Answer:
Exact Form d=3/2 or -4
Decimal Form d=1.5 Mixed (Number)(Form):1 1/2 or -4
Hoped I helped <3
Step-by-step explanation:
someone please help me on my math 2 of them are on my page. thanks:)
Answer:
I will but there are no problems/questions shown
Step-by-step explanation:
I need help with part c). Given that tan(pi/8)= sqrt(2)-1. Please provide a detailed answer.
[tex]b)\\\tan x=\dfrac{\sin x}{c\os x}\\\\\tan^2x=\dfrac{\sin^2x}{\cos^2x}=\dfrac{2\sin^2x}{2\cos^2x}=\dfrac{\sin^2x+\sin^2x}{\cos^2x+\cos^2x}\\\\=\dfrac{\sin^2x+\sin^2x+\cos^2x-\cos^2x}{\cos^2x+\cos^2x+\sin^2x-\sin^2x}=\dfrac{(\sin^2x+\cos^2x)-(\cos^2x-\sin^2x)}{(\cos^2x+\sin^2x)+(\cos^2x-\sin^2x)}\\\\=\dfrac{1-\cos2x}{1+\cos2x}\\\\\text{Used}:\\\\\sin^2x+\cos^2x=1\\\\\cos^2x-\sin^2x=\cos2x[/tex]
[tex]\tan^2\left(\dfrac{7\pi}{8}\right)=\dfrac{1-\cos\left(2\cdot\dfrac{7\pi}{8}\right)}{1+\cos\left(2\cdot\dfrac{7\pi}{8}\right)}=\dfrac{1-\cos\left(\dfrac{7\pi}{4}\right)}{1+\cos\left(\dfrac{7\pi}{4}\right)}=(*)\\\\\cos\left(\dfrac{7\pi}{4}\right)=\cos\left(2\pi-\dfrac{\pi}{4}\right)=\cos\left(-\dfrac{\pi}{4}\right)=\cos\left(\dfrac{\pi}{4}\right)=\dfrac{\sqrt2}{2}\\\\(*)=\dfrac{1-\frac{\sqrt2}{2}}{1+\frac{\sqrt2}{2}}=\left(\dfrac{2}{2}-\dfrac{\sqrt2}{2}\right):\left(\dfrac{2}{2}+\dfrac{\sqrt2}{2}\right)[/tex]
[tex]=\dfrac{2-\sqrt2}{2}\div\dfrac{2+\sqrt2}{2}=\dfrac{2-\sqrt2}{2}\cdot\dfrac{2}{2+\sqrt2}=\dfrac{2-\sqrt2}{2+\sqrt2}\\\\\text{Use}\ (a+b)(a-b)=a^2-b^2\\\\=\dfrac{2-\sqrt2}{2+\sqrt2}\cdot\dfrac{2-\sqrt2}{2-\sqrt2}=\dfrac{(2-\sqrt2)^2}{2^2-(\sqrt2)^2}\\\\\text{Use}\ (a-b)^2=a^2-2ab+b^2\\\\=\dfrac{2^2-2(2)(\sqrt2)+(\sqrt2)^2}{4-2}=\dfrac{4-4\sqrt2+2}{2}=2-2\sqrt2+1\\\\=(\sqrt2)^2-2(\sqrt2)(1)+1^2=1^2-2(1)(\sqrt2)+(\sqrt2)^2\\\\\text{Use}\ (a-b)^2=a^2-2ab+b^2\\\\=(1-\sqrt2)^2\\\\\text{Therefore}:[/tex]
[tex]\tan^2\left(\dfrac{7\pi}{8}\right)=(1-\sqrt2)^2\to\boxed{\tan\left(\dfrac{7\pi}{8}\right)=1-\sqrt2}[/tex]
[tex]c)\\\tan\left(\dfrac{\pi}{8}\right)=\tan\left(\pi-\dfrac{7\pi}{8}\right)=\tan\left(-\dfrac{7\pi}{8}\right)=-\tan\left(\dfrac{7\pi}{8}\right)\\\\=-(1-\sqrt2)=\sqrt2-1\\\\y=\sin(2x-1)+a\tan\dfrac{\pi}{8}\\\\\text{We know}\ -1\leq\sin(2x-1)\leq1.\\\\y\geq0\ \text{therefore}\ a\tan\dfrac{\pi}{8}\geq1\\\\\text{We have to move the graph at least one unit up}\\\\a(\sqrt2-1)\geq1\qquad\text{divide both sides by}\ (\sqrt2-1)>0\\\\a\geq\dfrac{1}{\sqrt2-1}\cdot\dfrac{\sqrt2+1}{\sqrt2+1}\\\\a\geq\dfrac{\sqrt2+1}{(\sqrt2)^2-1^2}[/tex]
[tex]a\geq\dfrac{\sqrt2+1}{2-1}\\\\a\geq\dfrac{\sqrt2+1}{1}\\\\a\geq\sqrt2+1\\\\Answer:\ \boxed{a=\sqrt2+1}[/tex]
Use inverse operations to solve the equation. -5x=65
Answer: x=-13
Step-by-step explanation:
X= 65/5
X=-13
Checked work .
-5x=65
-5x-13=65
65=65
Which value is equivalent to 40%
Answer:
Step-by-step explanation:
The answer to your question is 2/5,0.4,4/10,
write the sentences below as a mathematical expression.
1. the sum of a number and 9
2. 12 decreased by some number
3. some number decreased by 7
4. twice a number
5. 2 times a number
6. a number dived by 8
7. the quotient of a number and 3
8. double the sum of 8 and a number
1. a+9
2. 12-x
3. x-7
4. 2a
5. 2a
6. a:8
7. a/3
8. 2(8+a)
A classmate is 22 years younger than your instructor. Write an equation that will determine your classmate’s age (y) if given your instructor’s age (x). Use this equation to determine your classmate’s age.
Hey there, we are given quite a lot of information in this problem. First of all, let's make an equation.
y = x - 22
where y = student's age
where x = instructor's age
this equation is correct because x(instructor) - 22 will yield the student's age (y).
If the instructor were 44 years old, the student would be 22 years old.
y = 44 - 22
y = 22
If the instructor were 66 years old, the student would be 44 years old.
y = 66 - 22
y = 44
the graph of y=x2+11x+24
The graph of [tex]y=x^2+11x+24[/tex] is equivalent to the graph of this equation: A. y= (x + 8)(x + 3)
In Geometry, a factored form is a type of quadratic equation that is typically written as the product of two (2) linear factors and a constant;
f(x) = a(x - r)(x - r)
a is the leading coefficient.
r is the roots or x-intercets.
Based on the information provided, we can logically deduce the following quadratic function;
[tex]y=x^2+11x+24[/tex]
By factorizing the quadratic function above completely, we have the following;
[tex]y=x^2+11x+24\\\\y=x^2+8x+3x+24\\\\y=x(x+8)+3(x+8)\\\\y=(x+8)(x+3)[/tex]
Complete Question:
The graph of [tex]y=x^2+11x+24[/tex] is equivalent to the graph of which equation?
y= (x + 8)(x + 3)
y = (x + 4)(x + 6)
y= (x + 9)(x+2)
y = (x + 7)(x + 4)
what is the shortest driving distance from the hospital to the gas station?
Answer:
I'm sorry i couldn't understand your question. If you wanna take it litterally, around the world there is gas station that could be 5 minutes, 15 or 30 minute from a hospital. could you clarify me on your question
The table shows data from a survey about the number of times families eat at restaurants during a week. The families are either from Rome, Italy or New York, New York: Maximum Minimum Q1 Q3 IQR Median Mean σ Rome 16 0 3 13 10 8.5 8 5.4 New York 20 1 4.5 6 1.5 5.5 7.25 5.4 Which of the choices below best describes how to measure the center of this data? Both centers are best described with the mean. Both centers are best described with the median. The Rome data center is best described by the mean. The New York data center is best described by the median. The Rome data center is best described by the median. The New York data center is best described by the mean.
Final answer:
The center of a data set can be measured using the mean or the median. In this case, the Rome data center is best described by the mean, while the New York data center is best described by the median.
Explanation:
The center of a data set can be measured using two common ways: the mean and the median. The mean is found by adding up all the values and dividing by the total number of observations. The median is the middle value, or the number that separates the data into two equal halves. It is generally a better measure when there are extreme values or outliers.
In this case, based on the information provided, the Rome data center is best described by the mean, while the New York data center is best described by the median.
What does The difference of two numbers by 5 look like
Answer:
Step-by-step explanation:
Let the larger number = x
Let the smaller number = y
I can't really tell if I'm reading it correctly, but I think the answer is
x - y = 5
Answer:
Step-by-step explanation:
Suppose you have given two numbers say (x and y ).
Now we can have 3 conditions here:
i . x and y are equal
ii. x is greater than y
iii . y is greater than x .
For x and y are equal : - Difference between two numbers will be zero.
For x and y greater or lesser :- There will be some difference between two numbers x and y. And if this difference between x and y is 5, then it will look like:
x is greater than y
x - y = 5
or
y is greater than x
y - x = 5
twelve athletes are running a race. a gold medal is to be given to the winner, a silver is to be given to the second place finisher, and a bronze medal is to be given to the third place finisher. assume that there are no ties. in how many possible ways can 3 medals be distributed?
Final answer:
There are 1,320 possible ways to distribute the gold, silver, and bronze medals among twelve athletes with no ties.
Explanation:
The student has asked how many possible ways three medals can be distributed among twelve athletes, assuming there are no ties. This can be calculated using permutations since the order of medals (gold, silver, bronze) matters and each medal can only be given once.
For the gold medal, there are 12 potential athletes, for the silver there are 11 remaining athletes (since one has already received gold), and for the bronze, there are 10 athletes left. Therefore, the number of possible ways to distribute the three medals is:
12 (options for gold) × 11 (options for silver) × 10 (options for bronze) = 1,320 possible ways.
I posted this in the math because everyone is here! Please help!
A low level of cardiovascular endurance would likely lead to this health-related problem in a very important muscle:
Anemia
Astigmatism
Heart attack
Osteoporosis
Answer: I believe the answer is C
Step-by-step explanation:
Blaire needs more than 708 total points on assignments in her math class to pass. She only has 236 points and needs to do some extra credit assignments that are worth 59 points each.
59x + 236 > 708
How many extra credit assignments does Blaire need to complete in order to pass?
A.
x > 236
B.
x > 59
C.
x > 472
D.
x > 8
Answer: D) x = 8
Step-by-step explanation: In order to get this answer, you need to keep the 236 and add 59 evry time until you get 708.
Another thing is to multiply 59 by 8, which will give you 472. Now we add 472 and 236 and we get 708.
59 x 8 = 472 + 236 = 708.
56 + 56 + 56 + 56 + 56 + 56 + 56 + 56 = 472 + 236 = 708.
Hope this helped!
Plz mark brainliest!
Answer:
x>8
Step-by-step explanation:
I only answered so the other guy could get brainliest.
factor the expression using GCF 6y+3
Answer:
3(2y+1)
Step-by-step explanation:
First we need to find the factors of each term
6y = 2*3*y
3 = 3*1
The greatest common factor is 3. Take that out and what remains goes inside the parentheses
3(2y+1)
which of the following is equal to 9 • 4?
[tex]\sqrt{9*4}= \sqrt{36} =6[/tex]
A.) [tex]\sqrt{9}*\sqrt{4}=3*2=6[/tex]
B.) 18
C.) [tex]\sqrt{\frac{9}{4}}=\frac{3}{2}[/tex]
D.) 36
Your answer is A
The multiplication of 9 • 4 equals 36, which is the result of adding 9 to itself 4 times.
Explanation:The question 'which of the following is equal to 9 • 4?' is asking us to perform a multiplication operation. In Mathematics, when we multiply two numbers, we are essentially adding one of the numbers to itself the number of times indicated by the other number. Therefore, 9 multiplied by 4, which is written as 9 • 4, is equal to adding 9 to itself 4 times: 9 + 9 + 9 + 9.
Let's do the math:
9 + 9 = 1818 + 9 = 2727 + 9 = 36So, 9 • 4 equals 36. This is a basic multiplication concept that is foundational in math.
Which measurement is the most precise? A) 29 cm B) 28.8 cm C) 28.76 cm D) 28.762 cm
Answer:
A
Step-by-step explanation:
Allison is rolling her hula hoop on the playground. The radius of her hula hoop is 35 \text{ cm}35 cm. What is the distance the hula hoop rolls in 44 full rotations? Round your answer to the nearest \text{cm}cm.
To find the distance the hula hoop rolls in 4 full rotations, we calculate the circumference as 2πr and then multiply by 4. The total distance is then rounded to the nearest centimeter, resulting in 880 cm.
The question asks us to calculate the distance a hula hoop travels in 4 full rotations given its radius. The distance traveled in one rotation is equal to the circumference of the hoop.
To find the circumference, we use the formula C = 2πr, where r is the radius. Since the radius is given as 35 cm, the circumference is 2π×35 cm. To find the total distance for 4 rotations, we multiply the circumference by 4. This gives us 4×2π×35 cm. Using the approximate value of π (3.1416), we can calculate the distance, and then round it to the nearest centimeter.
Circumference C = 2π×35 cm = 219.91 cm
Total distance for 4 rotations = 4×C = 4×219.91 cm = 879.64 cm
Rounded to the nearest centimeter: 880 cm
find the value of x. please explain your answer:)
Answer:
x =16
Step-by-step explanation:
A right angle has 90 degrees.
The two given angles add to 90 degrees
3x + 2 + 40 = 90 Combine the left side
3x + 42 = 90 Subtract 42 from both sides
3x + 42 - 42 = 90 - 42 combine
3x = 48 Divide by 3
3x/3 = 48/3 Do the division
x = 16
Simplify 7/9 • 3/4 • 2/7
Answer:
[tex]\frac{1}{6}[/tex]
Step-by-step explanation:
[tex]\frac{7}{9}[/tex] × [tex]\frac{3}{4}[/tex] × [tex]\frac{2}{7}[/tex]
the 7 on the numerator/ denominator cancel to 1
the 3 and 9 cancel ( 3 → 1 and 9 → 3 )
the 2 and 4 cancel ( 2 → 1 and 4 → 2 )
= [tex]\frac{1}{3}[/tex] × [tex]\frac{1}{2}[/tex] × [tex]\frac{1}{1}[/tex]
multiply the remaining values on the numerators/ denominators
= [tex]\frac{1(1)(1)}{3(2)(1)}[/tex] = [tex]\frac{1}{6}[/tex]
5Y+2-3(4Y)=0
WHAT DOES THIS EQUAL
Answer: The Y in the problem = 2/7, Good Luck!
Step-by-step explanation:
Simplify both sides of the equation!
Answer:
the answer would be one
Step-by-step explanation:
you simply have to put the question in parts that makes it easy use PEMDAS
it is really helpful on math that looks like this
Can someone please help me with this question?
Answer:
A Jones has the best plus minus record
Step-by-step explanation:
The player wants the most "negative" score, which means he was one the ice when his team scored the most points and off the ice when his team was scored upon.
Answer:
11. a. See below. b. E. Simpson
Step-by-step explanation:
11. a. Graphing on the number line
You did a great job on this.
I just used red dots to make them more visible.
===============
11. b. Best plus-minus record
The player with the best plus-minus record is E. Simpson.
His plus-minus record of +9 means that his team has scored more often when he is on the ice than any other player.
explicit formula for 12,19,26,33,40
Answer:
Step-by-step explanation:
The common difference is 7
Since the common difference is 7
a_n = 12+(n-1)7
a_n = 12+7n -7
a_n = 5+7n
What are all the subsets of the set?
{-8,4}
A. Ø, {-8}, {4}
B. {-8}, {4}, {-8, 4}
C. {-8}, {4}
D. Ø, {-8}, {4}, {-8, 4}
The correct answer is D, which includes the empty set, each individual element as a subset, and the set itself containing both elements {-8, 4}.
Explanation:The question asks for all subsets of the set {-8, 4}. A subset of a set includes any set formed from its elements, including the empty set and the set itself. Therefore, the subsets of the set {-8, 4} are:
The empty set:So the correct answer is D: Ø, {-8}, {4}, {-8, 4}.
the graph of a proportional relationship contains the point 8 and 4 what is the corresponding equation enter your answer as a fraction in simplest form in the box
Answer:
[tex]y=\frac{1}{2}x[/tex].
Step-by-step explanation:
We have been given that the graph of a proportional relationship contains the point 8 and 4.
Since we know that a proportional equation is in form: [tex]y=kx[/tex], where k is constant of proportionality.
Let us substitute x=8 and y=4 in proportional equation to find constant of proportionality for our equation.
[tex]4=k*8[/tex]
Upon dividing both sides of equation by 8 we will get,
[tex]\frac{4}{8}=\frac{k*8}{8}[/tex]
[tex]\frac{4}{8}=k[/tex]
[tex]\frac{1}{2}=k[/tex]
Let us substitute k=1/2 in proportional equation.
[tex]y=\frac{1}{2}x[/tex]
Therefore, our desired equation will be [tex]y=\frac{1}{2}x[/tex].
What is the slope of the line 3x- 9y=4
Answer:
1/3 is your answer
Step-by-step explanation:
Note that in the slope intercept form, the equation looks like: y = mx + b
Isolate the y. First, subtract 3x from both sides
3x (-3x) - 9y = (-3x) + 4
-9y = -3x + 4
Next, to fully isolate the y, divide - 9 from both siedes
(-9y)/(-9) = (-3x + 4)/(-9)
y = (-3x + 4)/-9
Simplify
y = (1/3)x - 4/9
You're slope of the line (m in y = mx + b) is 1/3
~
Write the first five terms of the sequence defined by the explicit formula.
Answer:
(a) 112, 28, 7, (7/4), (7/16)
Step-by-step explanation:
The sequence is given by the explicit formula
[tex]a_{n} = 112 (\frac{1}{4} )^{n-1}[/tex]
The terms of the sequence are :
[tex]a_{1} = 112 (\frac{1}{4} )^{1-1} = 112 (\frac{1}{4} )^{0} =112 [/tex]
[tex]a_{2} = 112 (\frac{1}{4} )^{2-1} = 112(\frac{1}{4} ) =28 [/tex]
[tex]a_{3} = 112 (\frac{1}{4} )^{3-1} = 112(\frac{1}{4} )^{2} = 7 [/tex]
[tex]a_{4} = 112 (\frac{1}{4} )^{4-1}=112(\frac{1}{4} )^{3} = \frac{7}{4}[/tex]
[tex]a_{5} = 112 (\frac{1}{4} )^{5-1}=112 (\frac{1}{4} )^{4} = \frac{7}{16}[/tex]
As an estimation we are told 5 miles is 8 km.
Convert 34.5 km to miles.
34.5 kilometers is equal to 21.41 miles.
Explanation:To convert kilometers to miles, you can use the conversion factor 1 mile = 1.609 kilometers. So, to convert 34.5 kilometers to miles, you would multiply 34.5 by the conversion factor:
34.5 kilometers × 1 mile/1.609 kilometers = 21.41 miles
Therefore, 34.5 kilometers is equal to 21.41 miles.
Learn more about Converting kilometers to miles here:https://brainly.com/question/34149906
#SPJ12
What is the y-intercept if the line graphed? *please enter your answer as an ordered pair in the form (x,y)*
Which property yields step 2 in the following problem? Step 1: 12(x+4) Step 2: 12x + 48
Answer:
Distributive property
Step-by-step explanation:
12(x+4)
We would use the Distributive property to get to
12x+48
Distributive Property
x(a+b) = ax + bx
Sally skates 2/5 in 1/2 hour. How far does she skate in 2 hours
Question
Sally skates 2/5 in 1/2 hour. How far does she skate in 2 hours
Answer:
8/5Step-by-step explanation:
2/5 in 1/2 hour = 4/5 in 1 hour
4/5 * 2 = 8/5 (your answer)
or
2/5 * 2 * 2 =
8/5