac{A}{O}$\\\\\\where:\\\phantom{ww}$\bullet$ $\theta$ is the angle.\\\phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle.\\\phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle.\\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse.\\\end{minipage}}[/tex]
Given values:
O = 1A = √3H = 2Substitute these values into the six trigonometric functions:
[tex]\sin\theta=\dfrac{O}{H}=\dfrac{1}{2}[/tex]
[tex]\cos\theta=\dfrac{A}{H}=\dfrac{\sqrt{3}}{2}[/tex]
[tex]\tan\theta=\dfrac{O}{A}=\dfrac{1}{\sqrt{3}}=\dfrac{\sqrt{3}}{3}[/tex]
[tex]\csc\theta=\dfrac{H}{O}=\dfrac{2}{1}=2[/tex]
[tex]\sec\theta=\dfrac{H}{A}=\dfrac{2}{\sqrt{3}}=\dfrac{2\sqrt{3}}{3}[/tex]
[tex]\cot\theta=\dfrac{A}{O}=\dfrac{\sqrt{3}}{1}=\sqrt{3}[/tex]
Select the slope that would be parallel to y= 12.50x + 5
12.50
Step-by-step explanation:Parallel lines are lines that will never intersect.
Parallel Lines
Parallel lines run opposite of each other without intersecting. For lines to be parallel, they must have the same slope. The equation given to us is written in slope-intercept form. The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. So, the slope from the equation is 12.50.
Finding Parallel Lines
In order to find other lines that are parallel to the line given, all we need to do is write another equation with the same slope. However, 2 lines that are the same are not considered to be parallel. This means that for 2 lines to be parallel they must have the same slope but different y-intercepts. For example, a parallel line could be y = 12.50x + 6.
25-40x = x - 10
solve this radical equation
the 25-40x is supposed to be in a square root
help please answer the number 1 only thanyou
i will give brainliest
Answer:
[tex]\sin\theta=\dfrac{\sqrt{5}}{5}[/tex]
[tex]\cos\theta=\dfrac{2\sqrt{5}}{5}[/tex]
[tex]\tan\theta=\dfrac{1}{2}[/tex]
[tex]\csc\theta=\sqrt{5}[/tex]
[tex]\sec\theta=\dfrac{\sqrt{5}}{2}[/tex]
Step-by-step explanation:
The cotangent ratio is the reciprocal of the tangent ratio.
[tex]\cot \theta = \dfrac{1}{\tan \theta}[/tex]
Therefore, if cot θ = 2 then:
[tex]\dfrac{1}{\tan \theta}=2[/tex]
[tex]\tan \theta=\dfrac{1}{2}[/tex]
The tangent of an angle is defined as the ratio of the length of the opposite side to the length of the adjacent side in a right triangle:
[tex]\tan\theta = \sf \dfrac{opposite}{adjacent}[/tex]
Therefore, the length of the side opposite angle θ is 1 and the length of the side adjacent angle θ is 2.
[tex]\boxed{\begin{minipage}{9 cm}\underline{Pythagoras Theorem} \\\\$a^2+b^2=c^2$\\\\where:\\ \phantom{ww}$\bullet$ $a$ and $b$ are the legs of the right triangle. \\ \phantom{ww}$\bullet$ $c$ is the hypotenuse (longest side) of the right triangle.\\\end{minipage}}[/tex]
We can use Pythagoras Theorem to calculate the length of the hypotenuse, H:
[tex]1^2+2^2=H^2[/tex]
[tex]1+4=H^2[/tex]
[tex]H^2=5[/tex]
[tex]H=\sqrt{5}[/tex]
Therefore, the length of the hypotenuse is √5.
Now we have the lengths of the three sides of the right triangle, we can find the other trigonometric function of angle θ.
[tex]\boxed{\begin{minipage}{8cm}\underline{Trigonometric functions}\\\\$\sf \sin\theta=\dfrac{O}{H}\quad\cos\theta=\dfrac{A}{H}\quad\tan\theta=\dfrac{O}{A}$\\\\\\$\sf\csc\theta=\dfrac{H}{O}\quad\sec\theta=\dfrac{H}{A}\quad\cot\theta=\dfrac{A}{O}$\\\\\\where:\\\phantom{ww}$\bullet$ $\theta$ is the angle.\\\phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle.\\\phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle.\\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse.\\\end{minipage}}[/tex]
Given values:
O = 1A = 2H = √5Substitute these values into the six trigonometric functions:
[tex]\sin\theta=\dfrac{O}{H}=\dfrac{1}{\sqrt{5}}=\dfrac{\sqrt{5}}{5}[/tex]
[tex]\cos\theta=\dfrac{A}{H}=\dfrac{2}{\sqrt{5}}=\dfrac{2\sqrt{5}}{5}[/tex]
[tex]\tan\theta=\dfrac{O}{A}=\dfrac{1}{2}[/tex]
[tex]\csc\theta=\dfrac{H}{O}=\dfrac{\sqrt{5}}{1}=\sqrt{5}[/tex]
[tex]\sec\theta=\dfrac{H}{A}=\dfrac{\sqrt{5}}{2}[/tex]
[tex]\cot\theta=\dfrac{A}{O}=\dfrac{2}{1}=2[/tex]
Please help asap
Find the indicated measure for circle P.
26. The length FE in the circle is 6 units
27. The arc AE has a measure of 64 degrees
26. Calculating the length FEFrom the question, we have the following parameters that can be used in our computation:
The circle
Given that the lengths from the center to either chords are equal
This means that
FE = 6 units
27. Calculating the measure of arc AEFor the other circle, we have
BC = 58 degrees
AB = ED
The arc AE is calculated as
AE = 180 - BC - ED
Where
AB = ED = BC = 58 degrees
So, we have
AE = 180 - 58 - 58
Evaluate
AE = 64
Hence, the arc AE is 64 degrees
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Help which one is correct
the base of the triangle below is b. bc.
Given the values of the linear functions f(x) and g(x) in the tables, what is (f – g)(-1)?
The domain of the composite function (f - g)(-1) is derived to be 12 which makes c the correct option.
What is composite function?A function is composite when the co- domain of the first mapping is the domain of the second mapping
We shall evaluate the domains of the function (f - g)(-1) as follows:
Observing from the table of values, at the point x = -1 we have;
f(x) = 5 and g(x) = -7
So;
(f - g)(-1) = 5 - (-7)
(f - g)(-1) = 5 + 7
(f - g)(-1) = 12
Therefore, the value for domain of the composite function (f - g)(-1) is derived to be 12.
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I will give the BRAINIEST!!
It is 12pm and Maria and Nemzet are about to try and complete a jigsaw puzzle together before they have to get ready for a party that starts at Spes. If attempting this puzzle alone, it would take Maria 7
hours to complete it and it would take Nemzet 5 hours
Use the information above to choose all sentences which are true. Select all that apply
It will take them approximately 2.9 hours to finish the puzzle together. Therefore, options B, C are the correct answers.
Given that, Maria and Nemzet are about to try and complete a jigsaw puzzle.
Together attempting this puzzle alone, it would take Maria 7 hours to complete it and it would take Nemzet 5 hours
Here, 1/7 + 1/5 = 1/t
(5+7)/35 = 1/t
12/35 = 1/t
t=35/12
t=2.91
t=2.9 hours
Therefore, options B, C are the correct answers.
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100 Points! Algebra question. Photo attached. Thank you!
Answer:
a₁ = 121.5-------------------------
Use the formula for the sum of n terms of a GP:
Sₙ = a₁(1 - rⁿ) / (1 - r)And use the nth term formula:
aₙ = a₁*rⁿ⁻¹ = a₁*rⁿ/r ⇒rⁿ = aₙ*r/a₁We can rearrange the sum formula to solve for the first term:
Sₙ = a₁(1 - aₙ*r/a₁) / (1 - r) ⇒Sₙ = ( a₁ - aₙ*r) / (1 - r)Plugging in the given values, we get:
4860 = (a₁ - 3280.5*3)/(1 - 3)4860 = (a₁ - 9841.5)/ (-2)a₁ - 9841.5 = -2*4860a₁ - 9841.5 = -9720a₁ = 9841.5 - 9720a₁ = 121.5Therefore, the first term of the GP is 121.5.
please help with this
Answer:
F(- 3) = - 2 , F(0) = 0
Step-by-step explanation:
(a)
F(- 3) with x = - 3 is in the interval x < 0 , then
F(- 3) = 3x = x + 1 = - 3 + 1 = - 2
(b)
F(0) with x = 0 is in the interval x ≥ 0 , then
F(0) = 3x = 3 × 0 = 0
12,15,20,25,30,20,30,15,12,12
Answer:
The mode of this set of numbers is 12. If that is what you are looking for.
Which point is represented by 6 times the quantity cosine 11 pi over 6 plus i times sine 11 pi over 6 end quantity question mark
[tex]6\left[\cos\left( \frac{11\pi }{6} \right) +i\sin\left( \frac{11\pi }{6} \right) \right] \\\\\\ 6\left[\cfrac{\sqrt{3}}{2}~~,~-\cfrac{1}{2}i \right]\implies (3\sqrt{3}~~,~-3i) ~~ \approx ~~ \stackrel{ \textit{\LARGE S} }{(5.2~~,~-3i)}[/tex]
write answers that are not integers rounded to the nearest tenth
The value of x is 12.82, the value of z is 40.25.
Using Pythagorean theorem
50²= 39² + y²
y²= 2500- 1521
y= 32.28
Again Using Pythagorean theorem
z²= y²+ x²
z²- x²= 979
and, (39 + x)² = 50² + z²
(39 + x)² = 50² + (x² + 979)
1521 + 78x + x² = 2500 + x² + 979
78x = 1000
x ≈ 12.82
Substituting this value of x back into the first equation, we get:
z² - x² = 979
z² - (12.82)² = 979
z² ≈ 1620.12
Taking the square root of both sides, we get:
z ≈ 40.25
Therefore, the value of x is 12.82, the value of z is 40.25.
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Which function is represented by this graph?
-10 -8 -6 -4 -2
-10
-2
-6
-8
-10
2
4
6
8
10
The standard absolute value graph has been shifted 7 units to the right and 3 units down to get this graph.
That means we have answer B: f(x) = | x - 7 | - 3
Remember that the left-right shifts are opposite from what they would appear to be in the equation.
| x - 7 | shifts it right 7 units.
| x + 7 | shifts it left 7 units.
if a car left Lagos for portharcourt with the average speed of 60 km per hour, how long will it take for the car to arrive portharcourt?
Answer:
8 hours and 20 minutes
Step-by-step explanation:
Let's assume the distance between Lagos and Port Harcourt is approximately 500 kilometers. With an average speed of 60 km per hour, we can use the formula:
Time = Distance / Speed
Substituting the values, we get:
Time = 500 km / 60 km/h ≈ 8.33 hours
Therefore, it would take approximately 8 hours and 20 minutes for the car to travel from Lagos to Port Harcourt, assuming the distance is around 500 kilometers and the average speed is 60 km per hour. Please note that this is just an example calculation, and the actual time may vary depending on the distance and road conditions.
PLEASE PLEASE HELP WILL MARK BRAINLIST!!!!!!!!!!!!
Answer:
y ≤ - [tex]\frac{2}{7}[/tex] x
Step-by-step explanation:
the blue region indicates where the solutions lie
that is below the given line
the equation of the line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, 0) and (x₂, y₂ ) = (- 7, 2) ← 2 points on the line
m = [tex]\frac{2-0}{-7-0}[/tex] = [tex]\frac{2}{-7}[/tex] = - [tex]\frac{2}{7}[/tex]
the line crosses the y- axis at (0, 0 ) ⇒ c = 0
y = - [tex]\frac{2}{7}[/tex] x ← equation of line
the line is solid thus the region below is denoted by y ≤ , that is
y ≤ - [tex]\frac{2}{7}[/tex] x
2. Find the least number by which each of the given numbers should be multiplied so as to get a perfect square. Also, find the square root of the resulting number. a) 845 b) 1008
The least number by which each of the given numbers should be multiplied so as to get a perfect square are 5 and 7.
Here, we have,
we have
a) 845 =5×13×13
The smallest whole number is 5, by which 845 should be multiplied so as to get a perfect square.
Now , we get,
845 ×5=5×13×13×5
4225=5×13×13×5
√4225=65
b) 1008=2×2××2×3×3×3
The smallest whole number is 7, by which 1008 should be multiplied so as to get a perfect square.
Now , we get,
1008×7=2×2×2×2×3×3×7×7
7056=2×2×3×7
=84
Answer : 5 and 7
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HELP ASAPPPPPP
Given: line AB with endpoints A2,5and B−4,−2.
Identify the coordinates of the midpoint.
Answer:
(-1, 1.5).
Step-by-step explanation:
To find the midpoint of line segment AB with endpoints A(2, 5) and B(-4, -2), you can use the midpoint formula. The midpoint formula states that the midpoint (M) of a line segment with endpoints (x₁, y₁) and (x₂, y₂) is given by:
M = ((x₁ + x₂) / 2, (y₁ + y₂) / 2)
Let's calculate the midpoint using this formula:
x-coordinate of midpoint:
x = (2 + (-4)) / 2 = -2 / 2 = -1
y-coordinate of midpoint:
y = (5 + (-2)) / 2 = 3 / 2 = 1.5
Therefore, the midpoint of line AB is M(-1, 1.5).
(Worth 100 Brainly points) After a dreary day of rain, the sun peeks through the clouds and a rainbow forms. You notice the
rainbow is the shape of a parabola.
The equation for this parabola is y=-x² + 36
1.Create a table of atleast 4 values of the function that includes two points of intersection between the airplane and the rainbow
2.What is the domain and range of the rainbow? Explain what the domain and range represent.Do all of the values make sense in the situation. Why or why not.
3.what are the x and y intercepts of the rainbow. Explain what each intercept represents.
The table of at least 4 values of the function is
x 0 -6 6 3
y 36 0 0 27
The domain is All set of real values and the range: y ≤ 36
The x and y intercepts of the rainbow are x = (-6, 0) and (6, 0) y = (0, 36)
Creating a table of at least 4 values of the functionGiven that we have
y = -x² + 36
From the graph, we have the following values
x y
0 36
-6 0
6 0
Set x = 3
So, we have
y = -3² + 36
Evaluate
y = 27
So, we have
x y
0 36
-6 0
6 0
3 27
The domain and the rangeFrom the graph, we have
Domain: All set of real valuesRange: y ≤ 36These values mean that;
Domain: The time of the dayRange: The height of the sunFor the x and y intercepts of the rainbow, we have
x = (-6, 0) and (6, 0)
y = (0, 36)
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Which is equivalent to 49 2*
92x
0 gx
0 /g*
0 §g*
The expression that is equivalent to [tex]49^{\frac{3}{2}}[/tex] is given as follows:
D. 343.
What is the power of a power rule?The power of a power rule is used when a single base is elevated to multiple exponents.
Then the simplified expression is obtained keeping the base, while the exponents are multiplied.
The expression for this problem is given as follows:
[tex]49^{\frac{3}{2}}[/tex]
49 is the square of 7, hence:
49 = 7².
Then the expression can be simplified as follows:
[tex]7^2^{\frac{3}{2}}[/tex]
The multiplication of the exponents is of:
2 x 3/2 = 3.
(when we apply the power of power rule, we keep the base and multiply the exponents)
Hence:
7³ = 343.
Missing InformationThe problem is given by the image presented at the end of the answer.
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a
E
Calculator
Given that cos=, what is sin ?
Enter your answer, as a simplified fraction, in the boxes.
URGENT
The trigonometric value equation is solved and sin θ = 24/25
Given data ,
Let the triangle be represented as ΔABC
Now , the measure of sides of the triangle are
From the trigonometric relations , we get
sin θ = opposite / hypotenuse
cos θ = adjacent / hypotenuse
tan θ = opposite / adjacent
tan θ = sin θ / cos θ
And , sin² θ + cos² θ = 1
where the measure of cos θ = 7/25
On simplifying the equation , we get
sin θ = √ ( 1 - cos² θ )
sin θ = √ ( 1 - 49/625 )
sin θ = √576/625
sin θ = 24/25
Hence , the trigonometric relation is sin θ = 24/25
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14. If the cosine of an angle is
O 20
21
29
29
20
29
21
what is the cosine of the angle's complement?
29
A
The cosine of the angle's complement is 20/29
Let's start by using the fact that the sum of the measures of an angle and its complement is 90 degrees.
Let's call the angle A, and its complement B. Then we have:
cos A = 21/29
We want to find cos B. We know that cos B = sin A, because the sine of an angle is equal to the cosine of its complement.
So we need to find sin A.
We can use the Pythagorean identity:
sin²A + cos²A = 1
Substituting in cos A = 21/29, we get:
sin²A + (21/29)² = 1
Solving for sin A, we get:
sin A = ± 20/29
Therefore, we have:
cos B = sin A = 20/29
Hence, the cosine of the angle's complement is 20/29
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If GE = 42 and DH = 16, find GF
Based on the above. (see image attached), The value of GF in the rhombus is option A: 26.4
What is the value of the rhombus?A four-sided shape with equal side lengths is known as a rhombus. Equally sided four-sided figure is also referred to as an equilateral quadrilateral, because equilateral denotes that its sides have the same length.
Note that the properties of a rhombus are :
All the sides are equalOpposite angles are equaladjacent angles are supplementaryDiagonals are perpendicular bisector of each otherSo, note that:
DH = HF = 16
GH = HE = 21
Therefore, by Using Pythagoras theorem we can look for GF by:
GF = √21² + 16²
= √441 + 256
= √697
= 26.4007575649
= 26.4
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if you roll a 6 sided die 66 times what is the best prediction possible for the number of times you will roll a five
Answer:
11/66, or 11 times
Find the missing information:
In the figure below, mZPSR = 106°. Find m PTR.
The arc angle in the circle is as follows:
mPTR = 63 degrees.
How to find measure of an arc angle?The tangent intersection theorem states that If a tangent and a chord intersect at a point on a circle, then the measure of each angle formed is one-half the measure of its intercepted arc.
Therefore,
m∠PSR = 1 /2 (mPTR - mPR)
mPTR = ?
mPR = 149 degrees
m∠PSR = 106
Therefore,
106 = 1 / 2 (x - 149)
106 = 0.5x - 74.5
106 - 74.5 = 0.5x
31.5 = 0.5x
divide both sides by 0.5
x = 31.5 / 0.5
x = 63 degrees
Therefore,
mPTR = 63 degrees
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How many solutions does the system of equations below have?
y=-x-3
2y + 2x = -6
OA. No solution
B. Exactly 1 solution
C. More than 1 solution
D. At least 1 solution
There are more than one solution for the given system.
Hence the correct option is C.
The given system of equations is,
y=-x-3
2y + 2x = -6
Write the equation in the form of ax + by = c,
Therefore, the system be
x + y = -3
2x + 2y = -6
We know that,
The system of equations a₁x + b₁y = c₁ and a₂x + b₂y = c₂
If [tex]\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2}[/tex]
Then the system has more than one solution.
Therefore,
1/2 = 1/2 = -3/-6
= 1/2
Hence, this has more than one solution or roots.
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