Step-by-step explanation:
Rearrange the equations to solve.
cos(-3 • pi) = -1
cos((-3pi) / 4 radians) = -0.707
cos(5 • pi) = -1
cos((5pi) / 4 radians) = -0.707
They are the same because when multiplied, they are the same value, and always will be that way. They also have the same identity if you simplify and compare the results of that equation.
The value of cos (-3π/4) and the value of cos (5π/4) are same.
What are Trigonometric Ratios?Trigonometric ratios are the ratios which is described for two sides of a right angled triangle.
The main three trigonometric ratios are sine, cosine and tangent functions.
We know that,
cos (-3π/4) = cos (3π/4)
Now,
cos (3π/4) = cos (π + π/4)
And,
cos (5π/4) = cos (π - π/4)
Now, we know that,
cos (π + x) = -cos (x) and cos (π - x) = -cos (x)
So the value of cos (π + π/4) = -cos( π/4) and cos (π - π/4) = -cos( π/4)
Hence cos (3π/4) = cos (5π/4) = -cos( π/4)
Hence both the values are same.
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To make 3 litres of pale purple paint you mix:
1.5 litres red
1.25 litres of blue
0.25 litres of white paint.
a How much red paint is needed to make 8 litres of paint?
Answer:
4 litres.
Step-by-step explanation:
By proportion that would be:
1.5 * 8/3
= 12/3
= 4 litres.
PLEASE HELP ME ASAP!
A rug measures 5/6 foot long and 1/3 foot wide. What is the area of the rug?
5/18t2
5/18t3
1 3/18 t2
1 3/18 t3
Answer:
Length = 5/6 foot
Breadth = 1/3 foot
Area of rug = l×b
=5/6 × 1/3
= 5/18 Ft^2
Illustrate on a number line the solution set of each pair of simultaneous inequalities. x>-2;-4 <x <2
Answer:
See below
Step-by-step explanation:
Use this tool to plot
https://quickmath.com/webMathematica3/quickmath/graphs/inequalities/basic.jsp#form?v2=graph
The results are shown in the accompanying screenshots
look at the picture to solve it
Answer:
6^7
Step-by-step explanation:
To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.
To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 6 from 13 to get 7.
Answer:
6^7
Step-by-step explanation:
6^13/6^6 = 6^7
Please help me ASAP!!!!!
Step-by-step explanation:
when you are on that level of math that you get this type of question - this is totally easy.
we get the extreme point(s) of a function by finding the zeros of the first derivative of the function.
f'(x) = 4x - 8
so,
0 = 4x - 8
8 = 4x
x = 2
to determine whether it is a minimum or a maximum, we have 2 choices :
the quick way for a quadratic (parabola) equation by looking at the factor of x² : is it >0, then the parabola opens up upwards, and the extreme point is therefore a minimum. if it is <0, then it opens downward, and the extreme point is a maximum.
in our case : 2 is larger than 0, therefore minimum.
or the formal way for any type of function : create the second derivative and see, if it is >0 (minimum) or <0 (maximum) for the extreme x.
in our case
f''(x) = 4
this is larger than 0 for all x, so the extreme point is a minimum.
If X=3 and y= -2, find xy + 2y.
-2
-9
-10
-1
Answer:
-10 is the answer
Step-by-step explanation:
[tex]xy + 2y \\ putting \: the \: value \: of \: x \: and \: y \\ 3 \times ( - 2) + 2 \times ( -2 ) \\ - 6 - 4 \\ = - 10[/tex]
Write (9,-4) and (1,6) in slope intercept form,
Answer:
y = -5/4x + 7 1/4
Step-by-step explanation:
The difference in y (10) over the difference in x (8)
Elias was given a lock for his school locker. The lock contains numbers between
O and 59 (60 different numbers). If 3 numbers are used to unlock the lock, and
the numbers can't repeat, how many codes can his lock have?
Answer:
34,220
Step-by-step explanation:
Because order doesn't matter, but the numbers can't be repeated, we need to find the number of combinations where 3 individual numbers can be chosen out of 60 possible numbers using the binomial coefficient:
[tex]\binom{n}{k}=\frac{n!}{k!(n-k)!}\\ \\\binom{60}{3}=\frac{60!}{3!(60-3)!}\\\\\binom{60}{3}=\frac{60!}{3!(57)!}\\\\\binom{60}{3}=\frac{60*59*58}{3*2*1}\\ \\\binom{60}{3}=34220[/tex]
Thus, Elias can make 34,220 unique 3-number codes given 60 different numbers.
Question 1 options:
The Jones family is driving from San Antonio, Texas, to Anchorage, Alaska, which is a distance of 4304 miles. They have already driven 1639.2 miles.
How much farther does the family need to drive to reach Anchorage?
Enter your answer as a decimal in the box
Answer:
2664.8 miles left to drive
Step-by-step explanation:
4304 miles driven
subtract 1639.2 miles driven
total left is 2664.8 miles yet to drive
Someone please helppp
your friend house is 6.4 miles north and 12 miles west of your bank. how far is your friends house from your bank
Answer:
the answer is 76.8
Step-by-step explanation:
multiple of the number
Assuming the pizzeria is located at the
origin, write an equation of the circle in
which the pizzeria will deliver in standard
form where x and y represent the distance
from the pizzeria in miles.
The equation of the circle represented by the pizza is x^2 + y^2 = 4
How to determine the equation of the circle?The given parameters are:
Radius, r = 2
Center, (a,b)= (0,0) i.e. origin
The equation of the circle is calculated as:
(x - a)^2 + (y - b)^2 = r^2
This gives
(x - 0)^2 + (y - 0)^2 = 2^2
Evaluate the exponents
x^2 + y^2 = 4
Hence, the equation of the circle is x^2 + y^2 = 4
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You need a loan and your friend, Joey, will lend you the $1250 you need. He has you sign a promissory note for four years with an annual simple interest rate of 5.5%. What is the total amount that you will pay Joey at the end of the four years?
$1525
$4225
$2750
$275
Answer:
$1525
Step-by-step explanation:
5.5% out of $1250= 68,7568,75 x 4 (years) = 2751250 + 275 = 1525A scientist collected two sample sets of snowfall data. Which statistic should he use to compare the spread of the two sets of data?
The standard deviation statistic should use to measure the spread of the two sets of data.
What is the standard deviation?
It is defined as the measure of data disbursement, It gives an idea about how much is the data spread out.
As we know, the shape of a normal curve is dictated by its mean and standard deviation, hence standard deviations are important.
Thus, the standard deviation statistic should use to measure the spread of the two sets of data of snowfall which is collected by the scientist.
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Select the correct answer from each drop-down menu.
complete the statements about this function
f(x)= -2\x+1| + 2.
the vertex of the function is la
on the interval (-1,0), the function is
as x approaches positive infinity, the function approaches
infinity
The vertex of the function is a maximum and on the interval (-1,0), the function approaches negative infinity as x approaches positive infinity
How to interpret the function?The function is given as:
f(x)= -2|x+1| + 2
The above function is an absolute value function
An absolute value function is represented as:
y = a|x - h| + k
Where the vertex is:
Vertex = (h, k)
When a is less than 0, then the vertex is at maximum
By comparison, we have:
a = -2
(h,k) = (-1, 2)
-2 is less than 0
Hence, the vertex of the function is a maximum and on the interval (-1,0), the function approaches negative infinity as x approaches positive infinity
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The first sequence rule is multiply by 4 starting from 7. The second sequence rule is add 5 starting from 8. What is the first number that appears in both sequences?
28
56
112
225
Answer:
28
Step-by-step explanation:
28 is the number that appears first for both.
For first sequence:
7 × 4 = 28 × 4 = 112 × 4 = 448
For second sequence:
8 + 5 = 13 + 5 = 18 + 5 = 23 + 5 = 28
The descriptive statistics are shown.
Analyzing Misleading Graphs and Reports
Compare the measures. Describe what these measures indicate about the shape of the box-and-whisker plot.
The median is always at the center of the box, we can say the median of our question is also at the middle of the box.
What is a graph?A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.
The description of the measures given has been done below and also what they indicate about the shape of the box and whisker plot have been given.
From the given data we see that;
Mean = 39,500
Median = 20000
Mode = 23000
Minimum = 15,000
Maximum = 255000
A general view of a box and whisker plot has been attached.
From the attached file, we can see the following;
- whiskers to the left and right of the box.
- The box starts from the lower quartile and stops at the upper quartile.
- The median is at the middle of the box
- The minimum is at the end of the left whisker
- The maximum is at the end of the right whisker.
1) Now, since median is always at the center of the box, we can say the median of our question is also at the middle of the box.
2) The median is 20000 but the minimum which is the end of the left whisker is 15000 while the maximum which is the end of the right whisker is 255000. This means the minimum is very close to the median and as such the left whisker would be very short. In contrast, the right whisker will be very long since the maximum is far larger than the median.
3) Since the right whisker is far larger than the left whisker, then we can say the shape of the box and whisker plot is heavily skewed to the right.
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what is the slope of the line that passes through (4,-9) and
(1,3)?
Answer:
slope = - 4
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (4, - 9 ) and (x₂, y₂ ) = 1, 3 )
m = [tex]\frac{3-(-9)}{1-4}[/tex] = [tex]\frac{3+9}{-3}[/tex] = [tex]\frac{12}{-3}[/tex] = - 4
Answer:
[tex]m=-4[/tex]; the slope is -4
Step-by-step explanation:
[tex]slope=\frac{rise}{run} =\frac{y^2-y^1}{x^2-x^1}[/tex]
coordinates: (4,-9) (1,3)
[tex]\frac{3-(-9)}{1-4}=\frac{-12}{-3} =-4[/tex]
= -4 is your answer
hope this helped
~rere
In a school, 40% of the students have brown eyes. Find the experimental probability that in a group of 4 students, at least one of them has brown eyes. The problem has been simulated by generating random numbers. The digits 0-9 were used. Let numbers "0", "1", "2", and "3" represent the 40% of students with brown eyes. A sample of 20 random numbers is shown. 7918 7910 2546 1390 6075 1230 2386 0793 7359 3048 2816 6147 5978 5621 9732 9436 5971 3806 6173 1430 Experimental Probability = [?]%
Answer:
41.25%
Step-by-step explanation:
Of the 80 digits generated, 33 of them are 0,1,2, or 3.
(Yup, I counted them)
So, 33/80 = 0.4125 = 41.25%
Answer:
95%
Step-by-step explanation:
Step 1: Find samples with 0, 1, 2 or 3.
Example: count 7918 it has a one
Example two: count 2546 it has a two
Step 2: Once all the samples with 0, 1, 2 or 3 are counted put it into a fraction.
Example: For this particular question there were 19/20 samples with numbers 0, 1, 2 or 3.
Step 3: Change the fraction into a percentage after that you will have your final answer.
A jar made of 1/4 inch thick glass has an inside radius of 4.7 inches and total height of 13.3 inches (including the bottom thickness of glass). What is
the volume of the glass shell of the jar (in cubic inches)?
The volume of the cylindrical jar, considering it's radius and height, is of 923 in³.
What is the volume of a cylinder?The volume of a cylinder of radius r and height h is given by:
[tex]V = \pi r^2h[/tex].
In which problem, we have that r = 4.7 in, h = 13.3 in, hence the volume in cubic inches is given by:
[tex]V = \pi \times 4.7^2 \times 13.3 = 923[/tex]
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Find the equation of the line. Use exact numbers. y=y=y, equals x+x+x, plus
A coordinate plane. The x- and y-axes each scale by one. A graph of a line goes through the points zero, four and one, six.
The equation of a line that is passing through the points (0, 4) and (1, 6) will be y = 2x + 4.
What is the linear system?A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.
A coordinate plane. The x-axis and y-axis are each scaled by one.
A graph of a line goes through the points (0, 4) and (1, 6) will be
The equation of a line that is passing through the points (0, 4) and (1, 6) will be
y - 4 = [6 - 4 / 1 - 0] (x - 0)
y - 4 = 2x
y = 2x + 4
The graph is given below.
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Answer:y=x-5
Step-by-step explanation:
khan academy
Select the correct answer. which sum or difference is modeled by the algebra tiles? a. (-x2 2x 3) − (x2 − 2x − 1) = -2x2 2 b. (-x2 2x 3) − (-x2 2x 1) = -2x2 2 c. (-x2 2x 3) (-x2 2x 1) = -2x2 2 d. (-x2 2x 3) (-x2 − 2x − 1) = -2x2 2
The sum or difference modeled by the algebraic tiles is (-x²+2x+3) + (-x²-2x-1) = -2x²+2
How to determine the sum or difference?From the complete question, we have the following expressions:
(-x²+2x+3) and (-x²-2x-1)
Add both expressions
(-x²+2x+3) + (-x²-2x-1)
Expand
-x²+2x+3 -x²-2x-1
Collect the like terms
-x² -x² + 2x - 2x + 3 -1
Evaluate the like terms
-2x²+2
Hence, the sum or difference modeled by the algebraic tiles is (-x²+2x+3) + (-x²-2x-1) = -2x²+2
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The volume of this rectangular prism is 48,608 cubic centimeters. What is the value of b?
Answer:
b = 49 cm
Step-by-step explanation:
Volume of a rectangular prism = width × length × height
Given:
volume = 48,608 cm³width = 16 cmlength = bheight = 62 cmSubstituting the given values into the formula and solving for b:
⇒ 48608 = 16 × b × 62
⇒ 48608 = 992 b
⇒ b = 48608 ÷ 992
⇒ b = 49
Answer:
b = 49 cm
Step-by-step explanation:
Volume of a rectangular prism: length × width × height
V = L×W×H
v = 48,608 cm³l = b cmw = 16 cmh = 62 cmSubstitute the values above and solve for b:
48,608 = b × 16 × 62
48,608 = 992b
48,608/992 = 992b/992
49 = b
Final answer: 49 cm
Hope this helps!
Change the function f(x) = 2x ^ 2 + 8x + 5 into vertex form.
Answer:
[tex]f(x)=2(x+4)^2-27[/tex]
Step-by-step explanation:
Complete the square
[tex]f(x)=2x^2+8x+5\\f(x)=2(x^2+8x+\frac{5}{2})\\f(x)+2(\frac{27}{2})=2(x^2+8x+\frac{5}{2}+\frac{27}{2})\\f(x)+27=2(x^2+8x+16)\\f(x)+27=2(x+4)^2\\f(x)=2(x+4)^2-27[/tex]
This tells us that the vertex of the parabola is [tex](-4,-27)[/tex].
The graph of g is a translation 4 unit down of the graph of f(x) = 6x-4. The rate of change of g over the interval -2 ≤ x ≤ 4 is
The function g(x) is a linear function, and the rate of change over the interval -2 ≤ x ≤ 4 is 6
How to determine the rate of change?The function f is given as:
f(x) =6x - 4
When translated down by 6 units, the rule of translation is:
g(x) = f(x) - 4
So, we have:
g(x) = 6x - 4 - 4
Evaluate
g(x) = 6x - 8
The rate of change over -2 ≤ x ≤ 4 is then calculated using:
g'(x) = [g(b) - g(a)]/[b - a]
So, we have:
g'(x) = [g(4) - g(-2)]/[4 + 2]
Evaluate
g'(x) = [g(4) - g(-2)]/[6]
Calculate g(4) and g(-2)
g(4) = 6 * 4 - 8 = 16
g(-2) = 6 * -2 - 8 = -20
So, we have:
g'(x) = (16 + 20)/6
Evaluate
g'(x) = 6
Hence, the rate of change over the interval -2 ≤ x ≤ 4 is 6
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Whats the product 72x0.45
Answer:
72 times 0.45 is equal to 33.75
Step-by-step explanation:
You can use a calculator to find this out.
Answer:
32.4
Step-by-step explanation:
After repeatedly adding 0.45 a total of 72 times. You end up getting 32.5
To check the answer you divide 32.5 by 72 and receive 0.45. Checking the answer
A 500-room hotel collects $80 per occupied room each night. which expression represents the number of dollars the hotel collects on a night when v rooms are vacant?
1) If the diameter of a circle is changed from 8 cm to 4 cm, how will the circumference change?
A) increases by a factor of 2
B) decreases by a factor of 2
C) increases by a factor of 4
D) decreases by a factor of 4
Answer:
the answer is B.
Step-by-step explanation:
the formula for circumference of a circle is [tex]\pi[/tex]×diameter=C
[tex]\pi[/tex]·8=25.13
[tex]\pi[/tex]·4=12.56
12.56·2=25.13
and yet another i hope you all had fun doing these problems
Please help me with this question
Answer:
difference between town A and town B is 5.4 deg. celcius
Step-by-step explanation:
I added each row and divided by 5 to get the average for A and B
I subtracted the average
see attached picture showing the math
Select the correct answer. if you roll a single six-sided die, what is the probability of rolling an odd number? a. b. c. d. 3
Answer:
[tex]\frac{1}{2}[/tex]
Step-by-step explanation:
P(odd number)= [tex]\frac{3}{6}[/tex]
=[tex]\frac{1}{2}[/tex]