Answer:
-[tex]\sqrt{\frac{2-\sqrt{2}}{4}[/tex]
Step-by-step explanation:
The cosine half-angle formula is
[tex]cos\frac{\pi }{2}[/tex]=±[tex]\sqrt{\frac{1+cosx}{2} }[/tex]
we can write
[tex]cos \frac{3\pi }{8}[/tex]
as
[tex]cos\frac{\frac{3\pi }{4} }{2}[/tex]
=-[tex]\sqrt{\frac{1+cos\frac{3\pi}{4} }{2}[/tex]
=-[tex]\sqrt{\frac{1-\frac{\sqrt{2}}{2}}{2}[/tex]
=-[tex]\sqrt{\frac{2-\sqrt{2}}{4}[/tex]
(cosine is negative is in second quadrant)
Using the half angle identity, the exact value of cos 3 pi / 8 is (√2 - 1) / 2√2.
Given a trigonometric expression,
cos 3π/8
We have to find the exact value of this using the half angle identity.
The half angle identity in terms of cosine function is,
cos (x/2) = ± √[(1 + cos x) / 2]
Here the angle is 3π/8.
This can be written as,
3π/8 = 3π/4 / 2
Substituting to the formula,
cos (3π/4/2) = √[(1 + cos 3π/4) / 2]
Now,
cos 3π/4 = cos (π - π/4)
= -cos(π/4)
= - 1/√2
Substituting to the formula,
cos (3π/4/2) = √[(1 - 1/√2) / 2]
= (√2 - 1) / 2√2
Hence the value is (√2 - 1) / 2√2.
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Louis found two bakeries to provide bagels for his sub shop. The first bakery offers 350 bagels for $168.00 and the second bakery offers 475 bagels for $209. How much will Louis pay for 800 bagels if he buys from the bakery with the lower price?
Answer:
$352Step-by-step explanation:
Find out the price of one bagel by dividing the price by the number of bagels:
350 Bagels = $168
1 Bagel = $0.48
475 Bagels = $209
1 Bagel = $0.44
0.48 > 0.44
This means the second bakery has the lower price.
Louis wants 800 bagels, so multiply the price by 800.
0.44 * 800 = $352
You can check it's lower by comparing it with the first bakery.
0.48 * 800 = $384
384 > 352
John had 84 dollars, and his brother Fred owed 12 dollars to his friend. John gave his brother some money. Fred paid his debt and now both of them has the same amount left. How much money did John give Fred? PLZZZZ HELP!!!!!
[tex]The \: money \: of \: each \: after \: Fred \: paid \: his \: debt: \frac{84 - 12}{2} = \$36 \\ John \: gave \: Fred:36 + 12 = \$48[/tex]
Answer:
36
Step-by-step explanation:
Which expression is equivalent to
Answer:
[tex]\dfrac{7.7.7.7.7}{7.7}[/tex]
Step-by-step explanation:
Finding the expression of the value [tex]\dfrac{7^{5} }{7^{2}}[/tex] is just like taking the spread out value of the two variables raised to their exponents.
[tex]\dfrac{7^{5}}{7^{}}=\dfrac{7.7.7.7.7}{7.7}[/tex]
So if we multiply all the values together we get:
=[tex]\dfrac{16807}{49}[/tex]
=343
This method is just one of the methods that can be used to finding the quotient of a variable raised to an exponent.
How many cubes are needed to fill the rectangular prism PLZ HUUURRRRRYYYYYY
Kelly found some dimes and pennies in her dad's car . she found 5 coins in all. the coins totaled more than 20 cents, but less than 50 cents. What coins could Kelly have found?? Write the amount as a fraction of a dollar and as an equivalent decimal.
Answer:
21
Step-by-step explanation:
A rhombus has one diagonal that is 14 centimeters long and one diagonal that is 12. What is the area of the rhombus?
Answer:
168
14 times 12
Start with the standard formula for the area of a triangle, and rewrite it to solve for the base, b.
Answer:
2A/h = b
Step-by-step explanation:
The formula for area of a triangle is
A = 1/2 bh
Multiply each side by 2
2A = 2*1/2 bh
2A = bh
Divide each side by h
2A/h = bh/h
2A/h = b
Answer:
b=2A/h
Step-by-step explanation:
The formula for area of a triangle is
A = 1/2 bh
Multiply each side by 2
2*1/2 bh = 2A
bh = 2A
Divide each side by h
bh/h = 2A/h
b = 2A/h
A rectangle is 2/5 inches long and 1/3 inches wide. WORTH 20 POINTS!!!!!
What is the area of the rectangle?
Enter your answer in the box as a fraction in simplest form.
Answer:
2/15 inches squaredStep-by-step explanation:
Area = L * W
2/5 * 1/3 =
2 * 1 = 2
5 * 3 = 15
= 2/15 inches squared
What we do is find area
Area of rectangle=(l*w)
length=2/5
width=1/3
Area=2/5*1/3
Answer=2/15
Answer=2/15
Tamara found the solution of x^2=64 to be x=8.
What mistake did Tamara make in finding her solution?
A. She found the incorrect square root of 64.
B. She only found the square root of one side of the equation.
C. She only found the positive square root, not the negative square root
D. She found the cube root of 64 instead of the square root.
and D is not the answer
Answer:
C
Step-by-step explanation:
given
x² = 64 ( take the square root of both sides )
x = ± [tex]\sqrt{64}[/tex] = ± 8
Tamara omitted the negative square root → C
Tamara made the mistake of only finding the positive square root, not the negative square root.
Explanation:The mistake that Tamara made in finding the solution to the equation x^2=64 is that she only found the positive square root, not the negative square root.
When solving a quadratic equation like this, you need to consider both the positive and negative square roots, because both values satisfy the equation. So the correct solution to x^2=64 is x=8 and x=-8.
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Solve -9.4 > 1.7x + 4.2. I need this ASAP
Hello.
We are solving -9.4 > 1.7x + 4.2.
First we need to swap sides:
[tex]1.7x + 4.2 = -9.4[/tex]
Now we need to subtract 4.2 from both sides.
1.7x + 4.2 = -9.4
-4.2 . -4.2
Now let's combine -4.2 + 4.2 which is 0.
We get 1.7x < -9.4 - 4.2
Now let's divide both sides by 1.7
1.7x | -13.6
1.7 1.7
x < -13.6
1.7
So we just divided to get x < -8.
Answer:
[tex]\boxed{\bold{x<-8}}[/tex]
Step By Step Explanation:
Switch Sides[tex]\bold{1.7x+4.2<-9.4}[/tex]
Multiply Both Sides by 10[tex]\bold{1.7x\cdot \:10+4.2\cdot \:10<-9.4\cdot \:10}[/tex]
Refine[tex]\bold{17x+42<-94}[/tex]
Subtract 42 From Both Sides[tex]\bold{17x+42-42<-94-42}[/tex]
Simplify[tex]\bold{17x<-136}[/tex]
Divide Both Sides By 17[tex]\bold{\frac{17x}{17}<\frac{-136}{17}}[/tex]
Simplify[tex]\bold{x<-8}[/tex]
in the diagram of PARALLELOGRAM ABCD, segment BE is perpendicular to segment CED, segment DF is perpendicular to BFC and segment CE is congruent to segment CF.
Prove ABCD is a rhombus.
Answer:
In parallelogram ABCD
FD is perpendicular to BC
BE is perpendicular to CD
Consider triangle BEC and triangle DFC
FC = EC (Given)
Angle BEC = Angle DFC (=90°)
Angle BCE = Angle DCF (common)
Therefore triangle BEC is congruent to triangle DFC (AAS congruency)
DF = BE (CPCT)
Since the altitudes are equal their bases will also be equal
Therefore BC = DC
Therefore BC = DC = AD = AB
Therefore ABCD is a rhombus
Hope this helps!
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Since [tex]\(ABCD\)[/tex] is a parallelogram with all four sides congruent, [tex]\(ABCD\)[/tex] is a rhombus. Hence, [tex]\(ABCD\)[/tex] is proven to be a rhombus.
To prove that parallelogram [tex]\(ABCD\)[/tex] is a rhombus, we need to show that all sides are congruent.
Given:
1. [tex]\(ABCD\)[/tex] is a parallelogram.
2. [tex]\(BE \perp CED\).[/tex]
3. [tex]\(DF \perp BFC\).[/tex]
4. [tex]\(CE \cong CF\).[/tex]
Proof:
1. Parallelogram Properties:
- In a parallelogram, opposite sides are congruent and parallel.
- Therefore, [tex]\(AB \parallel CD\)[/tex] and [tex]\(AD \parallel BC\)[/tex].
- Also, [tex]\(AB \cong CD\)[/tex] and [tex]\(AD \cong BC\)[/tex].
2. Congruent Segments:
- [tex]\(CE \cong CF\) (given).[/tex]
- Since [tex]\(BE \perp CED\)[/tex] and [tex]\(DF \perp BFC\)[/tex], [tex]\(BE\)[/tex] and [tex]\(DF\)[/tex] are heights from [tex]\(B\)[/tex] and [tex]\(D\)[/tex] respectively to line [tex]\(CED\)[/tex].
3. Triangle Congruence:
- Consider [tex]\(\triangle CEF\)[/tex]. Since [tex]\(CE \cong CF\)[/tex] and [tex]\(BE \perp CED\)[/tex], [tex]\(DF \perp BFC\)[/tex], [tex]\(\triangle CEF\)[/tex] is isosceles with base [tex]\(EF\)[/tex].
4. Diagonals in Parallelogram:
- Diagonals of a parallelogram bisect each other.
- Since [tex]\(\triangle CEF\)[/tex] is isosceles and [tex]\(CE = CF\)[/tex], the diagonals [tex]\(BE\)[/tex] and [tex]\(DF\)[/tex] bisect each other at [tex]\(E\)[/tex] and [tex]\(F\)[/tex].
5. Symmetry and Congruence:
- Since diagonals bisect each other and the height from [tex]\(B\)[/tex] and [tex]\(D\)[/tex] are equal, segments from [tex]\(B\)[/tex] and [tex]\(D\)[/tex] to the diagonals are congruent.
6. Sides of Parallelogram:
- From symmetry and congruence, all sides of the parallelogram are equal.
- Therefore, [tex]\(AB \cong BC \cong CD \cong DA\)[/tex].
Conclusion:
Since [tex]\(ABCD\)[/tex] is a parallelogram with all four sides congruent, [tex]\(ABCD\)[/tex] is a rhombus.
Hence, [tex]\(ABCD\)[/tex] is proven to be a rhombus.
there are 5 teen age boys in the slack family. the boys drink 1 and 2 thirds of milk each day. at this rate, how many gallons of milk will the boys drink in a week?
A. 4 and 1 thirds
B. 11 and 2 thirds
C. 5 twentieth
D. 4 and 1 5th
1. Does the data in the table below represent exponential growth or exponential decay?
Hint: Are the values in the bottom row increasing or decreasing?
A
exponential growth
B
exponential decay
Exponential decay because it is decreasing
When making a telephone call using a calling card, a call lasting 5 minutes cost $0.95. A call lasting 13 minutes cost $1.75. Let y be the cost of making a call lasting x minutes using a calling card. Write a linear equation that models the cost of making a call lasting x minutes.
A. y = 10x - 981/20
B. y = -0.1x + 1.45
C. y = 0.1x + 0.45
The linear equation that models the cost of making a call lasting x minutes using a calling card is y = -0.1x + 1.45.
Explanation:To write a linear equation that models the cost of making a call lasting x minutes using a calling card, we can use the given information about two calls. If a 5-minute call costs $0.95 and a 13-minute call costs $1.75, we can set up two equations:
0.95 = 5m + b
1.75 = 13m + b
Solving these equations, we find that m = -0.1 and b = 1.45. Therefore, the linear equation that models the cost of making a call lasting x minutes is y = -0.1x + 1.45.
What is the volume of a square pyramid that has a base length of 5 inches and a height of 9 inches?
Answer:
75
Step-by-step explanation:
To find the volume of a squared pyramid use the formula:
Volume of a squared pyramid = × base area × height
Base area = Side× side
( A square has the same length and breadth)
= 5 × 5 = 25 in
Volume of a squared pyramid = [tex]\frac{1}{3}[/tex] × 25 × 9
= 75 [tex]in^{3}[/tex]
harold deposits $30 a week into a savings account. hid balance in his savings account grows by a constant rate. true or false
a pyramid has a height of 10 inches and a base with an area of 21 square inches. Find the volume of the pyramid
a.)35in^3
b.)210in^3
c.)105in^3
d.)70in^3
Answer:
70 in³ (answer d)
Step-by-step explanation:
The volume of a pyramid with base area A and height h is
V = (1/3)(A)(h).
Here, V = (1/3)(21 in²)(10 in) = 70 in³
Help, please!
Show how the GCF of the numbers 10 and 15 can be used to reduce the fractions [tex]\frac{10}{15}[/tex]
Answer: [tex]\frac{2}{3}[/tex]
Step-by-step explanation:
The greatest GCF is 5 because 5 goes into 15, and 10. Therefor, the answer would be 2/3.
* Hopefully this helps:) Mark me the brainliest:)!!!
Answer:
⅔
Step-by-step explanation:
Find all the factors of 10 and 15.
Factors of 10: 1, 2, 5, 10
Factors of 15: 1, 2, 3, 5, 15
The highest factor that is in both 10 and 15 is 5.
To reduce the fraction 10/15, divide both the numerator and denominator
by 5.
10/15 = (10 ÷ 5)/(15 ÷ 5) = ⅔
Write the ratio 14:56
In its simplest form
Answer:
14/14 = 1 and 56/14 = 4
Thus, 14:56 ratio simplified is 1:4
hope this helps:)sorry if it doesnt
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4x+5=2x+6 (what is x?)
Answer:
x = 1/2
Step-by-step explanation:
Subtract 2x from both sides
4x + 5x - 2x = 6
Combine 4x and -2x to get 2x.
2x + 5 = 6
Subtract 5 from both sides.
2x = 6 - 5
Subtract 5 from 6 to get 1.
2x=1
Divide both sides by 2.
x = 1/2
Is 2/10 equal to 4/5
Answer:
NO
Step-by-step explanation:
2/10 have a common term of 2. reduce both the numerator and denominator by dividing both by 2.
2/2 = 1
10/2 = 5
the reduced fraction woudl be 1/5
Answer:
No 2/10 is not the same as 4/5
Step-by-step explanation:
The reason why is because If you doubled 2/10 then it would be 4/20 not 4/5 and if you divided by 4/5 by 2 then it would be a complex fraction of 2/1/2 that is why the statement 4/5 is equal to 2/10 is false.
Evaluate the exponential function f(x)=8^x+1 Which value completes the table?
A.0
B.3
C.9
D.25
The value of exponential function, which completes the table for variable x at 1/3 is 3. The option B is correct.
Exponential function is the function in which the function growth or decay with the power of the independent variable.
The curve of the exponential function depends on the value of its variable.
The exponential function with dependent variable y and independent variable x can be written as,
[tex]y=a^x[/tex]
Here, [tex]x[/tex] is the variable in the power of a number.
Given information-
The given exponential function in the problem is,
[tex]f(x)=8^x+1[/tex]
The value of function at the value of variable x as 1/3 has to be find to complete the table. Put 1/3 in the above equation on the place of x as,
[tex]f(x)=8^{\frac{1}{3}}+1[/tex]
The number 8 can be written as the [tex]2^3[/tex]. Thus,
[tex]f(x)=(2^3)^{\frac{1}{3}}+1\\f(x)=(2)^{\dfrac{3\times1}{3}}+1\\f(x)=(2)^1+1\\f(x)=2+1\\f(x)=3[/tex]
Thus the value of exponential function, which completes the table for variable x at 1/3 is 3. The option B is correct.
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Pi is the ratio of _____ to ______
A. area to diameter
B. perimeter to area
C. radius to diameter
D. circumference to diameter
The answer is D. C ÷ d = π, where C is circumference and d is diameter.
Answer:
D. circumference to diameterStep-by-step explanation:
[tex]\text{The formula of a circumference of a circle:}\ C=d\pi\\\\d-diameter\\\\d\pi=C\qquad\text{divide both sides by}\ d\\\\\pi=\dfrac{C}{d}[/tex]
Point O is the center of the circle. What is the value of X?
Answer options: 24, 15, 27, 20
Answer: FIRST OPTION
Step-by-step explanation:
To solve this problem you must apply the Intersecting Secant-Tangent Theorem. By definition, when a secant line and a tangent lline and a secant segment are drawn to a circle from an exterior point:
[tex](Tangent\ line)^2=(Secant\ line)(External\ Secant\ line)[/tex]
The total measure of the secant shown is:
[tex]18+Diameter[/tex]
If the radius is 7, then the diameter is:
[tex]D=7*2=14[/tex]
Therefore:
[tex]Secant\ line=18+14=32[/tex]
You also know that:
[tex]External\ Secant\ line=18\\Tangent\ line=x[/tex]
Keeping the above on mind, you can substitute values and solve for x:
[tex]x^{2}=32*18[/tex]
[tex]x=\sqrt{576}\\x=24[/tex]
The measure of the side length of the tangent line PQ to the circle O is 25 units
What is the measure of side length x?From the image, Line segment PQ is a tangent line because it touches the curve at point Q.
Therefore, triangle PQO forms a right triangle.
Leg 1 of the right triangle = OQ = 7
Leg 2 of the right triangle = PQ = x
Hypotenuse = PO = 18 + 7 = 25
Now, to solve for the measure of side length x, we use the Pythagoras theorem:
PQ = √( PO² - OQ² )
Plug in the values:
x = √( 25² - 7² )
x = √( 625 - 49 )
x = √576
x = 24
Therefore, the value of x is 24.
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In a rhombus VENU, diagonals VN and EU intersect at S. If VN= 12 and EU=16, what is the perimeter of the rhombus?
Answer:
40 un.
Step-by-step explanation:
The diagonals of the rhombus bisect each other at right angle. This gives us that
[tex]VS=\dfrac{1}{2}VN=6\ un.;[/tex][tex]ES=\dfrac{1}{2}EU=8\ un. ;[/tex][tex]\angle VSE=90^{\circ}.[/tex]By the Pythagorean theorem,
[tex]VE^2=VS^2+ES^2,\\ \\VE^2=6^2+8^2,\\ \\ VE^2=36+64,\\ \\VE^2=100,\\ \\VE=10\ un.[/tex]
The sides of the rhombus are all of the same length, then the perimeter of the rhombus is
[tex]P_{VENU}=4\cdot 10=40\ un.[/tex]
the volume of a gold bar is 100cm cubed, the density of gold is 19.3g/cm cubed so what is the mass of the gold bar
➷ Use this formula:
density = mass / volume
Rearrange it for mass:
mass = density x volume
Substitute the values in:
mass = 100 x 19.3
Solve:
mass = 1930g
✽➶ Hope This Helps You!
➶ Good Luck (:
➶ Have A Great Day ^-^
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The sum of four and the product of three and a number x.
Answer:
4 + 3xStep-by-step explanation:
The product of three and a number x: 3 · x = 3x
The sum of four and the product of three and a number x:
4 + 3x
find the area of equilateral triangle of side 4 cm.
Answer:6.928
Step-by-step explanation: formula A=√ 3*(side^2/4)
The area would be 7 cm
Step-by-step explanation:See the image
What is the answer to 8x^3+125 by factoring the perfect cube?
Answer:
[tex]\large\boxed{8x^3+125=(2x+5)(4x^2-10x+25)}[/tex]
Step-by-step explanation:
[tex]8x^3+125=2^3x^3+5^3=(2x)^3+5^3\\\\\text{use}\ a^3+b^3=(a+b)(a^2-ab+b^2)\\\\=(2x+5)((2x)^2-(2x)(5)+5^2)\\\\=(2x+5)(4x^2-10x+25)[/tex]
The population of a small town is around 4500 in 2010. The population is decreasing at a rate of 1.5% per year. After what year would the population in the town drop below 4000.
The population of a town decreasing at a rate of 1.5% per year from an initial number of 4500 will drop below 4000 in approximately 9 years, around the year 2019.
Explanation:The topic of this question concerns a decrease in population over time, which is generally described using exponential decay in mathematics. When we talk about a decrease of 1.5% per year, we're looking at an exponential decay factor of 1 - 0.015 = 0.985. We follow this process to determine the duration for the population to reduce below 4000:
Start with the initial population: 4500 Multiply that by the decay factor for each year Reiterate this until the population falls below 4000
Basically, it means:
4500 * (0.985^n) < 4000
. By solving this inequality, we find that
n ≈ 8.29
. Therefore, we can estimate the town's population will drop below 4000 in the 9th year (since we can't have a fraction of a year), which would be
2019
if we start counting from 2010.
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The population of the town would drop below 4000 in 2024.
To determine the year when the population of the town drops below 4000, we can use the formula for exponential decay:
Population = Initial population × (1 - Decay rate)^Time
where:
Population is the population at a given time
Initial population is the initial population (in 2010, which is 4500)
Decay rate is the decrease rate per year (1.5% or 0.015)
Time is the number of years since 2010
We want to find the Time when the Population is less than 4000. So, we can set up an inequality:
4000 > 4500 × (1 - 0.015)^Time
Dividing both sides by 4500, we get:
0.889 > (1 - 0.015)^Time
Taking the natural logarithm of both sides, we get:
ln(0.889) > Time × ln(1 - 0.015)
Dividing both sides by ln(1 - 0.015), we get:
Time ≈ 13.92
Since we're looking for the year when the population drops below 4000, we round up to the nearest whole year. Therefore, the population of the town would drop below 4000 in 2024.