Answer:
[tex]b = \frac{2A}{h} - a[/tex]Step-by-step explanation:
[tex]A = \frac{1}{2} (a + b)h[/tex]Multiply both sides by 2
We have
2A = (a + b)h
Divide both sides of the equation by h
That's
[tex] \frac{(a + b)h}{h} = \frac{2A}{h} [/tex]We have
[tex]a + b = \frac{2A}{h} [/tex]Move a to the right side of the equation to make b stand alone
We have the final answer as
[tex]b = \frac{2A}{h} - a[/tex]Hope this helps you
5y-5y^2-5+2+2y+3y^2-1
Answer:
7y - 2y² - 4
Step-by-step explanation:
5y - 5y² - 5 + 2 + 2y + 3y² - 1
5y + 2y - 5y² + 3y² - 5 + 2 - 1 (combine like terms)
7y - 2y² - 4
Question 5 of 10
Which type of unemployment is characterized by a worker looking for a job
when there is no reason that he or she should not find one?
A. Structural unemployment
B. Seasonal unemployment
C. Frictional unemployment
D. Periodic unemployment
Find the range of f(x) = –x + 4 for the domain {–3, –2, –1, 1}.
Answer:
[tex]\boxed{ \{7, 6, 5, 3 \} }[/tex]
Step-by-step explanation:
The domain is all possible values for x.
The range is all possible values for f(x) or y.
The domain given is {-3, -2, -1, 1}.
Plug x as {-3, -2, -1, 1} and find the f(x) or y values.
[tex]f(-3)=-(-3)+4=7\\f(-2)=-(-2)+4=6\\f(-1)=-(-1)+4=5\\f(1)=-(1)+4=3[/tex]
The range is {7, 6, 5, 3}, when the domain is {-3, -2, -1, 1}.
Please someone help me im desperate
Find Tan0 , csc0, and cos0 where 0 is the angle shown in the figure. Give EXACT values, not decimal approximations.
Answer:
1. Tan θ = √11/5
2. Cosec θ = 6√11 /11
3. Cos θ = 5/6
Step-by-step explanation:
Let the side opposite to angle θ be y.
The value of y can be obtained by using the pythagoras theory as follow:
b² = 6² – 5²
b² = 36 – 25
b² = 11
Take the square root of both side.
b = √11
1. Determination of Tan θ
Tan θ =?
Opposite = √11
Adjacent = 5
Tan θ = Opposite /Adjacent
Tan θ = √11/5
2. Determination of Cosec θ.
We'll begin by calculating the Sine θ. This is illustrated below:
Sine θ =?
Opposite = √11
Hypothenus = 6
Sine θ = Opposite /Hypothenus
Sine θ = √11/6
Now, we shall determine Cosec θ as follow:
Cosec θ = 1/Sine θ
Sine θ = √11/6
Cosec θ = 1 ÷ √11/6
Cosec θ = 1 × 6/√11
Cosec θ = 6/√11
Rationalise the denominator
Cosec θ = 6/√11 × √11/√11
Cosec θ = 6√11 /11
3. Determination of Cos θ.
Cos θ =?
Adjacent = 5
Hypothenus = 6
Cos θ = Adjacent / Hypothenus
Cos θ = 5/6
A wave has a time period of 0.2 s Calculate the frequency of the wave.
Answer:
[tex]\huge\boxed{f = 5\ Hz}[/tex]
Step-by-step explanation:
Given:
Time period = T = 0.2 sec
Required:
Frequency = f = ?
Formula:
f = 1/T
Solution:
f = 1/0.2
f = 5 Hertz
Answer:
[tex] \boxed{\sf Frequency \ (f) \ of \ the \ wave = 5 \ Hz} [/tex]
Given:
Time Period (T) = 0.2 s
To Find:
Frequency (f) of the wave
Step-by-step explanation:
[tex] \sf Frequency (f) = \frac{1}{Time Period (T)} [/tex]
[tex] \sf f = \frac{1}{0.2} [/tex]
[tex] \sf f = \frac{1}{0.2} \times \frac{10}{10} [/tex]
[tex] \sf f = \frac{10}{2} [/tex]
[tex] \sf f = \frac{ \cancel{2} \times 5}{ \cancel{2}} [/tex]
[tex] \sf f = 5 \: Hz[/tex]
solve the equation 3), x=???? Please help me!!!
Answer:
x = {π/4, 7π/6, 5π/4, 11π/6} +2kπ . . . for any integer k
Step-by-step explanation:
[tex]\dfrac{\sin^3{x}}{1+\cos{x}}+\dfrac{\cos^3{x}}{1+\sin{x}}=\cos{2x}+2\cos{x}-1\\\\\dfrac{\sin{x}(1-\cos^2{x})}{1+\cos{x}}+\dfrac{\cos{x}(1-\sin^2{x})}{1+\sin{x}}=\cos^2{x}-\sin^2{x}+2\cos{x}-1\\\\\sin{x}(1-\cos{x})+\cos{x}(1-\sin{x})=\cos^2{x}-\sin^2{x}+2\cos{x}-1\\\\\sin{x}+\cos{x}-2\sin{x}\cos{x}=2\cos{x}-2\sin^2{x}\qquad\text{use $1=s^2+c^2$}\\\\\sin{x}+2\sin^2{x}-\cos{x}-2\sin{x}\cos{x}=0\\\\\sin{x}(1+2\sin{x})-\cos{x}(1+2\sin{x})=0\\\\(\sin{x}-\cos{x})(1+2\sin{x})=0[/tex]
This will have solutions where the factors are zero.
sin(x) -cos(x) = 0
Dividing by cos(x), we have ...
tan(x) -1 = 0
x = arctan(1) = π/4, 5π/4
1 +2sin(x) = 0
sin(x) = -1/2
x = arcsin(-1/2) = 7π/6, 11π/6
The four solutions in the interval [0, 2π] are x = {π/4, 7π/6, 5π/4, 11π/6}. Solutions repeat every 2π radians.
_____
Additional comment
We have made use of the factoring of the difference of squares:
(1 -a^2) = (1 -a)(1 +a)
and we have made use of the cosine double angle identity:
cos(2x) = cos(x)^2 -sin(x)^2
The "Pythagorean" identity for sine and cosine was used several times:
1 = sin(x)^2 +cos(x)^2
15 points! :( help asap!:(
(-1,-5)
(0,-3)
(4,5)
(9,15)
Answer:
(0,-3)
Step-by-step explanation:
You can plug in x and y into the equations to see if it works.
(-1,5)
2(-1)-(-5)=-2+5=3 Yes
(-1)+2(-5)=-1-10=-11 No
So (-1,5) Does NOT work.
(0,3)
2(0)-(-3)=0+3=3 Yes
(0)+2(-3)=0-6=-6 Yes
So (0,-3) DOES work.
If BH = 108, find DE.
Answer:
BH= 108 --> 1st until 6th space
so, 108/6 = 18 for each space
DE...?
DE only use 1 space so the answers is 18 unit
I hope this helps^_^
A group of friends went to lunch and spent a total of $76, which included the food bill and a tip of $16. They decided to split the bill and tip evenly among themselves
Complete question:
A group of 8 friends went to lunch and spent a total of $76, which included the food bill and a tip of $16. They decided to split the bill and tip evenly among themselves. Which equations and solutions describe the situation? Check all that apply. The equation 1/8(x+16)=76/8 represents the situation, where x is the food bill. The equation 1/8 (x+16)=76 represents the situation, where x is the food bill. The solution x=60 represents the total food bill. The solution x=60 represents each friend’s share of the food bill and tip. The equation 8(x+16)=76 represents the situation, where x is the food bill.
Answer:
The equation 1/8(x+16)=76/8 represents the situation, where x is the food bill
The solution x=60 represents the total food bill
Step-by-step explanation:
Given the following :
Total amount spent = $76
Amount paid as tip = $16
Number of friends = 8
Total Cost of lunch consists of:
Actual Cost of food + amount of tip
Let actual cost of food = x
Total cost of lunch is thus :
x + $16 = $76
If the friends are to each the bill equally:
Then:
Divide both sides by 8:
(1/8)* (x + 16) = 76/8
Therefore,
(x + 16) / 8 = 76/8
x + 16 = 76 / 8
(x + 16)/8 = 9.5
x + 16 = 9.5 * 8
x + 16 = 76
x = 76 - 16
x = 60
Answer:
A
and
C
Step-by-step explanation:
Can somebody please tell me if it’s right? i’ll mark u the brainliest
Answer:
Yes, you are correct.
Step-by-step explanation:
You are substituting the measure of angle x as the measure of angle a since they are congruent to each other.
A dress shop bought material for £4.65 a metre and sold it for £6.90 a metre. How much
profit would be made on a roll of 30 metres?
Answer:
£67.50
Step-by-step explanation:
On each metre of material, the shop makes a profit of ...
£6.90 -4.65 = £2.25
So, for 30 metres, the profit will total ...
30 × £2.25 = £67.50
A profit of £67.50 would be made on a 30-metre roll of material.
The volume of a sphere whose diameter is 18 centimeters is π cubic centimeters. If its diameter were reduced by half, its volume would be of its original volume.
Answer:
3053.5517 cm^3 ; 1/8
Step-by-step explanation:
Given the following :
Volume (V) of sphere = (4/3)πr^3 where r = radius
Diameter of sphere = 18 ; radius(r) = diameter / 2 = 18/2 = 9cm
V = (4/3) × π × 9^3
V = 1.3333 × π × 729
V = 3053.5517 cm^3
When diameter(d) is reduced to half
d = d/2
Volume (V1) of sphere with diameter 'd' =
V1 = (4/3)π(d/2)^3
Volume (V2) of sphere with diameter 'd' reduced to half, d = d/2, d/2 * 1/2 = d/4
V2 = (4/3)π(d/4)^3
V1 / V2 = [(4/3)π(d/2)^3] / [(4/3)π(d/4)^3]
V1 / V2 = (d/2)^3 / (d/4)^3
V1 / V2 = [d^3 / 2^3] / [d^3 / 4^3]
V1 / V2 = 8 / 64
V1 / V2 = 1 / 8
Answer:
first blank is 972
second blank is 1/8
yup
Step-by-step explanation:
Kelsey had $65 to spend on books. Each book cost $5.50, and there was a $7.50 fee for shipping. She let b equal the number of books she can purchase and wrote the inequality 5.50 b + 7.5 less-than 65 to represent the situation. Which statements describe the reasoning used to determine if Kelsey’s inequality is correct? Select two options. The inequality symbol is correct because she must spend less than $65. The inequality symbol is incorrect because she can spend up to and including $65. The expression 5.50b + 7.5 is correct because $5.50 per book is 5.50b and that is added to the shipping fee of $7.50 to determine the total purchase price. The expression 5.50b + 7.5 is incorrect because $5.50 per book and $7.50 should be combined to $9.50b to determine the total purchase price. The inequality symbol is correct because she cannot spend more than $65.
The statements that can be used to describe the reasoning used to determine if Kelsey’s inequality is correct include:
The inequality symbol is incorrect because she can spend up to and including $65. The expression 5.50b + 7.5 is correct because $5.50 per book is 5.50b and that is added to the shipping fee of $7.50 to determine the total purchase price.It should be noted that the inequality symbol is incorrect because she can spend up to and including $65.
Based on the information given, the correct expression that can be used to solve the question should be:
65 - (5.50b + 7.5)
In conclusion, the correct options are B and C.
Read related link on:
https://brainly.com/question/16904821
Answer:
B and C
Step-by-step explanation:
How do the number line graphs of the solutions sets of Negative 23 greater-than x and x greater-than-or-equal-to negative 23 differ?
Answer:
For "Negative 23 greater-than x" , highlight the left half of the number line starting at -23 and use a parenthesis ) on -23.
For "x greater-than-or-equal-to negative 23", highlight the right half of the number line starting at -23, and use a square bracket [ on -23.
Step-by-step explanation:
Start by locating the number -23 on the number line. Please see attached image to accompany the explanation.
In the first case: "Negative 23 greater-than x" , which is expressed mathematically as:
[tex]-23 >x[/tex]
notice that "x" has to be strictly smaller than the number -23, therefore those sought x values must reside to the left of the number -23, so we have to highlight that half of the number line. Apart from that, we need to include a symbol on top of the number -23, that indicates that -23 itself shouldn't be considered as part of the set, that symbol is by convention a parenthesis ).
In the second case: "x greater-than-or-equal-to negative 23", which is expressed mathematically as:
[tex]x\geq -23[/tex]
notice that "x" has to be greater than or equal to the number -23, therefore those sought x values must reside to the right of the number -23, so we have to highlight that half of the number line. Apart from that, we need to include a symbol on top of the number -23, that indicates that -23 itself should be considered as part of the set, that symbol is by convention a square bracket [.
Answer:
the answer is A
Step-by-step explanation:
Briefly describe this graph of a Femis wheel.
Answer: This is a periodic relation.
Step-by-step explanation:
This is a periodic relation, that can be modeled with a sinusoidal relation, that relates the height as a function of time.
Then we can write this as h(t) = A*sin(C*t + F) + B
Where A is the amplitude, C is a constant that depends on the period, F is a phase shift, and B is the midpoint of the function.
2*A is the distance between the maximum height and the minimum height.
B is the middle height of the Femis Wheel.
Hiiii can you help me ?
Answer:
842, 743, 394, 305, 836
Step-by-step explanation:
We arbitrarily chose the ones digit to start with as 2. (It must be 5 or less.) The other two digits are chosen by a random number generator, as shown in the attached.
The 5 three-digit numbers we chose are ...
842, 743, 394, 305, 836
Answer:
The only criteria the question gives are that there must be 5 numbers, and the numbers must have 3 digits. The ones digit in the numbers should go up by 1.
So, we can have 111, 112, 113, 114, and 115.
Hope this helps!
find all the missing elements. A=109 C=13 b=6 B=? a=? c=?
Answer:
B = 58°a = 6.6896c = 1.5915Step-by-step explanation:
Given two angles and the side between them, the first step must be to find the value of the third angle, the one opposite the given side. It will be ...
B = 180° -A -C = 180° -109° -13° = 58°
Using this information and the Law of Sines, you can find the remaining sides.
a/sin(A) = b/sin(B) = c/sin(C)
__
Then the missing sides are ...
a = b(sin(A)/sin(B)) = 6(sin(109°)/sin(58°)) ≈ 6.6896
c = b(sin(C)/sin(B)) = 6(sin(13°)/sin(58°)) ≈ 1.5915
The missing measures are ...
B = 58°
a = 6.6896
c = 1.5915
Answer: make sure to round !!B = 58°
a = 6.7
c = 1.6
Step-by-step explanation:
Tim owns a clothing store where he designs pairs of shorts, s, and T-shirts, t.
He sells the shorts for $12 and the T-shirts for $8 each. Tim can work 18
hours a day, at most. It takes him 30 minutes to design a T-shirt and 45
minutes to design a pair of shorts. He must design at least 12 items each
day, but he cannot design more than 30 items in one day. Which set of
inequalities below represents this scenario?
A. s 2 12 + $ ss 30 + tiss 24-0.66t, s2; 0; t2 0
B. s> 12-tss 30 - t Ss 24 -0.66t, s 2 0; t> 0
O c. s? 12-ts? 30-tss 24 -0.66t, s 2 0;t20
D. S 2 12-tss 30-ts 24 -0.66t, s 20; t 0
Answer:
The correct option is;
B. s ≥ 12 - t, s ≤ 30 - t, s ≤ 24 - 0.66·t
Step-by-step explanation:
The given parameters are;
The number of T-shirts, t, and shorts, s, Tim must design a day = 12
The maximum number of T-shirts and shorts Tim can design a day = 30
The maximum number of hours Tim can work = 18 hours
Therefore, we have;
The number of shorts Tim designs in a day is ≥ The minimum number of T-shirts and shorts Tim must design a day less the number of T-shirts Tim designs
Which gives;
s ≥ 12 - t
Also the number of shorts Tim designs in a day is ≤ The maximum number of T-shirts, and shorts, Tim can design a day less the number of T-shirts Tim designs
Which gives;
s ≤ 30 - t
The number of 45 minute period for the design of shorts in 18 hours = 18×60/45 = 24
The fraction of 36 minutes in 45 minutes = 36/45 = 0.667
Therefore we have;
The number of shorts Tim designs in a day is ≤ The number of 45 minute periods in 18 hours less the number of 36 minutes periods used to design T-shirts
Which gives;
s ≤ 24 - 0.66·t
The correct option is s ≥ 12 - t, s ≤ 30 - t, s ≤ 24 - 0.66·t.
Answer:
B. s> 12-tss 30 - t Ss 24 -0.66t, s 2 0; t> 0
Step-by-step explanation:
Hope this helps!!
Given that the trinomial x^2+ 11x + 28 has a factor of x +4, what is the other factor?
Answer:
the other factor is (x+7)
Step-by-step explanation:
Given x^2+11x+28
factor into
x^2+7x + 4x + 28
=x(x+7) + 4(x+7)
= (x+4)(x+7)
Answer: the other factor is (x+7)
Find the value of x so that the function has the given value.
j(x)=−4/5x+7; j(x)=−5
x=
Answer:
x = 3
Step-by-step explanation:
j(x) = 4/5(-5) + 7
= -4 + 7
= 3
Answer:
15
Step-by-step explanation: -4/5 x has to be -12 because -12+7 equals 5. Since we want to figure out x, we have to flip -4/5 x to 4/5x which would change the -12 to 12. What is a fourth of 12? It is three. 12+3 equals 15. This is the first right answer on all of the internet for this question!
We want to factor the following expression:
(x+4)^2 -4y^5 (x+4) + 4y10
We can factor the expression as (U – V)2 where U and V are either constant integers or single-variable
expressions.
1) What are U and V?
Answer:
U = x + 4 and V = 2y^5.
Step-by-step explanation:
Square root of (x + 4)^2 = x + 4
Square root of 4y^10 = 2y^5
U = x + 4 and V = 2y^5.
(U - V)^2 = U^2 - 2UV + V^2
= (x + 1)^2 - 2 (2y^5 (x + 1) + 4y^10
= (x + 1)^2 - 4y^5 (x + 4) + 4y^10
Answer:
U = x + 4 and V = 2y^5.
Step-by-step explanation:
please help!!!! Use the graph to complete the statement. O is the origin. Ry−axis ο Ry=x: (-1,2)
A. (1, -2) B. (-1, -2) C. (2, -1) D. (-2, -1)
Answer: D. (-2, -1)
Step-by-step explanation:
Here we do two reflections to the point (-1, 2).
First, we do a reflection over the line x = y. Remember that a reflection over a line keeps constant the distance between our point and the given line, so we have that for a pint (x, y), the reflection over the line y = x is:
Ry=x (x, y) = (y, x)
so for our point, we have:
Ry=x (-1, 2) = (2, -1)
Now we do a reflection over the y-axis, again, a reflection over a line keeps constant the distance between our point and the given line, so if we have a point (x,y) and we do a reflection over the y-axis, our new point will be:
Ry-axis (x,y) = (-x, y)
Then in our case:
Ry-axis (2, -1) = (-2, -1)
The correct option is D.
7 is subtracted from the quotient of 48 divided by the sum of 5 and differences of 11 and 8
Write it out as an equation:
(48 /(5+(11-8))) -7
Simplify:
(48/(5+3))-7
(48/8)-7
6-7 = -1
The answer is -1
What is the smallest positive integer $n$ such that $\frac{n}{n+101}$ is equal to a terminating decimal?
Answer:
n = 24
Step-by-step explanation:
Given the fraction:
[tex]$\frac{n}{n+101}$[/tex]
To find:
Smallest positive integer [tex]$n$[/tex] such that the fraction is equal to a terminating decimal.
Solution:
The rule that a fraction is equal to a terminating decimal states that, the denominator must contain factors of only 2 and 5.
i.e. Denominator must look like [tex]2^m\times 5^n[/tex], only then the fraction will be equal to a terminating decimal.
Now, let us have a look at the denominator, [tex]n+101[/tex]
Let us use hit and trial method to find the value of [tex]n[/tex] as positive integer.
n = 1, denominator becomes 102 = [tex]2 \times 3 \times 17[/tex] not of the form [tex]2^m\times 5^n[/tex].
n = 4, denominator becomes 105 = [tex]5 \times 3 \times 7[/tex] not of the form [tex]2^m\times 5^n[/tex].
n = 9, denominator becomes 110 = [tex]2 \times 5 \times 11[/tex] not of the form [tex]2^m\times 5^n[/tex].
n = 14, denominator becomes 115 = [tex]5 \times 23[/tex] not of the form [tex]2^m\times 5^n[/tex].
n = 19, denominator becomes 120 = [tex]5 \times 3 \times 2^3[/tex] not of the form [tex]2^m\times 5^n[/tex].
n = 24, denominator becomes 125 = [tex]2^0 \times 5 ^3[/tex] It is of the form [tex]2^m\times 5^n[/tex].
So, the answer is n = 24
What the answer question now
Step-by-step explanation:
Here,
radius (r)= 2cm
height(h)=5cm
now,
according to the question we must find the surface area of cylinder so,
by formulae ,
a= 2.pi.r(r+h)
now,
a= 2×3.14×2(2+5)
by simplifying it we get,
The surface area of cylinder is 87.92 cm^2.
Hope it helps
A geometric sequence has a common ratio of 22 and the 12th12th term is −12,288.−12,288.
What is the explicit rule that describes this sequence?
Answer:
Tₙ = -3(2)ⁿStep-by-step explanation:
The explicit rule for determining the nth term of a geometric sequence is expressed as Tₙ = arⁿ⁻¹ where;
a is the first term of the geometric sequence
r is the common ratio
n is the number of terms
If a geometric sequence has a common ratio of 2 and the 12th term is −12,288, then;
T₁₂ = ar¹²⁻¹
T₁₂ = ar¹¹
Given T₁₂ = -12,288 and r = 2, we can calculate the first term a
-12,288 = a2¹¹
a = -12,288/2¹¹
a = -12,288/2048
a = -6
Since the explicit rule for determining the nth term of a geometric sequence is expressed as Tₙ = arⁿ⁻¹, then for the sequence given, the explicit rule will be;
Tₙ = -6(2)ⁿ⁻¹
Tₙ = -6 * 2ⁿ * 2⁻¹
Tₙ = -6 * 2ⁿ * 1/2
Tₙ = -3(2)ⁿ
Hence the explicit rule that describes this sequence is Tₙ = -3(2)ⁿ
how to find y in this equation 11=12-14y
Solve the equation. 0.15 = y-0.45
Answer:
0.6
Step-by-step explanation:
0.6-0.45=0.15
The value of y from the given equation is 0.60.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
The given equation is 0.15=y-0.45.
The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.
Here, 0.15=y-0.45
y=0.15+0.45
y=0.60
Therefore, the value of y is 0.60.
To learn more about an equation visit:
https://brainly.com/question/14686792.
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a/4 + 4 = 6 please helppppp!
━━━━━━━☆☆━━━━━━━
▹ Answer
a = 8
▹ Step-by-Step Explanation
a/4 + 4 = 6
Multiply both sides:
a + 16 = 24
Subtract 16 from both sides:
16 - 16 = a
24 - 16 = 8
a = 8
Hope this helps!
CloutAnswers ❁
━━━━━━━☆☆━━━━━━━
Answer:
a = 8
Step-by-step explanation:
a/4 + 4 = 6
Subtract 4 from each side
a/4 + 4-4 = 6-4
a/4 = 2
Multiply each side by 4
a/4 * 4 = 2*4
a = 8
What is the answer that = n?
Answer:
n = 5
Step-by-step explanation:
To start off, we know that whenever the bases are the same, their exponents are equal to each other. Therefore, since both of the numbers bases are the same (both are z), we know that they will be equal.
The n can be distributed to the [tex]z^2[/tex] so that it now reads to be:
[tex]z^2^n = z^{10}[/tex]
Exponents are equal, so:
2n=10
Divide the 2 on both sides:
n=5
Answer:
n =5
Step-by-step explanation:
z^2^n
We know that a^b^c = a^ (b*c)
z^(2n)
This is equal to z^10
Since the bases are the same, the exponents are the same
2n = 10
Divide by 2
2n/2 = 10/2
n = 5
