Find the value of cos θ for the angle shown. A line is drawn from the origin through the point four comma negative square root of thirty-three. The angle theta is given as the measurement from the positive x axis counterclockwise to the line.
cos θ = seven-fourthscos θ = square root of thirty-three divided by four
cos θ = four-sevenths
cos θ = square root of thirty-three divided by seven
Answers
Answer
Cos θ = 4/7
Explanation
The angle θ is in the 3rd quadrant. So, it is positive.
cos θ = adjacent / hypotenuse
hypotenuse = √(4² + (√33)²)
= √(16 + 33)
= √47
= 7
Cos θ = 4/7
Answer:
Step-by-step explanation:
cos 0= 4/7
reason: i took the test
Related Questions
Draw a graph of the rose curve.
r = 2 sin 3θ, 0 ≤ θ ≤ 2π
Answers
Which of the following rules represents the set of ordered pairs?
{(1, 2), (2, 3), (4, 5), (7, 8)}
ƒ(x ) = 2x + 1
ƒ(x ) = -x + 4
ƒ(x ) = x + 1
Answers
f(x) = x + 1.....u will notice that if u sub in ur answer choices into this function, it come out true.
f(x) = x + 1.....when x = 1 and y = 2
2 = 1 + 1
2 = 2 (correct)
f(x) = x + 1...when x = 2 and y = 3
3 = 2 + 1
3 = 3 (correct)
it works for all ur points
so ur answer is : f(x) = x + 1 <==
The first three steps for solving the quadratic equation by completing the square are shown. Fill in the missing number in the last step
Answers
Answer:
AXxaXax
Step-by-step explanation:
An upscale resort has built its circular swimming pool around a central area that contains a restaurant. The central area is a right triangle with legs of 60 feet, 120 feet, and approximately 103.92 feet. The vertices of the triangle are points on the circle. The hypotenuse of the triangle is the diameter of the circle. The center of the circle is a point on the hypotenuse (longest side) of the triangle. The building permit the resort obtained requires that the resort state how much water the pool will hold so the city can manage the resort’s water rights effectively.
a.)What is the area of the largest section of the pool? Explain if you feel this area would be large enough to add a waterslide.
b.)How much water do you need to fill just the pool without the fish tank, if the average depth is 4 feet?
Answers
The largest section of the pool is 11307.2 square feet and it seems feasible to add a water slide based on this area. In order to fill the pool, considering that the average depth is 4 feet, approximately 338511.6 gallons of water would be needed.
Explanation:We will first find the area of the circular pool, keeping in mind that the hypotenuse of the triangle serves as the diameter. We will use the formula for the area of a circle, A = πr², where r is the radius of the circle. Here, the radius is half of the hypotenuse so it's 120 feet / 2 = 60 feet.
This makes the area of the circle A = π * 60² = 3600π square feet. This, minus the area of the triangle which can be calculated by (1/2) * base * height = (1/2) * 60 * 103.92 = 3117.6 square feet. So, the largest section of the pool is 3600π - 3117.6 = 11307.2 square feet.
Additional structures such as a water slide could be considered based on the remaining area. Due to size of the pool, it seems feasible to add a water slide without significantly disrupting the swimming space. However, additional calculations considering the base area of the slide would be required for a definitive answer.
The amount of water needed to fill the pool is calculated by multiplying the volume of the pool by the weight of the water. If the average depth of the pool is 4 feet, the volume of the pool (ignoring the central triangle) is 11307.2*4 = 45228.8 cubic feet. As 1 cubic foot of water equals roughly translates to 7.48 gallons, the pool would require approximately 45228.8 * 7.48 = 338511.6 gallons of water.
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Hillary age is 3 years greater than 2/3 times Lilly's age if Hillary is 19 years old how old is Lilly
Answers
Hillary = 3+2/3X
19=3+2/3X
16=2/3X
X= 16 / 2/3 = 16/1* 3/2 = 48/2
X=24
Lilly is 24
Hillary age = 19 years old
Hillary age is 3 years greater than 2/3 times Lilly's age =
2/3x + 3 = 19
2/3x = 16
x = 16 * 3/2
x = 24
answer
Lily is 24 years old
a tower casts a 450 ft shadow at the same time that a 4 ft child casts a 6 ft shadow. Write and solve a proportion to find the height of a tower
Answers
Answer:
[tex]x=300[/tex]
Step-by-step explanation:
Set up the proportion;
[tex]\frac{x}{450} =\frac{4}{6}[/tex]
then cross multiply;
[tex]6x=450[/tex] · [tex]4[/tex]
[tex]6x=1800[/tex]
[tex]x=\frac{1800}{6} =300[/tex]
[tex]x=300[/tex]
What is the equation of a line that goes through the point (0,−35)(0,−35) and has a slope of -1?
Select one:
a. y=x−35y=x−35
b. y=−x−35y=−x−35
c. y=−35x−1y=−35x−1
d. −35y=−x
Answers
y + 35 = -x
y = -x - 35
answer
b. y=−x−35
Answer:
y=−x−35 (Did it on college bridge)
Step-by-step explanation:
x - 2(x + 10) = 12 what's x
Answers
First, let's rewrite our problem.
x - 2(x + 10) = 12, solve for x.
To start us off, we need to apply the distributive property to the left side of the equation "-2(x + 10)", as since there is no sign between the number and the parenthesis, it is implied that we must multiply.
To distribute, we multiply the number outside of the parenthesis by all numbers inside the parenthesis.
For example;
2(1 + 3)
2(1) + 2(3)
2 + 6
8.
Now that we (hopefully) understand our concept, let's proceed to our equation to solve for x.
x - 2(x + 10) = 12
Apply the Distributive Property.
-2(x) - 2(!0)
-2x - 20.
We now have:
x - 2x - 20 = 12
Combine like-terms
-x - 20 = 12
Add 20 to both sides to isolate -x.
-20 + 20 = 0
12 + 20 = 32
Now we are left with:
-x = 32
However, we are not done as we still have x being multiplied by -1 (-x just means -1x). To get rid of the -1, we need to divide both sides by -1 to cancel them out.
-x / -1 = x
32 / -1 = -32
x = -32 is your solution.
I hope this helps!
If you add an expression to both sides of an equation, the resulting equation will have the same solution set as the original equation. In other words, they will be equivalent. This is true for all operations. As long both sides are treated the same, the equation will stay balanced.
You will also need to know how to combine like terms. But what are like terms to begin with? Like terms are defined as two terms having the same variable(s) (or lack thereof) and are raised to the same power. In mathematics, something raised to the first power stays the same. So, 5x and 10x are like terms because they both have the same variable and are raised to the first power. You don’t see the exponents because it doesn’t change the value of the terms.
To combine like terms, simplify add the coefficients and keep the common variable(s) and exponent.
The distributive property is another important rule you will need to understand. The distributive property is used mostly for simplifying parentheses in expressions/equations.
For example, how would you get rid of the parentheses here?
6(x + 1)
If there wasn’t an unknown in between the parentheses, you could just add then multiply. That is what the distributive property solves. The distributive property states that a(b + c) = ab + ac
So, now we can simplify our expression.
6(x + 1) = 6x + 6
To sum up how to solve algebraic equations:
Use the distributive property if needed
Combine like terms on both sides of the equation if needed
If you do one operation on one side of the equation, do the same on the opposite side
x - 2(x + 10) = 12
x - 2x - 20 = 12 <-- Using the distributive property
-x - 20 = 12 <-- Combing like terms
-x = 32 <-- Add 20 to both sides
x = -32 <-- Divide both sides by -1
So, x is equal to -32.
He lake is 60 miles away, and rene is driving at 40 miles per hour the entire time, how long will it take her to get to the lake
Answers
divide distance by speed
60/40 = 1.5
it will take 1 1/2 hours ( 90 minutes)
PLEASE HELP!!! The volume in cubic feet of a box can be expressed as , or as the product of three linear factors with integer coefficients. The width of the box is x-2.
Factor the polynomial to find linear expressions for the height and the length. Show your work.
Answers
x(x^2-6x+8)
x(x^2-2x-4x+8)
x(x(x-2)-4(x-2))
x(x-2)(x-4)
Since we are told that the width is (x-2) the length and height are:
x and (x-4)
To find linear 12/10/2023 for the height and length of the box, factor the given polynomial (x - 2)(...)
Explanation:To find linear expressions for the height and length of the box, we need to factor the given polynomial. The volume of the box can be expressed as (x - 2)(?)(?), where ? represents the linear expressions for height and length. Since we have two unknowns, we need to find two factors that when multiplied together give us the given polynomial.
To factor x^2 - 2x, we need to find two numbers that multiply to give -2 and add up to give -2. The factors are -1 and 2, so we can write the polynomial as (x - 1)(x - 2). Therefore, the linear expressions for the height and length are (x - 1) and (x - 2) respectively.
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Which two consecutive whole numbers is the value of √21 between?
A.4 and 5
B.10 and 11
C.21 and 22
D.42 and 43
Answers
4 and 5
______________________________
Explanation:
______________________________
Looking at the answers:
______________________________
we know that 4² = 16 ; and 5² = 25 ;
So: √16 = 4 ; and √25 = 5.
So: √21 must be between √16 and √25 ;
That is: √21 must be between 4 and 5 ; which is answer choice: [A] .
__________________________________________________________
Simplify
[tex] \frac{ \frac{1}{x+h} + \frac{1}{x} }{x} [/tex]
Answers
A restaurant offers a dinner special that lets you choose from 10 entrees, 8 dishes and 13 desserts you can choose one dish one desert how many meals possible
Answers
Which term best describes a proof in which you assume the opposite of what you want to prove?
Answers
Answer:
Contradictory Statement
Step-by-step explanation:
In contradictory statement , we basically describes a proof by assuming opposite of what we want to prove .
For example :
Prove that [tex]\sqrt{2}[/tex] is irrational .
Solution :
We will prove this by contradiction .
Let if possible [tex]\sqrt{2}[/tex] is rational .
[tex]\sqrt{2}=\frac{p}{q}[/tex] where p and q are integers and coprime such that [tex]q\neq 0[/tex]
On squaring both sides , we get
[tex]2q^2=p^2\\\Rightarrow 2|p^2\\\Rightarrow 2|p[/tex]
we get ,
p=2r
On squaring both sides, we get
[tex]p^2=4r^2\\\Rightarrow 2q^2=4r^2\\\Rightarrow q^2=2r^2\\\Rightarrow 2|q^2\\\Rightarrow 2|q[/tex]
So, 2 divides p and q which is a contradiction to the fact that p and are coprime .
Therefore, [tex]\sqrt{2}[/tex] is irrational .
In a random sample of 75 individuals, 52 people said they prefer coffee to tea. 99.7% of the population mean is between 84/80/74 % and 64/58/54%. (Choose the option closest to your answer.)
Answers
How can you use a number line to compare and order numbers?
Answers
Take the value '0' for example, the value on the right of zero is '1', which is a value bigger than zero, and the value to the left of '0' is '-1', which is a value smaller than zero.
Are there any rational numbers between 0.4 and 4/9
Answers
4/9 = 20/45
so the rational number in between can be 19/45
The population of Glendale this year is 3,200 more than half of last year’s population. The population this year is 26,300. Which equation could be solved to find last year’s population?
Answers
(1/2)x + 3200 - 3200 = 26300 - 3200
(1/2)x = 23100
(1/2)x * 2/1 = 23100 * 2/1
x = 46200
Last years population was 46,200
check:
1/2 (46200) + 3200 = 26300
23100 + 3200 = 26300
What's the circumference of a circular swimming pool with a diameter of 20 feet
Answers
circumference = Diameter x PI
using 3.14 for PI
3.14 x 20 = 62.8 feet
Rectangle R has varying length l and width w but a constant perimeter of 4 ft. A. Express the area A as a function of l. What do you know about this function? B. For what values of l and w will the area of R be greatest? Give an algebraic argument. Give a geometric arguement.
Answers
l = length of the rectangle
w = width of the rectangle
P = 4 ft, constant perimeter
Because the given perimeter is constant,
2(w + l) = 4
w + l = 2
w = 2 - l (1)
Part A.
The area is
A = w*l
= (2 - l)*l
A = 2l - l²
This is a quadratic function or a parabola.
Part B.
Write the parabola in standard form.
A = -[l² - 2l]
= -[ (l -1)² - 1]
= -(l -1)² + 1
This is a parabola with vertex at (1, 1). Because the leading coefficient is negative the curve is downward, as shown below.
The maximum value occurs at the vertex, so the maximum value of A = 1.
From equation (1), obtain
w = 2 - l = 2 - 1 = 1.
The maximum value of the area occurs when w=1 and l=1 (a square).
Answer:
The area is maximum when l=1 and w=1.
The geometric argument is based on the vertex of the parabola denoting maximum area.
George plays basketball in a week long camp On day 2 he scored 8 points On day 4 he scored 12 points Explain how to measure his average rate of change
Answers
Independent Data: Day 2 Independent Data: Day 4
Dependent Data: 8 points Dependant Data: 12 points
Then we find the difference between the two independent values and the two dependent values
4 - 2 = 2
12 - 8 =4
To find the rate we use the following formula
the difference of dependent value ÷ the difference of independent value =
4 ÷ 2 = 2
Hence the average rate of change is an increase of 2 points a day
Answer:
the average rate of change is an increase of 2 points a day
Step-by-step explanation:
It wont let me post a picture of the angles but they are verticle angles and the equations are (3x+8), (5x-40) and it says find m ABC.
The choices are 24, 56, 80, 90
Answers
5x - 40 = 3x + 8
5x - 3x = 8 + 40
2x = 48
x = 48/2
x = 24
m∠ABC = 3x + 8 = 3 * 24 + 8 = 80°
(or m∠ABC = 5x - 40 = 5 * 24 - 40 = 80°)
Answer:
the answer is 24 i hope this helps ...
find the area of triangle QRS.
Answers
Answer: 140 square units.
Step-by-step explanation:
The area of triangle with vertices [tex](x_1,y_1),(x_2,y_2)\ and\ (x_3,y_3)[/tex] is given by
[tex]\text{Area}=\frac{1}{2}[x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2][/tex]
Then area of triangle QRS with vertices (6,10), (2,-10) and (-9,5) is given by :-
[tex]\\\\\Rightarrow\text{Area}=|\frac{1}{2}[6(-10-5)+2(5-10)-9(10-(-10))]|\\\\\Rightarrow\text{Area}=|\frac{1}{2}[6(-15)+2(-5)+-9(20)]|\\\\\Rightarrow\text{Area}=|\frac{1}{2}[280]|\\\\\Rightarrow\text{Area}=140\text{ square units}[/tex]
Answer:
the answer is 140. I did the assignment
help help help help help please
Answers
If you place a cup of 210 degree Fahrenheit coffee on a table in a room that is 68 degrees fareinheit, and ten minutes later, it is 200 degrees fareinheit. How long will it be before the coffee is 180 degrees fareinheit? Use newtons law of cooling
Answers
Tf=Ts+(Ti-Ts)e^(-kt) where Tf is temp at time t, Ts is temp of surroundings, Ti is temp of object/fluid. So we need to find k first.
200=68+(210-68)e^(-10k)
132=142e^(-10k)
132/142=e^(-10k)
ln(132/142)=-10k
k=-ln(132/142)/10
k≈0.0073 so
T(t)=68+142e^(-0.0073t) so how long until it reaches 180°?
180=68+142e^(-0.0073t)
112=142e^(-0.0073t)
112/142=e^(-0.0073t)
ln(112/142)=-0.0073t
t= -ln(112/142)/(0.0073)
t≈32.51 minutes
Final answer:
According to Newton's Law of Cooling, it will take approximately 10.76 minutes for the coffee to cool from 210 degrees Fahrenheit to 180 degrees Fahrenheit when placed in a room with a temperature of 68 degrees Fahrenheit.
Explanation:
According to Newton's Law of Cooling, the rate at which an object cools is proportional to the temperature difference between the object and its surroundings. We can use this law to determine how long it will take for the coffee to reach a temperature of 180 degrees Fahrenheit.
First, we need to find the temperature difference between the coffee and its surroundings. The initial temperature of the coffee is 210 degrees Fahrenheit and the room temperature is 68 degrees Fahrenheit. Therefore, the initial temperature difference is 210 - 68 = 142 degrees Fahrenheit.We also know that after 10 minutes, the coffee's temperature has decreased to 200 degrees Fahrenheit. So the new temperature difference is 200 - 68 = 132 degrees Fahrenheit.Now we can set up a proportion to find the time it takes to reach a temperature of 180 degrees Fahrenheit. The ratio between the initial temperature difference and the time it takes for the coffee to cool to 180 degrees Fahrenheit is equal to the ratio between the new temperature difference and the total time it takes for the coffee to cool to 180 degrees Fahrenheit. Let's call the total time T: (142 / T) = (132 / 10). Cross-multiplying, we get 1420 = 132T. Dividing both sides by 132, we find that T = 10.76 minutes.Therefore, it will take approximately 10.76 minutes for the coffee to reach a temperature of 180 degrees Fahrenheit.
A herd of 39 horses has 33 white horses some black horses. What is the ratio of black horses to white horses?
Answers
There is 6 black horses, so 6/39.
Find the area of a parallelogram with sides of 6 and 12 and an angle of 60°.
A: 72√3 sq. units
B: 36√3 sq. units
C: 12√3 sq. units
Answers
Parallelogram diagram I believe down below. We must find the height and then the area using Pythagorean theorem. Since the green shaded part is a 30-60-90 triangle, the base is 1/2 the hypotenuse, therefore it is 3. Now we calculate the height with it.
A^2 + B^2 = C^2
A^2 + 3^2 = 6^2
A^2 + 9 = 36
A^2 = 27
A = 3√3
Therefore the height is 3√3
Now calculate the area using A = bh
A = bh
= (12)(3√3)
= 36√3
So the area is 36√3 square units.
I cannot be sure of this answer because you did not provide a diagram.
The area of the parallelogram will be equal to 36√3 square units.
What is an area?The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the parallelogram in a two-dimensional plane is called the area of the parallelogram.
Parallelogram diagram I believe down below. We must find the height and then the area using the Pythagorean theorem. Since the green shaded part is a 30-60-90 triangle, the base is 1/2 the hypotenuse, therefore it is 3. Now we calculate the height with it.
A ² + B² = C²
A² + 3² = 6²
A² + 9 = 36
A² = 27
A = 3√3
Therefore the height is 3√3. Now calculate the area using A = bh
A = b x h
A = ( 12 ) x ( 3√3 )
A = 36√3
So the area is 36√3 square units.
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the "h" value moves the graph up or down true or false ?
Answers
The answer to this question is FALSE.
Answer:
False
Step-by-step explanation:
Suposse that we are given a function f(x) and a constant value h.
1. Case:
If we take the function g(x)=f(x)+h, then the graph of the function g(x) will be the graph of the funcion f(x) moved up or down.
2.Case:
If we take the function g(x)=hf(x), then the graph of the function g(x) will be the graph of the function f(x) just taller or shorter.
3.Case:
If we take the function g(x)=f(x-h), then the graph of the function g(x) will be the graph of the fuction f(x) moved horizontally.
4. Case:
If we take the function g(x)=f(hx), then the graph of the function g(x) will be tha graph of the function f(x) wither or thiner.
For example:
If we take f(x)=sin(x) and h=2. Then, if we take g(x)=sin(2x) then f(0)=g(0)=0, which means that the graph of the functiction is not moved up or down. However, f(π/2)=sin(π/2)=1 and g(π/2)=sin(π)=0 which gives us a hint that the graph of the function became thiner.
Quadrilateral OPQR is inscribed in circle N, as shown below. What is the measure of ∠ROP?
41
67
113
139
Answers
Answer: The correct option is (A) 41°.
Step-by-step explanation: Given that quadrilateral OPQR is inscribed in circle N as shown in the figure.
Also, ∠ROP = (x+17)° and ∠RQP = (6x-5)°.
We are to find the measure of ∠ROP.
Since quadrilateral OPQR is inscribed in a circle, so it is a cyclic quadrilateral.
We know that the sum of the measures of opposite angles of a cyclic quadrilateral is 180°.
So, in cyclic quadrilateral OPQR, we have
[tex]m\angle ROP+m\angle RQP=180^\circ\\\\\Rightarrow (x+17)^\circ+(6x-5)^\circ=180^\circ\\\\\Rightarrow (7x+12)^\circ=180^circ\\\\\Rightarrow 7x^\circ=168^\circ\\\\\Rightarrow x^\circ=\left(\dfrac{168}{7}\right)^\circ\\\\\Rightarrow x^\circ=24^\circ.[/tex]
Therefore, we get
[tex]m\angle ROP=(x+17)^\circ=(24+17)^\circ=41^\circ.[/tex]
Thus, the measure of angle ROP is 41°.
Option (A) is CORRECT.
The function f(x) = –x2 + 28x – 192 models the hourly profit, in dollars, a shop makes for selling sodas, where x is the number of sodas sold and f(x) is the amount of profit. Part A: Determine the vertex. What does this calculation mean in the context of the problem? (5 points) Part B: Determine the x-intercepts. What do these values mean in the context of the problem? (5 points)
Answers
[tex]\bf \textit{ vertex of a vertical parabola, using coefficients}\\\\ \begin{array}{llccll} y = &{{ -1}}x^2&{{ +28}}x&{{ -192}}\\ &\uparrow &\uparrow &\uparrow \\ &a&b&c \end{array}\qquad \left(-\cfrac{{{ b}}}{2{{ a}}}\quad ,\quad {{ c}}-\cfrac{{{ b}}^2}{4{{ a}}}\right)[/tex]
check the picture below.
b)
[tex]\bf f(x)=-x^2+28x-192\implies 0=-x^2+28x-192 \\\\\\ x^2-28x+192=0\implies (x-16)(x-12)=0\implies x= \begin{cases} 16\\ 12 \end{cases}[/tex]
what does this mean? check the picture below, notice the x-intercepts points.