Answer:
19/90
Step-by-step explanation:
0.2(1)
We know that most recurring decimals like this have a 9
We know that it can't be anything over 99, or else all digits will repeat:
0.212121....
It will be a number over 90, which will be 19/90
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
Use number properties to simplify the following expression.
-5 + (5 + 3)
In the box below, show each step in simplifying the expression and explain which property you used in each step.
Answer:
-5 + (5 + 3) =(-5 + 5) + 3 = 0 + 3 = 3[tex]\\ \sf\longmapsto -5+(5+3)[/tex].
Remove brackets[tex]\\ \sf\longmapsto -5+5+3[/tex]
[tex]\\ \sf\longmapsto (-5+5)+3[/tex]
[tex]\\ \sf\longmapsto 0+3[/tex]
[tex]\\ \sf\longmapsto 3[/tex]
Trigonometric ratios
class 9
please answer my questions
Step-by-step explanation:
Hi there!
Please see the answer in the picture.
Hope it helps!
1. Approach
One is given a trigonometric equation with and one is asked to prove that it is true. Using the attached image, combined with the knowledge of trigonometry, one can evaluate each trigonometric function. Then one can simplify each ratio to solve. To yield the most accurate result, one has to each of the ratios in a fractional form, rather than simplifying it into a decimal form. Remember the right angle trigonometric ratios, these ratios describe the relationship between the sides and angles in a right triangle. Such ratios are as follows,
[tex]sin(\theta)=\frac{opposite}{hypotenuse}\\\\cos(\theta)=\frac{adjacent}{hypotenuse}\\\\tan(\theta)=\frac{opposite}{adjacent}\\\\csc(\theta)=\frac{hypotenuse}{opposite}\\\\sec(\theta)=\frac{hypotenuse}{adjacent}\\\\cot(\theta)=\frac{adjacent}{opposite}[/tex]
Please note that the terms (opposite) and (adjacent) are relative to the angle uses in the ratio, however the term (hypotenuse) refers to the side opposite the right angle, this side never changes its name. Use these ratios to evaluate the trigonometric functions. Then simplify to prove the identity.
2. Problem (9)
[tex]\frac{sin(60)+cos(30)}{1+sin(30)+cos(60)}=sin(60)[/tex]
As per the attached image, the following statements regarding the value of each ratio can be made:
[tex]sin(60)=\frac{\sqrt{3}}{2}\\\\cos(30)=\frac{\sqrt{3}}{2}\\\\sin(30)=\frac{1}{2}\\\\cos(60)=\frac{1}{2}[/tex]
Substitute,
[tex]\frac{sin(60)+cos(30)}{1+sin(30)+cos(60)}=sin(60)[/tex]
[tex]\frac{\frac{\sqrt{3}}{2}+\frac{\sqrt{3}}{2}}{1+\frac{1}{2}+\frac{1}{2}}=\frac{\sqrt{3}}{2}[/tex]
Simplify,
[tex]\frac{\frac{\sqrt{3}}{2}+\frac{\sqrt{3}}{2}}{1+\frac{1}{2}+\frac{1}{2}}=\frac{\sqrt{3}}{2}[/tex]
[tex]\frac{\frac{2\sqrt{3}}{2}}{1+\frac{1}{2}+\frac{1}{2}}=\frac{\sqrt{3}}{2}[/tex]
[tex]\frac{\frac{2\sqrt{3}}{2}}{1+1}=\frac{\sqrt{3}}{2}[/tex]
[tex]\frac{\sqrt{3}}{1+1}=\frac{\sqrt{3}}{2}[/tex]
[tex]\frac{\sqrt{3}}{2}=\frac{\sqrt{3}}{2}[/tex]
Thus, this equation is true.
2. Problem (10)
Use a similar strategy to evaluate this equation,
[tex]\frac{1-cos(30)}{sin(30)}=\frac{1-cot(60)}{1+cot(60)}[/tex]
Use the attached image to evaluate the ratios.
[tex]cos(30)=\frac{\sqrt{3}}{2}\\\\sin(30)=\frac{1}{2}\\\\cot(60)=\frac{1}{\sqrt{3}}[/tex]
Substitute,
[tex]\frac{1-cos(30)}{sin(30)}=\frac{1-cot(60)}{1+cot(60)}[/tex]
[tex]\frac{1-\frac{\sqrt{3}}{2}}{\frac{1}{2}}=\frac{1-\frac{1}{\sqrt{3}}}{1+\frac{1}{\sqrt{3}}}[/tex]
Simplify,
[tex]\frac{1-\frac{\sqrt{3}}{2}}{\frac{1}{2}}=\frac{1-\frac{1}{\sqrt{3}}}{1+\frac{1}{\sqrt{3}}}[/tex]
[tex]\frac{\frac{2-\sqrt{3}}{2}}{\frac{1}{2}}=\frac{1-\frac{1}{\sqrt{3}}}{1+\frac{1}{\sqrt{3}}}[/tex]
[tex]\frac{\frac{2-\sqrt{3}}{2}}{\frac{1}{2}}=\frac{\frac{\sqrt{3}-1}{\sqrt{3}}}{1+\frac{1}{\sqrt{3}}}[/tex]
[tex]\frac{\frac{2-\sqrt{3}}{2}}{\frac{1}{2}}=\frac{\frac{\sqrt{3}-1}{\sqrt{3}}}{\frac{\sqrt{3}+1}{\sqrt{3}}}[/tex]
[tex]2-\sqrt{3}=\frac{\frac{\sqrt{3}-1}{\sqrt{3}}}{\frac{\sqrt{3}+1}{\sqrt{3}}}[/tex]
[tex]2-\sqrt{3}=\frac{\sqrt{3}-1}{\sqrt{3}}*\frac{\sqrt{3}}{\sqrt{3}+1}}[/tex]
[tex]2-\sqrt{3}=\frac{\sqrt{3}-1}{\sqrt{3}+1}[/tex]
Rationalize the denominator,
[tex]2-\sqrt{3}=\frac{\sqrt{3}-1}{\sqrt{3}+1}[/tex]
[tex]2-\sqrt{3}=\frac{\sqrt{3}-1}{\sqrt{3}+1}*\frac{\sqrt{3}-1}{\sqrt{3}-1}[/tex]
[tex]2-\sqrt{3}=\frac{(\sqrt{3}-1)^2}{3-1}[/tex]
[tex]2-\sqrt{3}=\frac{3-2\sqrt{3}+1}{2}[/tex]
[tex]2-\sqrt{3}=\frac{4-2\sqrt{3}}{2}[/tex]
[tex]2-\sqrt{3}=2-\sqrt{3}[/tex]
Therefore, this equation is also true.
3x^3(4x^4)=?
i need this plz
Answer:
12x^7.
Step-by-step explanation:
3x^3(4x^4)=
3*4 * x^(3+4)
= 12x^7.
Chocolate bars come in packs of 8 and graham crackers come in packs of 12. What is the smallest number of chocolate bars and graham crackers we would need to buy so we don't have any left over?
Answer:
3 chocolate bars, and 2 graham crackers
Someone forgot the marshmallows...... :P
Step-by-step explanation:
Chocolate bars = 8 pack
Graham Crackers = 12pack
To have no crackers or chocolate left over, we need to find LCM
Factors of 8:
8, 16, 24, 32, 40, 48, 56, 72....
Factors of 12:
12, 24, 36, 48, 60, 72
The smallest LCM is 24
Chocolate bars:
24/8 = 3
Graham Crackers:
24/12 = 2
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
Answer:
3 packs of chocolate and 2 packs of crackers
Step-by-step explanation:
the lowest common multiple of 8 and 12 is 24. We can determine this by prime factorization:
Prime factors of 8: 2 x 2 x 2
Prime factors of 12: 2 x 2 x 3
multipyling the bottom rungs of our factor tree we get: 2 x 2 x 2 x 3 = 24.
If you need me to draw the factor tree, just ask.
15. What is the length of segment FG
Answer:
10.49
Step-by-step explanation:
FG= squareroot(10)(11) =10.49 took quiz too
Geometry I need help someone help me
Answer:
fohohcoufohohcouvhop
Step-by-step explanation:
typing mistake sorry
[tex]\\ \sf\longmapsto x+73=90[/tex]
[tex]\\ \sf\longmapsto x=90-73[/tex]
[tex]\\ \sf\longmapsto x=17[/tex]
Why?
Sum of two complementary angles is 90°
Ben wants to get a 94 in math class. His grade will be the average of two test scores. He scored an 89 on the first test. What grade does Ben need to get on his second test to meet his goal?
Answer:
Ben needs to get a 99% on his second test
Step-by-step explanation:
The average is the sum of both test scores, divided by the total number of test scores (2).
Let x by the grade Ben must receive on his second test.
(89 + x)/2 = 94
Multiply by 2 on both sides
89 + x = 188
Subtract 89 on both sides
x = 99
Check work:
(89 + 99)/2 = 188/2 = 99
Answer: 99
Concept:
Here, we need to know the idea of the average value.
In mathematics, average refers to the sum of a group of values divided by n, where n is the number of values in the group.
Average = Sum of value / number of values
Solve:
Given information
Scoring on first test = 89
Scoring on second test = x
Number of tests = 2
Average = 94
Given expression
Average = Sum of value / number of values
Substitute values into the expression
94 = (89 + x) / 2
Multiply 2 on both sides
94 × 2 = (89 + x) / 2 × 2
188 = 89 + x
Subtract 89 on both sides
188 - 89 = 89 + x - 89
[tex]\boxed{x=99}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
I WILL GIVE BRAINLIEST!! NO LINKS PLZ
4) Simplify.
Answer: [tex]\frac{\sqrt{5}}{6}[/tex]
==================================================
Work Shown:
[tex]\frac{\sqrt{10}}{3\sqrt{8}}\\\\\frac{\sqrt{10}*\sqrt{8}}{3\sqrt{8}*\sqrt{8}}\\\\\frac{\sqrt{10*8}}{3\sqrt{8*8}}\\\\\frac{\sqrt{80}}{3\sqrt{64}}\\\\\frac{\sqrt{80}}{3*8}\\\\\frac{\sqrt{16*5}}{24}\\\\\frac{\sqrt{16}*\sqrt{5}}{24}\\\\\frac{4*\sqrt{5}}{24}\\\\\frac{\sqrt{5}}{6}\\\\[/tex]
Note: In the second step, I multiplied top and bottom by [tex]\sqrt{8}[/tex] to rationalize the denominator.
Answer:
square root of 5 over 6 or 0.37267799…
Step-by-step explanation:
Multiply the numerator and denominator by the conjugate.
Using 20 boxes of nails a carpenter was able to finish 40 bird houses. Write an
equation that can be used to express the relationship between the total number of
birdhouses completed(t)and the boxes of nails(b) used.
Help ASAP!
Answer: 20 times 2 equal 40/ 40 divided by 2 is 20
Step-by-step explanation: Both of them should help you find the answer
y is inversely proportional to the square root of x. When y=7, x= 2.25. Write y in terms of x.
Answer:
y(x)=10.5/sqrt(x)
Step-by-step explanation:
Since y is inversely proportional to the square root of x, it can be written as y=a/sqrt(x). To compute a, we will use the point given in the question (2.25,7). 7=a/sqrt(2.25), a=10.5. The function is y(x)=10.5/sqrt(x)
all I've found is 1 but how do I work that out properly beaides guess and check
Answer:
1
Step-by-step explanation:
(1-x)/x=0
or, 1-x=0
or, -x=-1
or, x=1
Answer:
F(x) = 0 when x=1
Step-by-step explanation:
We need the numerator to equal zero
1-x = 0
Add x to each side
1-x+x = 0+x
1 =x
The denominator cannot equal zero( The denominator does not equal zero when x =1)
F(x) = 0 when x=1
Which expression is equivalent to 2(14x-3y+28+12.2-5y-17.5)
Answer:
28x-16y+45.4
Step-by-step explanation:
Add up all the variables inside the bracket by first grouping like terms
Then, multiply through by 2 ✅✅
Solve: MXC multiplied by IV. Show your answer in standard form. Standard Roman Number Numeral 1 1 5 V 10 50 L 100 C 500 D 1,000 M X-003 O A) 4,060 OB) 4,360 OC) 4,440
Answer:
4360
Step-by-step explanation:
MXC is 1090 and a IV is 4 so 1090 x 4 is 4360
14.
Which is the most reasonable measure for the length of
a bicycle?
C. 2 cm
B. 2 m
A. 2 mm
D. 2 km
Answer:
B 2 m
Step-by-step explanation:
2 cm and 2 mm are way to small they are less than the size of a cell phone
2 km is way to large it is larger than a car
explanation would be appreciated. i don’t understand
Answer:
[tex]28\sqrt{3}[/tex]
Step-by-step explanation:
The area of the big triangle is 1/2 b h = 1/2*6*(12^2 = 6^2 + x^2)
that ends up being [tex]\sqrt{108} = 36\sqrt{3}[/tex]
the small triangle are needs to be subtracted....
[tex]\frac{\left(4\cdot \:sin\left(90\right)\right)}{sin\left(30\right)}[/tex] that is the length of the unknown side...
1/2 B * h of that triangle get you to [tex]8\sqrt{3}[/tex]
just subtract the two areas
Answer:
(B) 28√3
Step-by-step explanation:
The area of quadrilateral ABED is equal to the area of triangle CDE subtracted from the area of triangle ABC.
Area of triangle CDE:
Triangle ABC is equilateral. All sides have length 12.
AB = BC = AC = 12
BE = 8
BE + EC = BC
8 + EC = 12
EC = 4
In an equilateral triangle, all angles measure 60°.
m<C = 60°
m<CDE = 30°
Triangle CDE is a 30-60-90 triangle.
DE = EC√3
DE = 4√3
area of triangle CDE = bh/2
area of triangle CDE = (EC)(DE)/2
area of triangle CDE = (4)(4√3)/2
area of triangle CDE = 8√3
Area of triangle ABC:
Side AC is a base of triangle ABC.
AC = 12
(1/2)AC = 6
The altitude of triangle ABC from side AC to vertex B measures
h = 6√3
area of triangle ABC = bh/2
area of triangle ABC = (AC)(h)/2
area of triangle ABC = (12)(6√3)/2
area of triangle ABC = 36√3
area of quadrilateral ABED = area of triangle ABC - area of triangle CDE
area of quadrilateral ABED = 36√3 - 8√3
area of quadrilateral ABED = 28√3
Can anyone please help me with this thank you
Answer:
x= 0, and x=4
Step-by-step explanation:
x² -x = 3x, we can subtract 3x from both sides
x² -x -3x = 0, combine like terms
x² -4x = 0 , factor x
x *( x-4) = 0, if the product of 2 numbers equals 0 at least one is 0
x=0 and
x-4 = 0, add 4 to both sides
x= 4
Answer:
x=4 simple thing with all problems like this, is if it has a exponent, then half the exponent and add it to the numerical digit on the right of the equals sign, and you have you answer
Step-by-step explanation:
A hardware store ordered 13 packs of
nails from a supplier. Each pack contains
155 nails. How many nails did the store
order?
Answer =530
Guys pleaseee help!!
Calculating a Rate of Change
Try
What is the vertical change from Point A to Point B?
10
y
9
What is the horizontal change from Point A to Point B?
8
7
6
What is the rate of change shown on the graph? Give
the answer as a decimal rounded to the nearest tenth.
if necessary
5
4
3
B
2
A
1
10
8
9
1
2
4
5
3
Done
Answer:
What is the vertical change from Point A to Point B? 1
What is the horizontal change from Point A to Point B? 2
What is the rate of change shown on the graph? Give
the answer as a decimal rounded to the nearest tenth.
if necessary: 0.5
Step-by-step explanation:
The rate of change, as the own name suggest, is the rate at which the function change its value. The function, in this case is changing with a rate of 0.5 because to each unit that x grows, y grows the half part of it.
I NEED HELP !!!
Find the measure of SR.
A.10
B.8
C.7
D.11
The measure of SR is 10.
The given figure has two secant segments and two external segments.
QU = secant segment
QS = secant segment
QP = external segment of QU
QR = external segment of QS
We need to find the measure of SR.
What is the theorem when two secant segments share the same endpoint outside a circle?It states that the product of the length of one secant segment and the length of its external segment equals the product of the length of the other secant segment and the length of its external segment.
Applying the secant theorem in the given figure.
QU x QP = QS x QR
( 9 + 7 ) x 9 = (8 + 3X-5) x 8
16 x 9 = (3 + 3X) x 8
144 = 24 + 24X
144 - 24 = 24X
120 = 24X
X = 120 / 24
X = 5
Now Putting X = 5 in SR = 3X-5
We get,
SR = 3 x 5 - 5
SR = 15 - 5
SR = 10
After applying the secant segment theorem we got the measure of SR as 10.
Learn more about secant segments in a circle here:
https://brainly.com/question/18760361
#SPJ5
Which value of x satisfies the equation
Answer:
Does the answer help you?
Pls help I tried basic answers like 50+50+80 =180 but it’s wrong so pls help
Answer:
x = 65 degrees
Step-by-step explanation:
x° + x° + 50° = 180°
2x + 50° = 180°
2x = 180° - 50°
2x = 130°
x = 130°/2
x = 65°
Suppose the following equation is true:
3^x=81^y
What is the connection between x and y?
Answer:
x=4y
Step-by-step explanation:
3^x=3^4y
x=4y
am I correct?
which answer is right?
Answer:
i think A
Step-by-step explanation:
the ratio of thomson's age to racheal's age is 2:3.racheal is 24 years old. how old is thomson?
2:3
Given Racheal = 24 years
Thomson = 2/3×24
= 2×8
= 16 years
Must click thanks and mark brainliest
Which equation represents a line which is parallel to the line y=7/6x−6?
7y-6x= -14
6x + 7y = 56
7x + 6y = 18
7x - 6y = -48
Answer:
6x+7y=56
Step-by-step explanation:
In order to have an equation that is parallel to another the slopes multiplied by one another must equal -1. In this case, the first slope is [tex]\frac{7}{6}[/tex] . So [tex]\frac{7}{6}[/tex]×what = -1
Normally you can just flip the numerator and denominator and add the opposite sign. So we can do that here. [tex]-\frac{6}{7} *\frac{7}{6} =-1[/tex]. So the equation should have [tex]-\frac{6}{7}[/tex].
But none of the answers obviously have that slope. If you try the second one, which looks different from the rest and will give you a negative x when you subtract it from both sides. Then you can divide by 7, you get [tex]y=-\frac{6}{7}x +8[/tex].
Factor Z squared minus 3Z -18
Answer:
z^2-3z-18
=(z^2+3z)+(-6z-18)
=z(z+3)-6(z+3)
=(z+3)(z-6)
for a mathematical statement to be an equation, the quantities on each side of an equal sign must be?
Answer:
equal or balanced
Step-by-step explanation
the = demonstrates the amounts need to be the same
Answer: Balanced.
Step-by-step explanation:
For an equation each side shall be equal (balanced) or else it's NOT an equation.
what is twelve less than a variable
Answer:
x-12
Step-by-step explanation:
Let the variable be x
12 less than
x-12
really need help to do step by step
Answer:
x/4+10=2
x/4=2-10
x/4=-8
x=-8 x 4
x=-32
Step-by-step explanation:
Select the type of equations.
consistent
equivalent
Inconsistent
Answer:
Step-by-step explanation:
This is a consistent dependent system. This means that the lines will eventually intersect in one place.
Inconsistent systems are parallel lines and equivalent systems represent a line completely overlapped by another line because they have the same equation.
