Given trigonometric expression in algebraic form would be,
cos(arcsin(x - h/r)) = ± [√(r² - (x - h)²)]/r
In this question, we need write the expression in algebraic form.
Given trigonometric expression is cos(arcsin(x - h/r))
Let y = arcsin(x - h/r)
so, sin(y) = (x - h)/r
By trigonometric identity,
sin^2(y) + cos^2(y) = 1
we have cos(y) = ±√(1 - sin²y)
cos(arcsin(x - h/r)) = ±√[1 - ((x - h)/r)^2]
= ± [√(r² - (x - h)²)]/r
Therefore, given trigonometric expression in algebraic form would be,
cos(arcsin(x - h/r)) = ± [√(r² - (x - h)²)]/r
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Which graph represents the equation y=2x+5
Answer:
The one where the line passes 5 on the y-axis. Last pic
Answer:
your fourth option is your answer
One cable company charges $50 per month for their basic plan, plus $75
installation. A second company charges $55 per month, but offers free
installation. For what number of months is the first plan cheaper than the
second plan?
Write your answer as a number, with no symbols, spaces, or words.
Your answer
Step-by-step explanation:
One cable company charges $50 per month for their basic plan, plus $75 installation. A second company charges $55 per month, but offers free installation. For what number of months is the first plan cheaper than the second plan?
50m + 75 < 55m
subtract 50m from both sides:
50m + 75 -50m < 55m - 50m
75 < 5m
divide both sides by 5:
75/5 < 5m/5
15 < m
or m > 15
so:
The first plan cheaper than the second plan after 16+ months
Determine if the statements are true or false
The standard form of 4.4 x 10-4 is 0.00044.
The standard form of 6.39 x 105 is 63,900,000.
The standard form of 3.02 x 10° is 3,020,000,000.
The statements are true or false.
The standard form of 4.4 x 10-4 is 0.00044.
= 4.4 * 10^-4
= 4.4/10^4
= 4.4/10000
0.00044 = 0.00044
This statement is true.
The standard form of 6.39 x 10^5
= 6.39 * 100000
= 639*1000
639000 ≠ 63,900,000
This statement is false
The standard form of 3.02 x 10^10 is 3,020,000,000.
= 3.02 * 10^10
= 3.02 *10000000000
= 3,020,000,0000
This statement is false.
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what is 28.5dived by 11 equal explain how you got the answer.
The solution to the statement is 2.591
How to determine the solution to the statement?From the question, we have the following mathematical statement that can be used in our computation:
what is 28.5dived by 11 equal
Rewrite the statement properly
So, we have
what is 28.5 divided by 11 equal
This means that we divide 28.5 by 11
So, we have the following representation
28.5/11
Evaluate the quotient
28.5/11 = 2.591
Hence, the result is 2.591
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A first number plus twice a second number is 8. Twice the first number plus the second totals 28. Find the numbers.
Answer:
x = 16, y = -4
Step-by-step explanation:
First, we can say that "x = the first number" and "y = the second number"
The first number plus twice the second number is 8:
x + 2y = 8
Twice the first number plus the second number totals 28:
2x + y = 28
Next, we solve the system of equations.
x + 2y = 8 ---> 2x + 4y = 16 ---> 2x = 16 - 4y
2x + y = 28 ---> 2x = 28 - y
16 - 4y = 28 - y
-4y + y = 28 - 16
-3y = 12
y = -4
Now, we plug "y = -4" into either one of the equations to find x:
x + 2(-4) = 8
x + -8 = 8
x = 8 + 8
x = 16
For the quadratic equation x2 + 4x - 5 = - x2 + 7
which is a,b,c
The coefficients of the quadratic equation are:
a = 2, b = 4, c = -12
What are the coefficients of the quadratic equation?
The general quadratic equation is:
a*x^2 + b*x + c = 0
In this case, we have the quadratic equation:
x^2 + 4x - 5 = -x^2+ 7
Let's move all the terms to the left side, then we will get:
x^2 + 4x - 5 + x^2 - 7 =0
Now group like terms:
x^2 + x^2 + 4x - 5 - 7 =0
2x^2 + 4x - 12 = 0
Comparing this with the general quadratic equation we can see that:
a = 2
b = 4
c = -12
These are the coefficients.
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if WX=22 and WY=26 what is WZ
Answer:
30
Step-by-step explanation:
WX = 22
WY = 26
WZ = 30
22 + 4 = 26
26 + 4 = 30
Do the following rectangles have the same perimeter, area, or both? a rectangle is labeled 4 centimeters along its left side and 5 centimeters along its top side. a rectangle is labeled 4 centimeters along its left side and 5 centimeters along its top side. a rectangle is labeled 10 centimeters along its left side and 2 centimeters along its top side. a rectangle is labeled 10 centimeters along its left side and 2 centimeters along its top side. choose 1 answer: choose 1 answer: (choice a) a same area only (choice b) b same perimeter only (choice c) c same area and perimeter
how large a sample is needed if we wish to be 96% confident that our sample proportion in the question (7) will be within 0.02 of the true fraction of the voting population.
The sample size for estimating the proportion is 2637.
Given,
How many people should be included in the sample if we want to have 96% confidence that our sample proportion will be within 0.02 of the true fraction of the voting population given the data?
E = 0.02
c = 96% = 0.96
[tex]\hat p[/tex] or P = 0.5 (We have no idea about P, in this case, take P = 0.5)
[tex]\hat p[/tex] = 1 - [tex]\hat p[/tex] = 0.5
Now,
α = 1 - c = 1 - 0.96 = 0.04
α/2 = 0.04/2 = 0.02
⇒ α/2 = 2.054 (using z table)
The sample size for estimating the proportion is given by,
[tex]n = Z^2_\alpha _/_2P(1-P)/E^2[/tex]
= (2.054/0.02)2 * 0.5 * 0.5
= 2636.8
= 2637
Hence, the size of sample is 2637.
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what would the answer be and this is the last question u get brainlist for givnig the answer
Answer:
8.56
Step-by-step explanation:
d=2
r=d/2
r=1
area of the circle=πr², but we also have to subtract the square from it
a=π2²
a= 12.56
now the area of the square is 2*2
the area of the shape 12.56-(2*3)
the area of the shape is 8.56
art 1 of 2 Question content area top Part 1 Swimming Pool, On a certain hot summer's day, people used the public swimming pool. The daily prices are $1.25 for children and $2.25 for adults. The receipts for admission totaled $294.75. How many children and how many adults swam at the public pool that day?
Step-by-step explanation:
x = number of children
y = number of adults
1.25x + 2.25y = 294.75
this has many different solutions.
we would need a total number of persons in the pool in order to solve that to a single solution.
so, it could be 131 adults and 0 children.
for every reduction of 5 adults we can add 9 children and keep the same total
so, it could be 126 adults and 9 children
121 adults and 18 children
116 adults and 27 children
...
1 adult and 234 children
how did I get to the 5 to 9 ratio ?
1.25 is 5/4.
2.25 is 9/4
so, I was looking for the smallest common multiple of 5 and 9. which is 45 or 5×9. there is no simpler ratio between them.
so, the ticket price of 9 children is the same as the ticket price of 5 adults.
in order to keep the total of $294.75, when I reduce the number of adults, I have to compensate by adding children with the same amount of ticket prices.
this does not charge the fact that your teacher gave you an incomplete problem to solve.
but maybe your teacher wanted you to discover this problem.
equation like that passes through (4,1) and perpendicular to y=1/2x-1
The equation of the line passing through (4,1) and perpendicular to y=1/2x-1 is y = -2x+9.
According to the question,
We have the following information:
A line passes through (4,1) and perpendicular to y=1/2x-1.
Now, the slope of the given line is 1/2.
We know that the slope of the perpendicular line is given by -1/m.
Slope of perpendicular line = -1/(1/2)
Slope of perpendicular line = -2
Equation of the required line:
(y-y') = m(x-x')
(y-1) = -2(x-4)
y-1 = -2x+8
y = -2x+8+1
y = -2x+9
Hence, the equation of the line passing through (4,1) and perpendicular to y=1/2x-1 is y = -2x+9.
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a neonate order is 0.03 mg/kg of a 1:10,000 solution. the patient weighs 4.4 lb. how many milliliters of the solution will be needed?
600 milliliters of the solution will be needed.
Given:
Let x be the solution needed.
A neonate order is 0.03 mg/kg of a 1:10,000 solution. the patient weighs 4.4 lb.
4.4 lb = 1.99581 kg
4.4 lb ≈ 2 kg
neonate order = 2*0.03
= 2*3/100
= 6/100
= 0.06 mg
1 : 10000 = 0.06 : x
1/10000 = 0.06/x
x = 0.06 * 10000 / 1
= 0.6*1000
= 6*100
= 600 milliliters.
Therefore 600 milliliters of the solution will be needed.
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asap
Calculate the value of x.
Answer:7.07 m
Step-by-step explanation:
ab=5
ab=bc
bc=5
(ab)^2+(bc)^2=(ac)^2
25+25=50
ac^2=50
ac=7.07
Madelyn was out at a restaurant for dinner when the bill came. Her dinner came to $30. After adding in a tip, before tax, she paid $38. 40. Find the percent tip.
Answer:
28%
Step-by-step explanation:
38.40 - 30 = 8.40
x : 100 = 8.40 : 30
x = 8.40 * 100 / 30
x = 840/30
x = 84/3 = 28%
z/m - z/n = 1 if m≠n
solve for z
pls do this fast
The solution for z is [tex]z=\frac{nm}{(n-m)}[/tex]
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
The equation is [tex]\frac{z}{m} -\frac{z}{n}=1[/tex]
On simplifying , we get
[tex]\frac{(zn-zm)}{nm} =1[/tex]
Multiply both sides by 'nm' , we get
[tex]zn-zm=nm[/tex]
Taking z as the common term in LHS , we get
[tex]z(n-m)=nm[/tex]
Divide by ( n - m ) on both sides ,we get
[tex]z=\frac{nm}{(n-m)}[/tex]
Since , n ≠ m
n - m ≠ 0
So , the solution is [tex]z=\frac{nm}{(n-m)}[/tex]
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A glitter glue recipe takes a mixture of
1
5
cup of glitter to
2
5
cup of glue.
For A, how many cups of glitter are used for 1 cup of glue?
For B, how many cups of glitter glue is made with 1 cup of glue?
A. cups of glitter
B cups of glitter glue
0.6 cup of gliter is used for 1 cup of glue and 1.6 cup of gliter glue is made with 1 cup of glue.
Part A
Given that,
15 cup of gliter is for 25 cup of glue ,
Therefore, "X" cup of gliter is for 1 cup of glue
X = (1*15)/25
X= 0.6 cup of gliter
Part B,
Given that,
From part A 0.6 cup of gliter is for 1 cup of glue
Thus, 1 cup of glue and 0.6 cup of gliter when mixed will form "Y" cup of gliter glue
Now, Y= 0.6 cup of gliter + 1 cup of glue
Y= 1.6 cup of gliter glue
which approximates to 2 cup of gliter glue.
find the value of u
8^2 + u^2 = 17^2
Answer:
u = 15
Step-by-step explanation:
It appears that you have already created an equation to solve for u and just need help solving it
So we have 8² + u² = 17²
==> simplify exponents
64 + u² = 289
==> subtract 64 from both sides
u² = 225
==> take the square root of both sides
u = 15
Consider the quadratic function f(x) = x2 – 5x + 12. Which statements are true about the function and its graph? Select three options. The value of f(–10) = 82 The graph of the function is a parabola. The graph of the function opens down. The graph contains the point (20, –8). The graph contains the point (0, 0).
The given problem can be solved by using the properties of the parabola.
The following statements are true about the function and its graph are as follows;
The value of a is 1 which is positive then the parabola opens upward.
What is a parabola?
A parabola is a plane curve that is mirror-symmetrical and roughly U-shaped in mathematics. It fits several seemingly disparate mathematical descriptions, all of which can be shown to define the same curves. A point and a line are two ways to describe
According to the question,
1. The value of the function when f(-10) is,
[tex]f(x)=x^2-5x+12\\\\f(-10) =(-10)^2-5(-10)+12\\\\f(-10)=100+50+12\\\\f(-10)=162[/tex]
So the first option is false.
2. The graph of the function is a parabola.
The value of a is 1 which is positive then the parabola opens upward.
3. The graph contains the point f(x) = 20,
[tex]f(x)=x^2-5x+12\\\\f(20) =(20)^2-5(20)+12\\\\f(20)=400-100+12\\\\f(20)=312\\[/tex]
The graph contains the point (20, 312).
4. The graph contains the point f(x) = 0,
[tex]f(x)=x^2-5x+12\\\\f(0) =(0)^2-5(0)+12\\\\f(0)=0-0+12\\\\f(0)=12\\[/tex]
The graph contains the point (0, 12).
Hence, the given problem can be solved by using the properties of the parabola. The following statements are true about the function and its graph are as follows;
The value of a is 1 which is positive then the parabola opens upward.
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f(x) = 2x ^2 - 3x + 1; k+2
Use the remainder theorem to find the remainder when f(x) is divided by x-k.
The remainder will be (k - 1) or (2k - 1) after using the remainder theorem.
What is a polynomial?Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.
[tex]\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n[/tex]
The remainder theorem:
f(x) = 2x² - 3x + 1
f(x) is divided by (x - k)
The remainder = f(k)
The remainder = 2k² - 3k + 1
After factoring:
(k - 1)(2k - 1)
The remainder will be (k - 1) or (2k - 1)
Thus, the remainder will be (k - 1) or (2k - 1) after using the remainder theorem.
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What is the yield on a corporate bond with a $1000
face value purchased at a discount price of $950, if
it pays 6% fixed interest for the duration of the
bond?
The yield on a corporate bond with a face value of $1000 after removal of discount would be =$60.
What is interest rate?Interest rate can defined as the payment received by an individual after investing a particular amount of money for a given period of time.
The principal amount after removal of $950 discount = $1000
The rate of interest (R) = 6%
The time of investment (T) = 1
Then the simple interest;
= P × T × R/100
= 1000 × 1 × 6/100
= 6000/100 = $60
Therefore, the yield of the corporate bond would be extra $60.
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Determine if the triangles below are similar. If so, state the reason and write the similarity statement.
QRS is similar to _______.
A. Similar due to AA . Triangle QRS is similar to triangle VUT.
B. Similar due to SSS and a scale factor of 0.29. Triangle QRS is similar to triangle VUT.
C. Not similar
D. Similar due to SSS and a scale factor of 3.5. Triangle QRS is similar to triangle TUV.
E. Similar to due SAS and a scale factor of 0.29. Triangle QRS is similar to triangle TUV.
The correct statement is "Similar, due to SSS and a scale factor of 0.29. Triangle QRS is similar to triangle VUT".
What is similarity in triangles?Two triangles are similar if they have the same ratio of corresponding sides and equal pair of corresponding angles. If two or more figures have the same shape, but their sizes are different, then such objects are called similar figures.
Given that, two triangles Δ QRS and Δ VUT
We have,
QR/VU = RS/UT = QS/VT = 2/7 = 0.29
Hence, the two triangles are similar by SSS property with a scale factor of 0.29
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Jeremy has $120 in his savings account and katie has $180 in her account. Each week jeremy adds $14 to his account, and katie adds $10 to hers. How many weeks will it be before jeremy and katie have the same amount of money saved up?.
It will takes 15 weeks before Jeremy and Katie have the same amount of money saved up.
Define Expression
An expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
Given,
Jeremy has balance in his savings account = $120
Each week Jeremy adds amount to his account = $14
Katie has balance in her savings account = $180
Each week Katie adds amount to her account = $10
Let, x = number of weeks
At the end of each week Jeremy has = 120 + 14x
At the end of each week Katie has = 180 + 10x
As we want to have same amount in both the account for that just equate the values of each week of Jeremy and Katie.
120 + 14x = 180 + 10x
14x - 10x = 180 - 120
4x = 60
x = 15
Hence, it will takes 15 weeks before Jeremy and Katie have the same amount of money saved up.
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A local recreation center offers a yearly membership and charges
an additional fee for aerobics classes as shown in the table.
Number of classes (x)
1
5
10
15
Total cost (y)
270
290
315
340
a. Write an equation in slope-intercept form that represents the total cost of the membership.
b. Carly spent $500 one year. How many aerobics classes did she take?
An equation in slope-intercept form that represents the total cost of the membership is y = 5x + 265.
The number of aerobics classes that Carly took at $500 one year is 47 aerobics classes.
How to write an equation in slope-intercept form?In order to write the equation in slope-intercept form, we would have to determine the slope of the line representing the total cost of the membership.
Mathematically, the slope of any straight line can be calculated by using this formula;
Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope, m = (y₂ - y₁)/(x₂ - x₁)
Substituting the given parameters into the formula, we have;
Slope, m = (290 - 270)/(5 - 1)
Slope, m = 20/4
Slope, m = 4
At point (1, 270), an equation of this line in slope-intercept form can be calculated by using this standard formula:
y = mx + c
Where:
m represents the slope.x and y are the points.c represents the intercept.Substituting the given points into the formula, we have;
y = mx + c
270 = 5(1) + c
Intercept, c = 270 - 5
Intercept, c = 265.
Therefore, the required equation is given by:
y = 5x + 265
For the number of aerobics classes at $500 one year, we have:
500 = 5x + 265
5x = 500 - 265
5x = 235
x = 235/5
x = 47 aerobics classes.
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Janice currently has 26 marbles and is collecting 3 per week. Oliver currently has 10 marbles and is collecting 5 per week. how many weeks will it take so that janice and oliver have the same amount of marbles?
It will take 8 weeks so that janice and oliver have the same amount of marbles.
What do you mean by linear expression?
An algebraic expression known as a linear expression has terms that are either constants or variables raised to the first power. Alternatively put, none of the exponents can be greater than 1.
Coefficients in linear equations can be either positive or negative values. The exponent is important. The entire equation becomes non-linear when a single variable is raised to a power greater than 1.
Let number of weeks be x
According to question, Janice currently has 26 marbles and is collecting 3 per week and Oliver currently has 10 marbles and is collecting 5 per week.
This means ,
26 + 3x = 10 + 5x
26 - 10 = 5x - 3x
16 = 2x
x = 16/2 = 8
Therefore, it will take 8 weeks so that janice and oliver have the same amount of marbles.
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3x - y = 17
4x + y = -3
Answer:
x = 7, y = 4
Step-by-step explanation:
simultaneous equation:
3x-y=17
4x+y=-3
Solving for x: add the two equations together to cancel out y (-y + y = 0)7x = 14divide both sides by 7 to get the value of 1 xx = 7solving for y: substitue the value of x (7) into any equation (we'll use the top one for ease)3(7) - y = 17so in other words; 21 - y = 17subtract 21 from both sides to get the value of -y-y = -4therefore, y = 4what percent is 1/3 of a circle
Answer:
120
Step-by-step explanation:
360
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The product of twice a number and six is the same as the difference of eleven times the number and 7/6. find the number
Answer:
2x X 6 = 11x - 7/6
12x = 11x - 7/6
12x - 11x = -7/6
x = - 7/6
Step-by-step explanation:
let the unknown be x
twice of the number is 2x multipled by 6
2x(6) equating to eleven times the number 11x minus 7/6
gives an equation as in step 1
multiply 6 by 2x to give a more simple equation
collect like terms so you have an equation as in step 3
simplify to get your final answer
Help, The distance between point (2, 2) and point (8, 2) is 6 units on a coordinate plane. Which other pairs of points are also 6 units apart? Select all that apply.
6.2 in.
8 in.
I need help with this
What is the area of one of the triangles
What is the area of the entire square
Answer:
the area for the entire scale is 8 inches
the area for one of the triangles is 6.2 inches
Step-by-step explanation:
Answer:
Step-by-step explanation:
Area of the triangle is:
A = 1/2 * (Base * Height)
A = 1/2 * (b * h)
A = 1/2 * (8 * 6.2)
A = 1/2 * 49.6
A = 24.8
Area of the square is:
A = Base * Height
A = b * h
A = 8 * 6.2
A = 49.6
