Answer:
a. 1/3pi+kpi and 2/3pi+kpi
Step-by-step explanation:
2Sec²x
=2+2tan²x-(tan²x)²=-1
Let tan²x=u
-u²+2u+2=-1
-u²+2u+3=0
u²-2u-3=0
(u+1)(u-3)=0
u=-1,u=3
(tan x)²=-1(No solution)
(tan x)²=3
>>tan x=±sqrt(3)
I) tan x=sqrt(3)
>>tan(pi/3)=sqrt 3
Tan(pi+A) =tanA
Tan(pi+pi/3)=tan(pi/3)
>>tan(4/3pi)=sqrt(3)
>>x=4/3pi and 1/3pi
General solution: 1/3pi+kpi
ii) tan x=-sqrt(3)
x=2/3pi(At 2nd quadrant)
x=5/3pi(at 4th quadrant)
General solution: 2/3pi+kpi
Find the equivalent exponential expression. (5^5)^4
Answer:
5^20
Step-by-step explanation:
since you have brackets around (5^5) you can multiply the exponents. if you think about it what you're essentially doing is
(5 * 5 * 5 * 5 * 5) * (5 * 5 * 5 * 5 * 5) * (5 * 5 * 5 * 5 * 5) *
(5 * 5 * 5 * 5 * 5)
which is why you can multiply the exponents to simplify
What is the sum of the polynomials?
(6x+7+x²) + (2x²-3)
-x²+6x+4
3x²+6x+4
9x + 4
9x² +4
Answer:
3x^2 + 6x + 4
Step-by-step explanation:
6x + 7 + x^2 + 2x^2 - 3 = 3x^2 + 6x + 4
Answer:
3x²+6x+4
Step-by-step explanation:
Given:
(6x+7+x²) + (2x²-3)
Aim:
To add the polynomials
Solution:
Removing brackets first:
6x+7+x²+2x² - 3Collecting like terms to each other,
6x+7-3+2x²+x²Simplifying,
6x+4+3x²Rewriting it as,
3x²+6x+4Second choice is accurate.
Please Simplify 3√7 / 5√7
Step-by-step explanation:
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2. If D is the midpoint of segment AB, explain using transformations why AC = BC. Use complete sentences. (10 points)
AC is equal to BC by the corresponding side of a congruent triangle.
What is a line segment?
A line segment is a straight line with finite length, and thus, have to endpoints(points on either ends).
The midpoint of a line segment means a point that lies in the mid of the given line segment.
If D is the midpoint of segment AB, then AD = BD.
So in a triangle ACD and BCD
AD = BD (by midpoint D)
angle ADC = angle BDC = 90
CD = CD (common)
Therefore, triangle ACD and BCD are congruent.
Hence, AC = BC by the corresponding side of a congruent triangle.
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Label the vertices and all the elements needed. Find x. Give reasons!
Answer:
Step-by-step explanation:
Divide : (8a^2b^4 - 20a^4b^5 + 48a^6b^6) by 4a^2b^4
Hey there ! please refer to the attachment .
I hope its help you !
how many didgits are in 136.08
Answer:
5
Step-by-step explanation:
Count the digits.
Which inequality is shown in this graph?
OA. ys-3x+3
OB. y2-3x+3
OC. ys 3x+3
OD. y23x+3
Answer:
A
Step-by-step explanation:
The line is shaded below, so we can eliminate B and D.
Also, the line has negative slope, so this eliminates C.
The inequality of the graph is y ≤ -3x + 3.
The correct option is A.
What is inequality?In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.
The inequality graph has two points on the line (0, 2) and (2, -3).
And the shaded region of the graph is left to the line made by points (0, 2) and (2, -3).
The line passing through the points (0,2) and (2,-3) can be written in a slope-intercept form as:
y = mx + b
where m is the slope and b is the y-intercept.
The slope of the line is given by:
m = (y2 - y1) / (x2 - x1) = (-3 - 2) / (2 - 0) = -5/2
The y-intercept can be found by substituting the coordinates of either point into the equation:
y = mx + b
2 = (-5/2)(0) + b
b = 2
So the equation of the line is:
y = (-5/2)x + 2
The shaded region of the graph is to the left of this line. Since the line has a negative slope, any point below the line will satisfy the inequality y ≤ -3x + 3. Therefore, the correct answer is A.
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in the diagram, triangle ABC is similar to triangle EDC. a. is line AB parallel to line DE? b. show that triangle ACD is similar to triangle ECB. c. find the measure of angle CAD. d find line ED. e. find line AD explain your reasoning
The measure of the angle CAD is 40 degrees, the length of ED is 12 units, and the length of AD is 12 units.
What is the similarity law?It is defined as the law to prove that the two 2-dimensional have the same shape, but it is not compulsory to have the same size. The ratio of the corresponding sides is in the same proportions and the corresponding angles are congruent.
Triangle ABC ~ EDC
Angle ACD = Angle BCE = 90 degree (vertically opposite angle)
Angle ACB = Angle DCE = 90 degree (vertically opposite angle)
BE ║ AD
Angle EBC = Angle CDA = 40 degree (alternative angles)
Triangle ABC ~ Triangle EDC
Angle ABC = Angle CDE
Angle BAC = Angle DEC
∴ AB ║ DE
Triangle ACD ~ Triangle ECB
Angle EBC = Angle CDA and
Angle BEC = Angle CAD
∴ Triangle ACD ~ Triangle ECB
Angle A + Angle E = 180 degree
∠x + 50 + 50 + ∠x = 180
∠x = 40
Angle CAD = 40 degree
We know,
Angle A = Angle E = Angle B = Angle D = 90 degree
So ABCD is a square
AB = ED = 12
AD = AB = BE = ED = 12
Thus, the measure of the angle CAD is 40 degrees, the length of ED is 12 units, and the Length of AD is 12 units.
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What is the slope of a line that is parallel to the line y = 3/4x + 2?
Answer:
in this form the first one next to the x is the slope and the added value is the y intercept
if something is parrell that means the same slop so
3/4
Hope This Helps!!!
r,u,t,s are positive
RXS=15
SXT=3
TXV=7
RXV=??
Answer:
35
Step-by-step explanation:
R × S = 15 could be 5 × 3 = 15, 3 × 5 = 15
15 × 1 = 15, 1 × 15 = 15
S ×T =3 From our previous step we can see that S could be 1 or 3 or 5 or 15.
Given that S×T =3, will make sense that S is 1 or 3
If S is 1 then T is 3 and if S is 3 then T is 1, so multiplied will give 3.
T×V=7 From previous step we see that T could be 1 or 3.
Since T×V = 7 it will make sense that T is 1, and therefore V is 7.
T ×V = 7, S ×T =3, R × S = 15, R × V = ??
1 × 7 = 7, S ×1 = 3, R × 3 = 15, 5 × 7 = ??
3 ×1 = 3, 5 × 3 = 15, 5 × 7 = 35
ignore the answer i clicked on, i did not mean to click it
Answer:
20√2Step-by-step explanation:
The diagonal of a square is given as, √2 × side. Rearranging this formula to calculate the side of the square, we get, side = diagonal/√2 = (√2 × diagonal)/2 . Thus, the perimeter of the square can be calculated using the formula, P = 2√2 × diagonal.
Diagonal = 5 * 2 = 10
P = 2√2 * 10
P = 20√2
Marilyn is having shelves installed to create a corner pantry. the length of one wall is 21 inches and the length of the other wall is 25 inches. the contractor who is making the shelves, which are shaped like right triangles, needs to know the measure of the angle opposite the short side of the pantry, m∠a. what is the measure of that angle? round your answer to the nearest degree.
Answer:
He says the answer is 40°
Step-by-step explanation:
Answer is on brainly, here is the link to the answer. Hope it helps with your question!
https://brainly.com/question/4354055?referrer=searchResults
Hope this helps!
If not, I am sorry.
im always having problems with this i need someone to explain please
For every meter there are 3.281 feet. The perimeter of the yard is 188ft. Divide 188 by 3.281 and you get 57.3 (rounded to 1dp). Round that up to the nearest meter and you get 58. So, Mr Smith needs 58 meters of fencing for his yard.
Estimate the solution to the following system of equations by graphing.
Line I is a perpendicular bisector
Line I is a perpendicular bisector because it bisects another line at right angles via the point of intersection or midpoint. See the Perpendicular Bisector Theorem below.
What is the perpendicular bisector theorem?According to the theorem of perpendicular bisector, any locus on the perpendicular bisector is equidistant from the terminal points of the line segment on which it is created.
Thus, Line I is a perpendicular bisector because it bisects another line at right angles via the point of intersection or midpoint. See the attached image.
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Find the length of the unknown side. Round your answer to the nearest whole number.
Image of a right triangle with legs labeled 7 meters each. The hypotenuse is unknown.
7 meters
9 meters
10 meters
12 meters
Answer: 10
Step-by-step explanation:
√( 7^2 + 7^2 ) = 10
Parallelogram ABCD has vertices: A(-3, 1), B(3, 3), C(4, 0), and D(-2, -2). In two or more complete sentences, explain how you can use the coordinates of the vertices to prove that parallelogram ABCD is a rectangle.
please help
Step-by-step explanation:
via the distance formula (based on Pythagoras) I can prove that ABC is a right-angled triangle, and that ADC is fully congruent to ABC.
so, together these 2 triangles (joined at their Hypotenuses, the diagonal AC) build a rectangle.
The graph below shows the solution to which system of inequalities?
Answer:
C
Step-by-step explanation:
The horizontal line, y=2, is solid and shaded above, so it represents
[tex]y \geqslant 2[/tex]
The slanted line, y=x is dashed and shaded below, so it represents y<x.
Answer
Answer is A
Step-by-step explanation:
When you eat certain foods, sugar is immediately released into your bloodstream. many doctors say kids should only take in 6 teaspoons (24 grams) of added sugar each day. jack is making lemonade for his school and wants to follow that recommendation. he wants to make 206 servings, following the recommendation, how many grams of sugar will he use?
Answer:
4,944
Step-by-step explanation:
If x is 300 percent of 25 and y is 25 percent more than
40, the x is what percent of y?
al 50%
c) 66.5%
b) 75%
d) 150%
Anyone here to help me!!!
Answer:
d) 150%
Step-by-step explanation:
[tex]x=25*300\%=25*3=75\\[/tex]
[tex]y=25\%*40+40=50[/tex]
[tex]x/y*100\%=75\div50*100\%=150\%[/tex]
Answer:d
150%
Step-by-step explanation:
A man bought a car for Gh55,000.00 and sold it for Gh65,000.00. Find the percentage gain.
Answer:
18.18%
Step-by-step explanation:
(65000-55000)/55000×100
Shape a is enlarged to give shape b a) what is the scale factor of the enlargement? b) mark with a cross the centre of enlargement
The scale factor of the enlargement will be 3. Then the center of enlargement is marked in the diagram.
What is dilation?Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered.
Shape A is enlarged to give shape B.
Then the scale factor of the enlargement will be
⇒ 3 / 1
Then the center of enlargement is marked in the diagram.
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Construct a rectangle with sides 6cm and 4cm.
Answer:
Step-by-step explanation:
Answer:
First, draw a line segment AB = 6 cm.Draw a ray AX with pencil and compass such that ∠BAX = 90°. Draw an arc of 4 cm with point A which intersects AX at D.Similarly, draw ray BY such that ∠ABY = 90°. Draw an arc of 4 cm with point B which intersects BY at C.Join CD.Thus ABCD is the required rectangle.1 2 3 4 5 6 7 8 9 10 11 12 13
Mark this and return
If a new data point at 12 is added to the graph, which will
be true?
O The mean will increase, and the median will stay the
same.
O The median will increase, and the mean will stay the
same.
O The mean will increase more than the median, but
both will increase.
O The median will increase more than the mean, but
both will increase.
Answer:
The mean will increase more than the median, but both will increase.
[third option listed]
Step-by-step explanation:
the median of a data set is the number in the middle [when listed from lowest to highest in value]
1 2 3 4 5 6 7 8 9 10 11 12 13
is the current median
let's consider what adding 12 would mean--it would mean that we move the median slightly higher [further along in the data set] because there are more numbers (but let's try this out to confirm:)
1 2 3 4 5 6 7 8 9 10 11 12 12 13
[if a median placement is shared between two numbers, the mean/average of those two numbers is taken, and that is considered to be the median]
so, 7.5 is the current median
(this is an increase of 0.5)
--
the mean of a data set is what we commonly refer to as the "average"
[you find this value by adding all of the numbers in the data set together and dividing by the number of terms in the data set]
1 2 3 4 5 6 7 8 9 10 11 12 13
mean of original data set:
1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 [= 91]
_______________________________________
13
[91 ÷ 13 = 7]
because our number is greater than our original mean [12 > 7], we know that the mean must increase:
[91 + 12 = 103]
[103 ÷ 14 ≈ 9.36]
[we had an increase of 2.36]
so, median increased by 0.5, mean increased by 2.36
so, both values increased, whilst the mean increased by more than the median [as to be expected]
you could also express this as "The mean will increase more than the median, but both will increase." [third option listed]
hope this helps!! :)
erved,
The graph of function fis shown on the coordinate plane. Graph the line representing function g, if g is defined as shown below.
g(x) = 2f(x-1)
Using the graph attached, If g(x) = 2f(x-1), the graph of the function will be: g(x) = x - 7.
What is the function about?Using the graph, the function is:
f(x-1) =1/2 (x-1) - 3
f(x-1) = 1/2x - 1/2 - 3/1
f(x-1) = 1/2x - 7/2
So:
g(x) = 2f(x-1)
g(x) = 2 (1/2x - 7/2)
g(x) = x - 7
Therefore,:
At x = 0, y = -7
y = 0, x = -7
Thus, Using the graph attached, If g(x) = 2f(x-1), the graph of the function will be: g(x) = x - 7.
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Got it right on Plato/Edmentum UωU <3
Suppose the u.s. government put a 'special 20 percent luxury tax' on the retail price of expensive and fancy yachts in order to collect more taxes from boat owners. assume the price elasticity for these yachts is elastic at 2.50. conclusion: we can probably expect that yacht sales will go down and the government will not collect lots of new tax revenues.
True. We can probably expect that yacht sales will go down and the government will not collect lots of new tax revenues.
It is given that the US government has put a 20% luxury tax and the price elasticity for these yachts is elastic at 2.50.
Due to the new tax on luxury goods, it can be estimated that the sales of yachts go down as the maximum retail price of the yachts will become more expensive. This can mean that fewer people than before will be able to afford the yachts. Due to fewer sales, the government will not have enough tax revenues.
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I am greater than 62 but less than 67
Can someone help me on this please
Answer:
17.7 (2 dp)
Step-by-step explanation:
[tex] \sqrt{ {16}^{2} + {7.5}^{2} }[/tex]
Ann reads 15 pages in 30 minutes. how many pages she can read in 2 hours
Answer:
60
Step-by-step explanation:
2hrs = 120
120/30= 4
4×15=60
Answer:
60 pages :)
Step-by-step explanation:
First we turn the hours into minutes to make it easier :)
1 hr = 60 minutes
2 hrs = 120 minutes
Now that we have done that, we divide :)
120/30 =4
And now we multiply 1 more time :)
4 x 15 = 60
Have an amazing day!!
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