The exact value of cos(67.5°) is found using half-angle identities in trigonometry, which leads to the solution √(2 - √2)/2.
Explanation:To find the exact value of cos (67.5°), we can use the half-angle identity for cosine which states that cos(θ/2) = ± √ ((1+cosθ)/2). In this case, to find the cosine of 67.5 degrees, we effectively need to calculate the half-angle of 135 degrees.
Thus, cos(67.5°) = cos(135°/2) = √ ((1+cos135°)/2) = √ ((1 - √2/2)/2). This further simplifies to √(2 - √2)/2.
This is because the cosine of 135 degrees equals -√2/2 (as it's in the second quadrant where cosine is negative).
Therefore, the exact value of cos(67.5°) is √(2 - √2)/2.
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Which is different? X=-1/2y+4 or x=1/4y+-1/2
Joe was given $20 for his birthday.He then saved $10 per week from his allowance.Write a function to represent this situation
Answer:
20 + 10w = total cash saved
According to Okun's law, if the unemployment rate goes from 6% to 2%, what
will be the effect on the GDP?
A. It will decrease by 11%.
B. It will increase by 5%.
c. It will decrease by 5%.
D. It will increase by 11%.
Answer: D
Step-by-step explanation:
Okun's law says that a country's gross domestic product (GDP) must grow at about a 4% rate for one year to achieve a 1% reduction in the rate of unemployment.
Option D is correct.
Since, According to Okun's law a country's gross domestic product (GDP) must grow at about a 4% rate for one year to achieve a 1% reduction in the rate of unemployment.
So, if the unemployment rate goes from 6% to 2%, that is reduce by 4%
Therefore, GDP is increase by 4(4 %) = 16 %
Thus, most appropriate answer is option D, that is GDP will increase by 11% .
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Evaluate C7, 5).
A. 21
B. 42
C. 1,008
=======================================
C(n, r) = (n!)/(r!*(n-r)!) is the combination formula
C(7, 5) = (7!)/(5!*(7-5)!)
C(7, 5) = (7!)/(5!*2!)
C(7, 5) = (7*6*5!)/(5!*2!)
C(7, 5) = (7*6)/(2!) ..... note the "5!" terms divided and canceled
C(7, 5) = (7*6)/(2*1)
C(7, 5) = 42/2
C(7, 5) = 21
How many x-intercepts appear on the graph of this polynomial function?
f(x)= x4-5x2
The x-intercepts appear on this polynomial are 3 x intercepts.
Step-by-step explanation:
To find the x intercepts of the polynomial [tex]f(x)=x^{4} -5x^{2}[/tex] is by equating [tex]f(x)=0[/tex]
Thus, the equation becomes
[tex]\begin{array}{r}{x^{4}-5 x^{2}=0} \\{x^{2}\left(x^{2}-5\right)=0}\end{array}[/tex]
Equating, we get,
[tex]x^{2}=0,\left(x^{2}-5\right)=0[/tex]
[tex]x=0[/tex], [tex]\begin{aligned}x^{2}-5 &=0 \\x^{2} &=5 \\x &=\pm \sqrt{5}\end{aligned}[/tex]
Thus, the x-intercepts are [tex]x=0, x=\sqrt{5} , x=-\sqrt{5}[/tex]
Hence, the x-intercepts appear on this polynomial are 3 x intercepts.
Answer:
1 x-intercepts
Step-by-step explanation:
has same question on a test
of the 50 students who took the test 23 earned A's what percent of the students earned A's
1. Mr. Jackson buys a pair of shoes for $41.12. He
hands the clerk a $50 bill.
Answer:
Mr Jackson should get $8.88 back.
Step-by-step explanation:
$50 - $41.12 = $8.88
8-4 skills practice trigonometry
Answer:
what do you need?
Step-by-step explanation:
Answer:
4
Step-by-step explanation:
0.48 = log x solve for x
Answer: x≈3
Step-by-step explanation:
0.48 = log x , this could also be written as :
[tex]log_{10}[/tex] x = 0.48 , that is
x = [tex]10^{0.48}[/tex]
x = 3.01995172
x≈ 3
The solution to the equation 0.48 = log x is approximately 3.02 after converting it from logarithmic form into exponential form and calculating 10 to the power of 0.48.
Explanation:To solve the logarithmic equation 0.48 = log x we have to rewrite this equation in exponential form. A logarithm log_b(x) = y in exponential form is represented as b^y = x. Considering that in your question it's not specified, this likely means a base of 10 is being used. Hence, the equation 0.48 = log x can be converted into exponential form: 10^0.48 = x.
Performing the calculation with a calculator (or by hand if you know how), we find x ≈ 3.02. Therefore, the solution for x in the given equation is approximately 3.02.
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What is
AE?
Enter your answer in the box.
Answer:
[tex]AE=20\ units[/tex]
Step-by-step explanation:
we know that
If two triangles are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent
In this problem
Triangles AEB and DEC are similar by AA Similarity Theorem
so
[tex]\frac{AB}{DC}=\frac{AE}{DE}[/tex]
substitute the given values and solve for x
[tex]\frac{10}{4}=\frac{2x+10}{x+3}[/tex]
Multiply in cross
[tex]10x+30=8x+40\\10x-8x=40-30\\2x=10\\x=5[/tex]
Find the length side AE
[tex]AE=2x+10[/tex]
substitute the value of x
[tex]AE=2(5)+10=20\ units[/tex]
Describe the transformations.
Given the function [tex]f(x)[/tex]
[tex]f(x)+k[/tex] — will shift the graph vertically by k
[tex]f(x-k)[/tex] — will shift the graph horizontally by k
[tex]kf(x)[/tex] — will stretch the graph vertically by k
[tex]f(kx)[/tex] — will stretch the graph horizontally by k
Audrey needs 2.4 pounds if flour for birthday cakes and 3.75 pounds of flour for wedding cakes. if she plans on baking 72 birthday cakes and 5 wedding cakes, how many pounds of flour will she need?
Answer:
She will need 191.55 pounds of flour.
Step-by-step explanation:
Given:
Audrey needs 2.4 pounds if flour for birthday cakes and 3.75 pounds of flour for wedding cakes.
If she plans on baking 72 birthday cakes and 5 wedding cakes.
Now, to find pounds of flour will she need.
So, the pounds of flour for 72 birthday cakes:
[tex]2.4\times 72[/tex]
[tex]=172.8\ pounds.[/tex]
And, the pounds of flour for 5 wedding cakes:
[tex]5\times 3.75[/tex]
[tex]=18.75\ pounds.[/tex]
Now, to get the pounds of flour she need we add the pounds of flour to make 72 birthday cakes and 5 wedding cakes:
[tex]172.8+18.75[/tex]
[tex]=191.55\ pounds.[/tex]
Therefore, she will need 191.55 pounds of flour.
Rayshawn has a certain amount of money if he spends $20 then he has 1/3 of the original amount how much money did Rayshawn have originally
Answer:
Rayshawn originally had $30.
Step-by-step explanation:
i) Rayshawn has a certain amount of money. Let us say this amount is $x.
ii) Rayshawn spends $20 which means that he is left with $(x - 20)
iii) it is also given that amount of money left after spending $20 is [tex]\dfrac{1}{3}[/tex] of the original amount, $x, the amount remaining is [tex]\dfrac{\$x}{3}[/tex].
iv) from the information given in ii) and iii) we get
$(x - 20) = [tex]\dfrac{\$x}{3}[/tex], Therefore we get 3x - 60 = x , therefore 2x = 60,
Therefore x = $30. Rayshawn originally had $30.
Therefore, Rayshawn had $60 initially.
If Rayshawn spends $20 and ends up with 1/3 of the original amount, we can deduce that $20 represents 2/3 of the original amount.
since 1 - 1/3 = 2/3. Thus, each part (1/3) of the original amount corresponds to $20. Consequently, to find the original amount, we multiply $20 by 3, yielding $60. Therefore, Rayshawn originally had $60. This conclusion emerges from understanding that after spending $20, Rayshawn retains 1/3 of his original funds, implying that the $20 spent was equal to 2/3 of his initial sum. Thus, the inverse operation, multiplying by 3, unveils the original amount. Therefore, Rayshawn had $60 initially.
(3x-2 / 6)-(4x+1 / 4) = 3
Answer:
x = -43/6
Step-by-step explanation:
To solve this equation, you solve for 'x' by isolating it. This means to move every other number to the other side of 'x'. You can move numbers when they 'cancel' out by doing the opposite (Adding and subtracting are opposites. Dividing and multiplying are opposites).
[tex]\frac{3x-2}{6}-\frac{4x+1}{4} = 3[/tex]
[tex]\frac{3x-2}{6}*\frac{2}{2}-\frac{4x+1}{4}*\frac{3}{3} = 3[/tex] Multiply each fraction by a fraction that equals '1'. (2/2 = 1 and 3/3 = 1). This will give them a common denominator.
[tex]\frac{(3x-2)*2}{6*2}-\frac{(4x+1)*3}{4*3} = 3[/tex] Multiply
[tex]\frac{(6x-4)}{12}-\frac{(12x+3)}{12} = 3[/tex]
[tex]\frac{(6x-4)-(12x+3)}{12}= 3[/tex] Combine the fractions with the same denominator
[tex]\frac{(6x-4)-12x-3}{12}= 3[/tex] Subtract binomials. -(12x+3) is -12x-3
[tex]\frac{6x-4-12x-3}{12}= 3[/tex] Remove unnecessary brackets
[tex]\frac{-6x-7}{12}= 3[/tex] Combined like terms.
[tex]\frac{-(6x+7)}{12}= 3[/tex] Factor out the negative in the top.
[tex]-(6x+7)= 3*12[/tex] Multiplied both sides by 12
[tex]-(6x+7)= 36[/tex] Simplified right side
[tex]6x+7= -36[/tex] Divided both sides by -1
[tex]6x= -36-7[/tex] Subtract 7 from both sides
[tex]6x= -43[/tex] Simplified right side
[tex]x= \frac{-43}{6}[/tex] Divided both sides by 6. Answer in fraction form.
x = 7.166..67 Answer in decimal form
Therefore x is -43/6 or about 7.17.
How many solutions does this system of equation have x+1=2y x-1=2y
Answer:
0
Step-by-step explanation:
These are two lines with equal slopes and different y intercepts so they will be parallel and will never intersect
What is the product of (x-3) and (x+7)
Answer: (x−3)(x+7)
=(x+−3)(x+7)
=(x)(x)+(x)(7)+(−3)(x)+(−3)(7)
=x^2+7x−3x−21
=x^2+4x−21
The product of (x-3) and (x+7) is x² + 4x - 21
The product of (x - 3) and (x + 7) can be found as follows:
(x - 3)(x + 7)
open the bracket by multiplying
Therefore,
x(x) +x(7) - 3(x) - 3(7)
x² + 7x - 3x - 21
combine like terms
x² + 4x - 21
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7x(3x2) and (7x3)x2
Answer:
what is the question
Step-by-step explanation:
CAN YALL HELP ME WITH THIS ONE PLEASE...
Answer:
x = 130°
Step-by-step explanation:
Segment AC tangent to circle O then ∠A = 90°
Segment BC tangent to circle O then ∠B = 90°
finally ,
x = 360 -(90+90+50) = 360-230 = 130
Answer:
x = 130°
Step-by-step explanation:
Five fractions equivalent to 1/2
Answer:
2/4, 3/6, 4/8, 5/10, 6/12
Step-by-step explanation:
Equivalent fractions are fractions that have the same value or represent the same part of an object. If a pie is cut into two pieces, each piece is also one-half of the pie. If a pie is cut into 4 pieces, then two pieces represent the same amount of pie that 1/2 did. We say that 1/2 is equivalent to 2/4.
Fractions are determined to be equivalent by multiplying the numerator and denominator of one fraction by the same number. This number should be such that the numerators will be equal after the multiplication. For example if we compare 1/2 and 2/4, we would multiply 1/2 by 2/2 which would result in 2/4 so they are equivalent.
To compare 1/2 and 3/7 we would multiply 1/2 by 3/3 to produce 3/6. Since 3/6 is not the same as 3/7, the fractions are not equivalent.
Fractions equivalent to 1/2 are 2/4, 3/6, 4/8, 5/10, 6/12 ...
Fractions equivalent to 1/3 are 2/6, 3/9, 4/12, 5/15, ...
Fractions equivalent to 1/4 are 2/8, 3/12, 4/16, 5/20, ...
Fractions equivalent to 1/5 are 2/10, 3/15, 4/20, 5/25, ...
Fractions equivalent to 2/5 are 4/10, 6/15, 8/20, 10/25, ...
Answer:2/4 3/6 4/8 5/10 6/12
19.25 as an equation
Sara's earnings vary directly with the number of hours she works. The data is shown in the graph. If x = number of hours worked, and y = earnings, which equation models Sara's direct variation?
A) y = 5x
B) y = 10x
C) y = 5 + x
D) y = 10 + x
Answer:
answer is y=10x
Step-by-step explanation:
multiply time by 10 to equal models sara's direct variaton.
The equation models Sara's direct variation if, Sara's earnings vary directly with the number of hours she works, which is y = 10x, so option B is correct.
What is a graph?A collection of objects is arranged in a graph, where some object pairings are conceptually "linked." Each pair of connected vertices is referred to as an edge, and the objects are represented by mathematical abstractions known as vertices.
Given:
Sara's earnings vary directly with the number of hours she works,
x = number of hours worked, and y = earnings,
The equation for the above statement can be written as shown below,
earnings = number of hours worked × salary
Assume the salary is a then,
y = ax
If she gets a salary of $10 then,
y = 10x
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The distance between Matt's house and his school is 3 inches on the map. The actual distance is 1.5 miles. What is the
of the map?
1 inch = 2 miles
1 inch = 0.5 mile
3 inches = 1 mile
1.5 inches = 1 mile
Answer:
b
Step-by-step explanation:
Find the equation of the line which has slope of -5 and y-intercept 7. Give your answer in the form y=mx+b
Answer:
y = - 5x + 7
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + b ( m is the slope and b the y- intercept )
Here m = - 5 and b = 7, thus
y = - 5x + 7 ← equation of line
Good morning ☕️
Answer:
y = -5x + 7Step-by-step explanation:
y=mx+b
m = slope = -5
b = y-intercept = 7
then the equation is : y = -5x + 7
:)
Help please this is for my homework that is due to tomorrow!!
The given polygons are similar
Step-by-step explanation:
By observing the given diagrams, we can see that the respective angles are congruent.
Two shapes are said to be similar if they have same shapes or one shape is created by uniformly increasing or decreasing the side of other.
For this purpose we find the scale factor of greater to smaller image, if the scale factor is same for each side then the two shapes are similar
So,
The scale factor is:
[tex]\frac{EF}{AB} = \frac{3}{1} = 3\\\\\frac{FG}{BC} = \frac{9}{3} = 3\\\\\frac{GH}{CD} = \frac{15}{5} = 3\\\\\frac{EH}{AD} = \frac{21}{7} = 3[/tex]
We can see that the scale factor is same for all sides.
Hence,
The given polygons are similar
Keywords: Polygons, similarity
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You solved a linear system with two equations and two variables and got the equation -6=-6. How many solutions does the systems of equations have?
Answer:
The system of equations will have an infinite number of solutions.
Step-by-step explanation:
i) when we arrive at a solution of a linear system with two equations and two
variables and the solution of the equation does not give the value of any
variable but rather is in the form of an identity like the one given, that is
-6 = -6, then we can say that the two equations are exactly the same and
that the system of equations will have an infinite number of solutions.
Which of the following inequalities matches the graph?
A.) 3x - > 4
B.) 3x - 4y < 2
C.) 3x - 2y < 4
D.) The Correct inequality is not listed.
Answer:
c
Step-by-step explanation:
going negative stops at 4
Graph the line y=Mx+b for the given values m=-2/3, b=-1
Answer:
See below for the graph:
Step-by-step explanation:
Need t in degrees not just solve for t
An exterior angle is equal to the sum of the two opposite inside angles.
T + 31 = t + t-29
Simplify:
T + 31 = 2t -29
Add 29 to both sides:
T + 60 = 2t
Subtract 1t from both sides:
T = 60
x times x + 3 to the power of 2 equals 48 , what is x ?
Answer:
I believe the answer to this question is: X=square root(39), and square root(-39).
Help me please, I’ll give brainliest
Answer:
x=11
Step-by-step explanation:
since ad bisects bac, bad=dac
32=3x-1
+1 +1
3x=33
/3 /3
x=11