Answer:
see explanation
Step-by-step explanation:
If A +B = 45° then tan(A+B) = tan45° = 1
Expanding (1 + tanA)(1 + tanB)
= 1 + tanA + tanB + tanAtanB → (1)
Using the Addition formula for tan(A + B)
tan(A+B) = [tex]\frac{tanA+tanB}{1-tanAtanB}[/tex] = 1 ← from above
Hence
tanA + tanB = 1 - tanAtanB ( add tanAtanB to both sides )
tanA + tanB + tanAtanB = 1 ( add 1 to both sides )
1 + tanA + tanB + tanAtanB = 2
Then from (1)
(1 + tanA)(1 + tanB) = 2 ⇒ proven
if you reflect ΔFGH across the x-axis, what will be the coordinates of the vertices of the image ΔF'G'H
Answer:
A
Step-by-step explanation:
Under a reflection in the x- axis
a point (x, y ) → (x, - y )
Hence
F(- 2, - 1 ) → F'(- 2, 1 )
G(2, 2 ) → G'( 2, - 2 )
H(4, - 3 ) → H'(4, 3 )
If u=(3+2i) and v=(3-2i) what is uv?
Answer:
13
Step-by-step explanation:
u=(3+2i) v=(3-2i)
uv = (3+2i)(3-2i)
FOIL
first: 3*3 = 9
outer: -2i*3 = -6i
inner: 2i*3 = 6i
last = 2i*-2i = -4i^2 =-4 (-1) = 4
Add together
9-6i+6i +4 = 13
Answer:
13.
Step-by-step explanation:
uv = (3 + 2i)(3 - 2i)
= 9 - 6i + 6i - 4i^2 Note that i^2 = -1 so we have
9 -4 * -1
= 13.
On the planet kudzu, the probability that an animal is blue is 0.20. The probability that the animal has two heads is 0.20. Which statement is true? Help ASAP, thanks!!
Correct Option is C.
Independent Event:
Independent events are those events whose occurrence is not dependent on any other event. For example, if we flip a coin in the air and get the outcome as Head, then again if we flip the coin but this time we get the outcome as Tail. In both cases, the occurrence of both events is independent of each other.
Here, Some animals may be blue without two heads and also may be with two heads without blue.
So, It is an independent event, As there occurrence is not dependent on other events.
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The amount in dollars an electrician charges in terms of the number of hours worked is represented by the function y=22x+42.
From the function, Identify all the phrases that hold true for the situation.
Answer:
Step-by-step explanation:"
The electrician charges an initial fee of $42", AND "The electrician charges $22 for every hour worked" is true.
The equation is y=22x+42. The formula is y=mx+b.m is the slope, or is this case, the number of dollars for every "x", which is the number of hours worked. So you have to pay $22 for every hour the electrician works.b is the y-intercept, or the amount it starts with, in this case, you have to pay a fee of $42 even when the electrician worked 0 hours. This is because $42 is the amount it starts with.On a graph, the line will start at (0,42) because that is when you start paying. And then it will increase by 22 for each hour, so the next coordinate would be (1,64).
The given function y=22x+42 represents the electrician’s charges. The electrician charges $22 for each hour worked and has a flat service fee of $42.
Explanation:
The given function y=22x+42 stands for the electrical work charges in terms of hours worked. Here 'y' represents the total amount charged, 'x' represents the number of hours worked, '22' is the hourly rate and '42' is likely a fixed service fee regardless of the hours worked. So the aspects that holds true for this function are: (1) The electrician charges $22 per hour of work, (2) The electrician has a fixed service fee of $42 whether or not they have worked any hours
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Use the substitution method to solve the system of equations choose the correct ordered pair
Answer:
C. (4,28)
Step-by-step explanation:
The substitution method requires you to input a specified number in place of a variable. In this case, the variable 'x' should be replaced by the number 4. Using the order of operations, we know that multiplication should be applied before subtraction. When we replace 'x' with 4, we get the equation 'y=8(4)-4'. Multiplying 8 and 4 gives us 32. If we subtract 4 from 32, we get 28. The answer ends up being 'y=28'.
That is the first part of our solution. What we are actually looking for is an ordered pair. We know ordered pairs are written in the form (x, y). First, we need to find the 'x'. The 'x' has been given to us from the beginning, it is 4. Next is the 'y'. This is what we needed to find using substitution. We ultimately concluded that the 'y' is equivalent to 28. Therefore our ordered pair is (4, 28), the letter choice C.
I hope this helped you and that I clearly elaborated on the answer choice.
Malcolm can run a race at a speed of 6 minutes per mile, while Joshua runs at 8 minutes per mile. In a 10-mile race, how many minutes after Malcolm crosses the finish line will Joshua cross the finish line if they start the race together?
Answer:
20 minExplanation:
The time to cross the finish line may be found using the speed vs. time equation:
speed = distance / timeFrom which you can solve for time:
time = distance / speed.Using the last equation, you can find the difference in the times for Malcolm and Joshua, but, since the speed must be expressed in miles per minutes, and the given data are minutes per mile, first you must convert the data.
Miles per minute is the inverse of minutes per mile, so the corresponding speeds are:
Malcolm's speed: 1 / (6 min/mile) = (1/6) miles/minJoshua's speed: 1 / (8 min/mile) = (1/8) miles/minTime for Malcom: 10 miles / [ 1/ (6 miles/min) ] = 10/(1/6) min = 60 minTime for Joshua: 10 miles / [ 1/ ( 8 miles/min) ] = 10/(1/8) min = 80 minDifference in times: 80 min - 60 min = 20 minHence, Joshua will cross the finish line 20 minutes after Malcolm crosses the finish line.
which number is prime ?
A : 8
B : 6
C : 13
D : 10
C : 13
8 is not a prime number since it's dividable by multiple numbers. For example 2(4), 1(8)
6 is not a prime number since it's dividable by 3(2), 1(6)
13 is a prime number because it's only dividable by itself.
10 is not a prime number because it can be divided by 5(2), 1(10)
So only 13 matches as a prime number.
Solve the following inequality algebracially -2 < x/3 + 1 <5
Answer:
-9 < x < 12Step-by-step explanation:
[tex]-2<\dfrac{x}{3}+1<5\qquad\text{subtract 1 from both sides}\\\\-2-1<\dfrac{x}{3}+1-1<5-1\\\\-3<\dfrac{x}{3}<4\qquad\text{multiply both sides by 3}\\\\(3)(-3)<3\!\!\!\!\diagup^1\cdot\dfrac{x}{3\!\!\!\!\diagup_1}<(3)(4)\\\\-9<x<12[/tex]
find the quotient. PIC PROVIDED PLATO
Answer:
D is the correct option
Step-by-step explanation:
2x-3/x ÷ 7/x²
Change the division sign into multiplication and the second term will be flipped(denominator will become numerator)
2x-3/x * x²/7
x will be cancelled out by x²
2x-3/1 * x/7
Now multiply 2x-3 by x
2x²-3x/7
Take x as a common:
x(2x-3)/7
Thus the correct option is D....
The function y=-4(x - 3)2 + 8 shows the daily profit (in hundreds of dollars)
of a taco food truck, where x is the price of a taco (in dollars). Find and
interpret the zeros of this function,
Select two answers: one for the zeros and one for the interpretation.
O
A. Interpretation: The zeros are where the daily profit is $0.00.
O B. Zeros: x = 3 - V3 = 1.58 and x = 3 + v = 4.41
O
c. Interpretation: The zeros are where the price of a taco is $0.00.
O D. Zeros: x = 3 and x = -3
Answer:
Step-by-step explanation:
To find the zeros, set y=-4(x - 3)2 + 8 = 0. Then -4(x - 3)^2 = -8, and:
4(x - 3)^2 = 8. Dividing both sides by 4 yields (x - 3)^2 = 2.
Taking the square root of both sides yields x - 3 = ±2, so that
x = 3 ±2, or x = 5 and x = 1. These are the zeros. The correct interpretatioon is A: where the daily profit is $0.
Answer:
Interpretation: The zeros are where the daily profit is $0.00.
Zeroes are x = 1.58 and x = 4.41.
Step-by-step explanation:
Given function,
[tex]y=-4(x-3)^2+8[/tex]
For finding the zeros,
y = 0,
[tex]-4(x-3)^2+8=0[/tex]
[tex]-4(x-3)^2=-8[/tex]
[tex](x-3)^2=2[/tex]
[tex]x-3=\pm \sqrt{2}[/tex]
[tex]\implies x = 3\pm \sqrt{2}[/tex]
[tex]\implies x\approx 4.41\text{ or }x=1.58[/tex]
Hence, the zeroes of the function are x = 1.58 and x = 4.41,
∵ x represents the price of a taco and y represents daily profit,
Therefore, the zeroes are where the daily profit is $ 0.00.
Draw a graph of this linear inequality y<2
Answer:
Observe the attached image
Step-by-step explanation:
The inequality we have is:
[tex]y <2[/tex]
This means that the region represented by this inequality includes all the values below the horizontal line [tex]y = 2[/tex].
To graph this region, draw a dotted horizontal line that intersects the y axis at [tex]y = 2[/tex]. Then shade all the region that is below the horizontal line, as shown in the attached image.
Solve Ax + By = −C for x.
The value of x from the given algebraic expression Ax + By = −C would be x = (-C - By)/ A.
What is a linear equation?A linear equation is an equation that has the variable of the highest power of 1. The standard form of a linear equation is of the form Ax + B = 0.
In order to solve x, if we isolate the x variable from the rest of the other variables.
Given algebric expression;
Ax + By = -C
1. Subtract By from the right side
Ax + By -By = -C -By
Ax = -C - By
2. Divide A
x = (-C - By)/ A
Hence, The value of x from the given algebraic expression Ax + By = −C would be x = (-C - By)/ A.
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Use the information given in the diagram. Tell why UX=VW and UVW=WXU (51)
its given if already with all the dashes and circle thingys so it's A I'm quite sure
Reflexive property and transitive property.
The answer is option D.
What is Reflexive property?In algebra, the reflexive assets of equality state that a number is continually the same as itself. Reflexive belongings of equality. If a is various, then. a = a.
What is transitive property?In math, if A=B and B=C, then A=C. So, if A=5 for instance, then B and C should both also be five with the aid of the transitive property. That is actually—a foundational property of—math because numbers are constant and both facets of the equals signal need to be equal, by definition.
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Julio is visiting Bridal Veil Falls in Telluride Colorado. From the top of the 365 foot waterfall he looks down at an angle of depression of 27° and spots a bear fishing in the stream. To the nearest foot, how far is the bear from the base of the waterfall?
To find the distance from the bear to the base of the waterfall, we can use the tangent function, which relates the angle of depression to the distance. Using the given angle of depression of 27° and height of 365 feet, we can calculate that the bear is approximately 632 feet from the base of the waterfall.
Explanation:To find the distance from the bear to the base of the waterfall, we can use the tangent function, which relates the angle of depression to the distance.
In this case, we have an angle of depression of 27° and a height of 365 feet.
Let's denote the distance we're trying to find as x.
The tangent of the angle of depression is equal to the opposite side (365 feet) divided by the adjacent side (x).
So we can set up the equation tan(27°) = 365/x and solve for x.
Rearranging the equation, we have x = 365/tan(27°). Plugging in the values and using a calculator, we find that x is approximately 632 feet.
The bear is approximately 717 feet away from the base of the waterfall.
To find out how far the bear is from the base of the waterfall, use trigonometry, specifically the tangent of the angle of depression. Tangent relates the opposite side and the adjacent side in a right triangle.
1. Given Information:
- Height of the waterfall (opposite side), h = 365 feet.
- Angle of depression, [tex]\( \theta = 27\textdegree[/tex].
2. Formulate the Tangent Function:
The tangent of an angle in a right triangle is given by [tex]\( \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \)[/tex].
So in our case, [tex]\( \tan(27\textdegree) = \frac{365}{d} \)[/tex].
3. Solving for d (the distance from the base of the waterfall to the bear):
Rearranging for d:
[tex]\[ d = \frac{365}{\tan(27\textdegree)} \][/tex]
4. Calculate the Value:
Using a calculator to find [tex]tan(27\textdegree)[/tex] which is approximately 0.5095.
[tex]\[ d = \frac{365}{0.5095} \approx 716.5 \text{ feet} \][/tex]
5. Round to the Nearest Foot:
[tex]\[ d \approx 717 \text{ feet} \][/tex]
So, the distance between the bear and base of the waterfall is approximately 717 feet.
What is the solution to the system
Answer:
hello : (5,2,2)
Step-by-step explanation:
put x = 5 in this equation : y=3(5)-13=15-13=2
put x= 5 and y=2 and z=2 in the first and second equation you have -3(5)+4(2)+2(2)=-3 -15+8+4 =-3 so :-3=-3 .....right
2(5)-4(2)-2 =0 10-8-2=0 so : 0=0 .....right
evaluate (root5+root2)^2+(root8-root5)^2
Answer
2(10 - √10) or 13.68 to the nearest hundredth.
Step-by-step explanation:
(√5 + √2)^2 + (√8 - √5)^2
= 5 + 2 + 2√5√2 + (8 + 5 - 2√8√5)
= 7 + 2√10 + 13 - 2√40
= 20 + 2√10 - 2√40
= 20 + 2√10 - 4√10
= 20 - 2√10
= 2(10 - √10).
AB id a diameter of a circle centered at o. C is a point on the circle such that angle BOC is 60 degrees.if the diameter of the circle is 5 inches the length of the chord ac expressed in inches is
A.3
b. 5 square root 2 over 2
c.5 square root 3 over 2
d. 3 square root 3
e. none of the above
Answer:
Option c). 5 square root 3 over 2
Step-by-step explanation:
see the attached figure to better understand the problem
step 1
Find the measure of angle AOC
we know that
m∠AOC+m∠BOC=180° ----> by supplementary angles
m∠BOC=60° ---> given value
m∠AOC+60°=180°
m∠AOC=180°-60°=120°
step 2
we know that
The triangle AOC is an isosceles triangle
OA=OC=2.5 in -----> the radius of the circle
m∠CAO=m∠OCA ----> base angle
we have that
2m∠CAO=180°-m∠AOC
2m∠CAO=180°-120°
m∠CAO=30°
step 3
Find the measure of the chord AC
we know that
Applying the law of sines in triangle AOC
sin(30°)/2.5=sin(120°)/AC
AC=(2.5)sin(120°)/sin(30°)
sin(30°)=1/2
AC=(2.5)sin(120°)/(1/2)
AC=(5)sin(120°)
Remember that
sin(120°)=sin(60°)
sin(60°)=√3/2
substitute
AC=(5√3)/2
5 square root 3 over 2
How do I answer 9 and 10. (With a picture). Thanks!
Answer:
The option you have selected in the photo, 20 + 0.15x < 15 + 0.20x
Step-by-step explanation:
Your data plan per month would have a flat rate of 15 and then add on 20 cents per MB of data used. The equation would be 15 + 0.20x.
Sally's is a flat 20 and adding on 15 cents per MB of data. The equation would be 20 + 0.15x.
The question wants Sally's less than yours or Sally < You, so your answer is:
20 + 0.15x < 15 + 0.20x
If one kilogram equals 2.2 pounds, how many kilograms equal 112 pounds? Round your answer to the nearest hundredth, if necessary.
Answer: 50.91 kilograms
Step-by-step explanation: Divide the number of pounds by the number of pounds in a kilogram.
112/2.2 = 50.91
There are 50.91 kilograms in 112 pounds.
Consider the function represented by 9x + 3y = 12 with x as the independent variable. How can this function be written
using function notation?
f(x)=
x+4
Mark this and return
Save and Exit
Next
Submit
Answer:
f(x)=-3x+4
Step-by-step explanation:
We need to solve for y.
9x+3y=12
Subtract 9x on both sides.
3y=-9x+12
Divided both sides by 3.
y=-3x+4
Replace y with f(x).
f(x)=-3x+4
Answer:
[tex]f(x)=-3x+4[/tex]
Step-by-step explanation:
the function represented by [tex]9x + 3y = 12[/tex]
To write the given equation in f(x), we need to solve for y
Lets solve the given equation for y
[tex]9x + 3y = 12[/tex]
Subtract 9x from both sides
[tex]3y =-9x+12[/tex]
Now divide whole equation by 3, divide each term by 3
[tex]y =-3x+4[/tex]
To write it as a function , finally we replace y with f(x)
[tex]f(x)=-3x+4[/tex]
Point G is rotated 90ﾟ the coordinate of the pre image point G was (7 ,-5), and its image G is at coordinate (5, 7) what is the direction of the rotation
Answer: The direction of the rotation is counterclockwise about the origin.
Step-by-step explanation:
A Rotation is a transformations in which a figure is rotated about a specific point, which is the know as "Center of rotation". Rotation is described in terms of degrees. The initial figure is called "Pre-image" and the rotated figure is called "Image". According to Rule for 90° counterclockwise rotation about the origin:[tex](x,y)[/tex] → [tex](-y, x)[/tex]
In this case, we can observe that the coordinates of the Pre-image of the Point G are:
[tex](7 ,-5)[/tex]
And the coordinates of its Image are:
[tex](5, 7)[/tex]
Then:
[tex](x,y)[/tex] → [tex](-y, x)[/tex]
[tex](7 ,-5)[/tex] → [tex](5, 7)[/tex]
Therefore, the direction of the rotation is counterclockwise about the origin.
what is the value of the expression? (9÷3)+4(6-7)
Step-by-step explanation:
(9÷3)+4(6-7)
=(3)+4(1)
=3+4
=7
Answer:
-1
Step-by-step explanation:
According to PEMDAS, we must start with what's in the parenthesis:
(9/3)=3
and
(6-7)=-1
Which leaves us with the equation 3+4(-1)
The next step would be multiplication:
4(-1)=-4
Leaving us with 3+(-4), which simplifies to:
3-4=-1Hope this helps!
Circle A has a radius of 6. Which circles are congruent
to circle A? Check all that apply.
E
circle D
circle E
circle F
circle G
circle H
Answer:
The correct answer options are:
Circle E
Circle F
Step-by-step explanation:
We are given that a circle A has a radius of 6 and we are to determine whether which of the circles from the answer options are congruent to circle A.
We know that radius is the distance from the center of the circle to any point on circle's circumference.
Circle E, F show the radius of 6, therefore they are congruent to circle A.
Solve the equation. 9+ m/5 =19
Answer:
m = 50
Step-by-step explanation:
Simplify:
9 + m/5 = 19
9 + 1/5m = 19
1/5m + 9 = 19
Subtract 9 from both sides:
1/5m + 9 - 9 = 19 - 9
1/5m = 10
Multiply both sides by 5:
5 ⋅ ( 1/5m ) = ( 5 ) ⋅ (10)
Therefore m = 50The table gives the populations of three countries in 2013.
United States
3.16 x 108
Brazil Germany
1.96 * 108 8.0 x 107
Arrange the sums and differences in increasing order of their values.
the difference of
the populations
of Germany and
Brazil
the sum of the
populations of
the United States
and Brazil
the difference of
the populations
of Brazil and the
United States
the sum of the
populations of
Brazil and
Germany
Answer:
Arranging the sum and differences in increasing order of their values.
1) Difference of the populations of Germany and Brazil = 1.16 X 10^8
2) Difference of the populations of Brazil and the United States = 1.2 X 10^8
3) Sum of the populations of Brazil and Germany = 2.76 X 10^8
4) Sum of the populations of the United States and Brazil = 5.12 X 10^8
Step-by-step explanation:
Population of United States: 3.16 X 10^8
Population of Brazil : 1.96 X 10^8
Population of Germany: 8 X 10^7
a) the difference of the populations of Germany and Brazil
Difference of the populations of Germany and Brazil = 1.96 X 10^8 - 8 X 10^7 = 116000000 = 1.16 X 10^8
b) the sum of the populations of the United States and Brazil
Sum of the populations of the United States and Brazil = 3.16 X 10^8 + 1.96 X 10^8 = 512000000 = 5.12 X 10^8
c) the difference of the populations of Brazil and the United States
Difference of the populations of Brazil and the United States = 3.16 X 10^8 - 1.96 X 10^8 = 120000000 = 1.2 X 10^8
d) the sum of the populations of Brazil and Germany
Sum of the populations of Brazil and Germany: 1.96 X 10^8 + 8 X 10^7 = 276000000 = 2.76 X 10^8
Arranging the sum and differences in increasing order of their values.
1) Difference of the populations of Germany and Brazil = 1.16 X 10^8
2) Difference of the populations of Brazil and the United States = 1.2 X 10^8
3) Sum of the populations of Brazil and Germany = 2.76 X 10^8
4) Sum of the populations of the United States and Brazil = 5.12 X 10^8
1pt Which of these constructions will NOT result in a point of concurrency?
O A. the three altitudes of a triangle
B. the three angle bisectors of a triangle
C. the three midsegments of a triangle
O D. the three medians of a triangle
O
E. the three perpendicular bisectors of a triangle
The constructions will NOT result in a point of concurrency is C. the three midsegments of a triangle.
What forms the three central segments of a triangle?The central segment is parallel to the sides of the non-intersecting triangles. There are three congruent triangles formed by the central segment and sides of the triangle. Every triangle has three central segments.
The central segment is a line segment connecting the midpoints of the two sides of a triangle. Each triangle has three central segments because each triangle has three sides. The center segment of the triangle is parallel to the third side of the triangle and half the length of the third side.
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Plot the point (2,-pi/4)
Answer:
Step-by-step explanation:
Attached below. pi = 180°
Answer:
a
Step-by-step explanation:
negitive 7 over 18 minus negitive 9 over 4 equals?
Answer:
1 31/36 is your answer
Step-by-step explanation:
Find common denominators. Note that what you do to the denominator, you must do to the numerator;
(-7/18)(2/2) = (-14/36)
(-9/4)(9/9) = (-81/36)
Combine the terms:
(-14/36) - (-81/36)
Note that two negative signs directly next to each other equals a positive sign.
(-14/36) + 81/36
-14/36 + 81/36
(-14 + 81)/36
Combine like terms. Solve the parenthesis:
(67)/36
Change to a mixed fraction:
(67/36) = 1 31/36
1 31/36 is your answer.
~
the average of 20 numbers is 0. among them at least how many of them can be greater than 0.
a. 19.
b.10
c.0
d.1
Answer:
The correct option is A.
Step-by-step explanation:
The correct option is A.
According to the given statement:
Average of 20 numbers= 0.
So we have avg = sum/20.
That implies sum = 0.
Hence at the most, there can be 19 positive numbers.
(Such that if the sum of these 19 positive numbers is x, 20th number will be -x)....
2 2/3 + 12 6/8 how do I work this
Answer:
[tex]\large\boxed{2\dfrac{2}{3}+12\dfrac{6}{8}=15\dfrac{5}{12}}[/tex]
Step-by-step explanation:
[tex]2\dfrac{2}{3}+12\dfrac{6}{8}=2\dfrac{2}{3}+12\dfrac{6:2}{8:2}=2\dfrac{2}{3}+12\dfrac{3}{4}\\\\\text{Find}\ LCD:\\\\\text{List of multiples of 3:}\ 0,\ 3,\ 6,\ 9,\ \boxed{12},\ 15,\ ...\\\text{List of multiples of 4:}\ 0,\ 4,\ 8,\ \boxed{12},\ 16,\ ...\\\\12=3\cdot4\\\\\text{therefore}\\\\\dfrac{2}{3}=\dfrac{2\cdot4}{3\cdot4}=\dfrac{8}{12}\\\\\dfrac{3}{4}=\dfrac{3\cdot3}{4\cdot3}=\dfrac{9}{12}\\\\2\dfrac{2}{3}+12\dfrac{3}{4}=2\dfrac{8}{12}+12\dfrac{9}{12}=(2+12)+\dfrac{8+9}{12}=14+\dfrac{17}{12}\\\\=14+1\dfrac{5}{12}=15\dfrac{5}{12}[/tex]