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Using trigonometric ratio
[tex]\begin{gathered} \cos x^{\circ}=\frac{adjacent}{\text{hypotenuse}} \\ \text{cosx}=\frac{5}{8} \\ \cos x=0.625 \\ x=\cos ^{-1}0.625 \\ x=51.3178125465 \\ x=51^{\circ} \end{gathered}[/tex]Related Questions
The function f(x)=x - 3x2 + 2x rises as x grows very large. O A. True O B. False
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Let's find the limit:
[tex]\lim _{x\to\infty}f(x)=\lim _{x\to\infty}(x^3-3x^2+2x)=\lim _{x\to\infty}x^3=\infty^3=\infty[/tex]Therefore, we can conclude that the function rises as x grows very large.
Answer:
True
A witch brewed a magical invisibility potion. There is a proportional relationship between the amount of potion the witch drinks (in milliliters), x, and the amount of time she is invisible (in minutes. After drinking 1 milliliter of potion, the witch was invisible for 5 minutes. Write the equatio for the relationship between x and y. y
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x represents the amount of portion in millimeters
y represents the time she was invisible
Write out an equation to show the variation relationship
Since the variation is direct
Then
[tex]\begin{gathered} x\propto y \\ x=k\times y \end{gathered}[/tex]To get the value of k
when x= 1 mm, y = 5 minutes
[tex]\begin{gathered} k\text{ = }\frac{x}{y} \\ =\frac{1}{5}\text{ mm/min} \end{gathered}[/tex]The relationship between x and y will be
[tex]\begin{gathered} \text{substitute k in x=}ky \\ x=\frac{1}{5}\times y \\ x=\frac{y}{5}\text{ (this is the relationship)} \end{gathered}[/tex]I need help asap I took a picture of my question.
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The equation of a line in the slope intercept form is expressed as
y = mx + c
where
m = slope
c = y intercept
The equation of the given line is
y = 2x + 4
By comparing both equations,
slope of the given line is 2
We would find a perpendicular line to this line passing through the given point. Recall, if two lines are perpendicular, the slope of one line is the negative reciprocal of the slope of the other line. This means that the slope of the perpendicular line passing through point K is - 1/2. We would find the y intercept by substituting x = 0, y = - 1 and m = - 1/2 into the slope intercept equation. We have
- 1 = - 1/2 * 0 + c
c = - 1
The equation of the perpendicular line is
y = - x/2 - 1
We would find the point of intersection by equating both lines. We have
2x + 4 = -x/2 - 1
Multiplying through by 2,
4x + 8 = - x - 2
4x + x = - 2 - 8
5x = - 10
x = - 10/5 = - 2
Substituting x = - 2 into the perpendicular line equation,
y = - - 2/2 - 1 = 1 - 1
y = 0
The point of intersection is (- 2, 0)
We would find the distance between K(0, - 1) and (- 2, 0) by applying the formula for finding the distance between two points which is expressed as
[tex]\begin{gathered} \text{Distance = }\sqrt[]{(x2-x1)^2+(y2-y1)^2} \\ x1\text{ = 0, y1 = -1} \\ x2\text{ = - 2, y2 = 0} \\ \text{Distance = }\sqrt[]{(-2-0)^2+(0-1)^2}\text{ = }\sqrt[]{4\text{ + 1}}\text{ = }\sqrt[]{5} \\ \text{Distance = 2.2}4 \end{gathered}[/tex]Write the first 5 terms of the arithmetic sequence. *a =-23 + 17(n + 1)
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Let's determine the first 5 term under the arithmetic sequence formula:
How to simplify 2a x a x 3a +b x4b
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Answer
6a³ + 4b²
Step-by-step explanation
Given the expression:
[tex]2a\times a\times3a+b\times4b[/tex]Combining similar terms (terms with the same variable):
[tex]\begin{gathered} (2a\times a\times3a)+(b\times4b)= \\ =\lbrack(2\times3)(a\operatorname{\times}a\operatorname{\times}a)\rbrack+\lbrack4(b\operatorname{\times}b)\rbrack= \\ =6a^3+4b^2 \end{gathered}[/tex]quar OT rate in die table below Number of Pizzas 1 Number of Students 4. 8 12 16 2 3 4 Multiply the number of pizzas by 8 to find the number of students. Multiply the number of pizzas by 4 to find the number of students. Multiply the number of students by 4 to find the number of pizzas. Multiply the number of students by 8 to find the number of pizzas.
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From the given table,
1 Pizza corresponds to 4 students
2 Pizza corresponds to 8 students
3 Pizza corresponds to 12 students
4 Pizza corresponds to 16 students
As you notice, for every pizza there are 4 students,
so the multiplier is 4.
2 pizza x 4 = 8 students
3 pizza x 4 = 12 students
4 pizza x 4 = 16 students
The answer is Option B. Multiply the number of pizza by 4 to find the number of students
Need help finding 2 more points on the line for question # 12(3,8) and (-4,8)Slope:8-8/-4-3 = 0/-7
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ANSWER
The slope between the two points is 0
EXPLANATION
Given that;
(3, 8) and (-4, 8)
Slope is defined as the gradient of a line
The formula for determining slope is given below as
[tex]\text{ Slope = }\frac{\text{ rise}}{\text{ run}}[/tex]Where
rise = y2 - y1
run = x2 - x1
So, we have
[tex]\text{ Slope = }\frac{\text{ y}_2\text{ - y}_1}{\text{ x}_2\text{ - x}_1}[/tex]In the given point, let x1 = 3, y1 = 8, x2 = -4 and y2 = 8
[tex]\begin{gathered} \text{ slope = }\frac{\text{ 8 - 8}}{\text{ -4 - 3}} \\ \\ \text{ slope = }\frac{\text{ 0}}{\text{ -7 }} \\ \text{ slope = 0} \end{gathered}[/tex]Therefore, the slope between the two points is 0
Consider the functionfIWhich graph is the graph of function ??
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Answer:
Explanation:
Given:
[tex]f(x)\text{ = }\frac{x^2-3x}{x-9}[/tex]To find:
the graph that represents the function f
To determine the graph, we need to check if the expression can be simplified:
[tex]\begin{gathered} x^2-\text{ 3x = x\lparen x - 3\rparen} \\ x^2\text{ - 9 is a differenc of two squares} \\ x^2\text{ - 9 = \lparen x - 3\rparen\lparen x + 3\rparen} \end{gathered}[/tex][tex]\begin{gathered} f(x)\text{ = }\frac{x(x\text{ - 3\rparen}}{(x\text{ - 3\rparen\lparen x + 3\rparen}} \\ \\ f(x)\text{ = }\frac{x}{x\text{ + 3}} \\ \\ After\text{ simplifying, we still have a rational function} \\ We\text{ need to get the vertical asymptote} \end{gathered}[/tex][tex]\begin{gathered} vertical\text{ asymptote is the value of x when the denominator is equated to zero:} \\ x\text{ + 3 = 0} \\ x\text{ = -3} \\ This\text{ means at x = -3, there is no domain and the graph will not pass through this point} \\ There\text{ will be a vertical dashed line at this point} \end{gathered}[/tex]We will check the options for the graph that satisfies the above:
Only option B has a vertical dased line at x = -3. Also the graph doesn't pass t
Which of the following statements are true about the graph of f(x) =1/4 cos(x+pi/3)-1 2 answers
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The given function is written in the form of:
[tex]f(x)=a\cos (bx-c)+d[/tex]in which a = 1/4, b = 1, c = -π/3, and d = -1.
The amplitude of the function is A, hence, the amplitude is 1/4. Statement A is true.
In addition, the vertical shift of the function is D, hence, the vertical shift is 1 unit down since d is -1. Statement 2 is false.
In addition, the horizontal shift or phase shift of a cosine function is C. Therefore, the horizontal shift is -π/3 or π/3 to the left. Statement D is true.
Katherine is a personal chef. She charges $100 per three-person meal. Her monthly expenses are $3,075. How many three-person meals must she sell in order to make a profit of at least $1,950?
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Given,
Katherine charges for three-person meal is $100.
The monthly expenses of katherine is $3075.
The amount of profit she want is $1950 atleast.
The total amount she have to earned in the month is,
[tex]\begin{gathered} \text{Total earning amount = amount for expenses+amount of profit} \\ =3075+1950 \\ =\text{ \$ 5025 } \end{gathered}[/tex]The number of three-person meals must she sell in order to make a profit of at least $1,950,
[tex]\text{Number of meals = }\frac{total\text{ earning amount}}{\cos t\text{ of one three person meal}}[/tex]Substituting the values then,
[tex]\begin{gathered} \text{Number of meals = }\frac{5025}{100} \\ =50.25 \\ \approx51 \end{gathered}[/tex]Hence, she must sell 51 three person meal to get atleast profit of $1950.
find X if on angle is 65 and the other is (3y+2)
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The angle opposite to equal sides are equal. So two angle are equal to 65 degree each and one angle is (3y + 2).
Determine the value of varaible y, by using angle sum property of triangle.
[tex]\begin{gathered} 3y+2+65+65=180 \\ 3y=180-132 \\ =48 \\ y=\frac{48}{3} \\ =16 \end{gathered}[/tex]So value of y is 16.
Complete the statements to describe the outcomes of operations with the following numbers. Q and b are non-zero rational numbers. x and y are Irrational numbers. Select the word that best completes each statement. To select a word, click the menu and then click the desired word. To choose a different word, click the menu and click the new word. a + b is-Select an Answer- rational. Xy is Select an Answer- Irrational. a + x is-Select an Answer- rational. b.xis -Select an Answer- Irrational.
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a + b is ALWAYS rational
a + x is SOMETIMES rational
x.y is SOMETIMES irrational
b.x is ALWAYS irrational
Which of the following functions has a vertical asymptote at x=3, a horizontal asymptote at f(x)=2, and a root at x=5?
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To have a vertical asymptote, is the value in which the denominator is zero, therefore if vertical asymptote x=3, then the denominator must be x-3.
Then we find the root, which is the x-intercepts, let's find them:
[tex]\begin{gathered} \frac{-4}{x-3}+2=0 \\ \text{ }\frac{-4}{x\text{ - 3}}=\text{ - 2} \\ \text{ -4 = - 2\lparen x - 3\rparen} \\ \text{ }\frac{-4}{\text{ -2}}=\text{ x - 3 } \\ \\ 2=x\text{ - 3} \\ x=5 \end{gathered}[/tex]So, the function D has the requirements
If x = 14 , what value of Y is a solution to this equation ? A. -7 B. -8 C. -10 D. -30
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Given
Graph
Procedure
Point-slope is the general form y-y₁=m(x-x₁) for linear equations. It emphasizes the slope of the line and a point on the line (that is not the y-intercept).
Point 1. (-2,0)
Point 2. (2,-2)
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{-2-0}{2--2} \\ m=-\frac{2}{4} \\ m=-\frac{1}{2} \end{gathered}[/tex]y=mx+b
replacing (x,y) with point 1
[tex]\begin{gathered} y=mx+b \\ 0=-\frac{1}{2}(-2)+b \\ 0=1+b_{} \\ b=-1 \end{gathered}[/tex]we obtain the equation:
[tex]y=-\frac{1}{2}x-1[/tex]If x = 14 , what value of Y is a solution to this equation?
[tex]\begin{gathered} y=-\frac{1}{2}(14)-1 \\ y=-7-1 \\ y=-8 \end{gathered}[/tex]The answer is y=-8
The graph of F(x), shown below has the same shape as the graph of G(x)=x^3 -2 but it is shifted to the left 2 units. What is its equation?
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Given that
[tex]G(x)=x^3-x^2[/tex]If this function is then sifted 2 units to the left
Then the new function
[tex]F(x)=(x+2)^3-(x+2)^2[/tex]The graph is shown
THE ANSWER IS OPTION D
use Euler circles to determine if the Argument is valid or invalid
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Let's use Euler circles, to represent the argument.
As you can observe in the diagram above, the given argument is true because it's being proved that all P is R, basically because P is a subset of R.
Label the median on the trapezoid.Then fill in the in the list
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Given:
The trapezoid ABCD is given.
To find:
Label the median and fill in the blanks.
Explanation:
Let us label the median first.
Here, a line EF is a median.
It connects the midpoint of the legs. (It bisects each leg).
It is always parallel to both BC, and AD.
It is the average of the two parallel legs.
(-3, 1) and (2, 1) Different quadrants, so add the absolute values.Horizontal distance from (-3, 1) to y-axis: | __ | = ___Horizontal distance from (2, 1) to y-axis: | __ | = ___Distance from (-3, 1) to (2, 1) is ___ + ___ = ___ .
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Here, we want to make additions
Firstly, we want the horizontal distance from (-3,1) to y-axis
We take the x-coordinate into consideration;
[tex]\begin{gathered} =\text{ (-3-0) = }-3 \\ \text{can also be (0-(-3)) = }3 \end{gathered}[/tex]But since we are considering the absolute value, we only take the positive and it is equal to 1
Secondly, we want the horizontal distance from (2,1) to y-axis
This is same as above, considering the x-axis value, we hav
Lstly, we
In ADEF, the measure of ZF=90°, DE = 52 feet, and FD = 14 feet. Find the measure of D to the nearest degree.
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EXPLANATION
In order to find the measure of
[tex]\cos x=\frac{adjacent\text{ cathetus}}{\text{Hypotenuse}}[/tex][tex]x=\cos ^{-1}(\frac{14}{52})[/tex][tex]x=74.38^o\approx74^o[/tex]The answer is 74 degrees.
solve the following equation for G. be sure to take into account whether a letter is capitalized or not .H-3q=qr
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H - 3q = gr
make g the subject of the relation.
H - 3q = gr
divide through by r
[tex]\begin{gathered} H\text{ - 3q = gr} \\ \frac{H}{r}\text{ - }\frac{3q}{r}\text{ = g} \end{gathered}[/tex]Final answer
[tex]g\text{ = }\frac{H}{r}\text{ - }\frac{3q}{r}\text{ or g = }\frac{H\text{ - 3q}}{r}[/tex]identify the function as exponential growth or exponential decay. then identify the growth factor or decay factor. y=9(1/2)^r
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We have the function:
[tex]y=9\cdot(\frac{1}{2})^r[/tex]The growth/decay factor is the number that is the base of the exponent. For this function, the value of this factor is 1/2.
As this value is smaller than 1, the factor is a decay factor.
Answer: the decay factor is 1/2.
Please see attached picture below to help me pleaseplot 1 1/2 and 2 1/4 on the number line
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The given mixed numbers are:
[tex]1\frac{1}{2},2\frac{1}{4}[/tex]The first thing we need to do is convert it into improper fractions, as follows:
[tex]\begin{gathered} 1\frac{1}{2}=\frac{1\times2}{2}+\frac{1}{2} \\ 1\frac{1}{2}=\frac{2}{2}+\frac{1}{2} \\ 1\frac{1}{2}=\frac{3}{2} \end{gathered}[/tex]Now, continue with 2 1/4:
[tex]\begin{gathered} 2\frac{1}{4}=\frac{2\times4}{4}+\frac{1}{4} \\ 2\frac{1}{4}=\frac{8}{4}+\frac{1}{4} \\ 2\frac{1}{4}=\frac{9}{4} \end{gathered}[/tex]In order to plot them on the number line, for the first fraction 3/2, we need to divide the unity into 2 equal parts, and then count 3 of these divisions, that would be 1 1/2 or 3/2, is the same:
Now for the 2 1/4 or 9/4 (they are the same), we need to divide the unity into 4 equal parts and then count 9 of these divisions, then:
For the following relation, give the domain and range, and indicate whether it is a function.{(a, 9), (j, 6), (b, 5), (h, 2)}Domain: {Range:{Is it a function?✓ Select an answerNoYes
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Domain = all the possible x values
Range = set of possible y values.
(x,y)
Domain = { a , j , b , h }
Range = { 9 , 6 , 5 , 2 }
Since each input value has one output value, it is a function.
Two bond funds pay interest at rates that differ by 4%. Money invested for one year in the first fund earns $600 interest. The same amount invested in the other fund earns $800. Find the lower rate of interest (in percent). %
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Given:
The first fund earns $600 and the second fund earns $800.
Let x% be the lower rate of interest.
And x+4% be the higher rate of interest.
The difference between the amounts is,
[tex]800-600=200[/tex]It means,
[tex]\begin{gathered} 4\text{ percent of n =200} \\ \text{Where n is the amount invested. } \\ \frac{4}{100}\times n=200 \\ n=\frac{200\times100}{4} \\ n=5000 \\ It\text{ gives } \\ \text{x percent of }5000=600 \\ \frac{x}{100}\times5000=600 \\ x=\frac{600}{50} \\ x=12 \\ \text{Same way,} \\ \text{x percent of }5000=800 \\ \frac{x}{100}\times5000=800 \\ x=\frac{800}{50} \\ x=16 \end{gathered}[/tex]Alternative way,
For the first fund. let a be the lower rate and a+4 be the higher rate.
[tex]ax=600[/tex]For second fund,
[tex]\begin{gathered} x(a+4)=800 \\ ax+4x=800 \\ 600+4x=800 \\ 4x=800-600 \\ x=\frac{200}{4} \\ x=50 \end{gathered}[/tex]So,
[tex]\begin{gathered} ax=600 \\ 50a=600 \\ a=\frac{600}{50} \\ a=12 \\ \Rightarrow a+4=12+4=16 \end{gathered}[/tex]Answer: The lower rate of interest is 12%
Hi there, I need help I'm struggling with my algebra 2 class. sine, cosine.
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Given: A right-angled triangle with AB=30 units, BC=40 units, and AC=50 units.
Required: To find the trigonometric ratio cos(A).
Explanation: The trigonometric ratio cosine is defined as the ratio of the adjacent side to the triangle's hypotenuse.
[tex]cos(\theta)=\frac{adjacent\text{ }side}{hypotenuse}[/tex]Here, in triangle ABC, the adjacent side for angle BAC is AB, and AC is the triangle's hypotenuse.
Hence
[tex]\begin{gathered} cos(A)=\frac{AB}{AC} \\ =\frac{30}{50} \\ =\frac{3}{5} \end{gathered}[/tex]Final Answer:
[tex]cos(A)=\frac{3}{5}[/tex]Find the sum.(2x + 3y) + (4x + 9y)
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Given the expression:
[tex](2x+3y)+(4x+9y)[/tex]To find the sum, we can group the similar terms and then do the addition:
[tex]\begin{gathered} (2x+3y)+(4x+9y)=2x+3y+4x+9y \\ =2x+4x+3y+9y=6x+12y \end{gathered}[/tex]therefore, the sum is 6x+12y
I have no idea how to do this I need to get this paper done tonight
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Given:
[tex]\sin\theta=0.47[/tex][tex]0<\theta<90[/tex]Find-:
The value of
[tex]\cos\theta[/tex]Explanation-:
Use trignomertic formula:
[tex]\sin^2\theta+\cos^2\theta=1[/tex]So the value is:
[tex]\begin{gathered} \sin^2\theta+\cos^2\theta=1 \\ \\ \cos^2\theta=1-\sin^2\theta \\ \\ \cos\theta=\sqrt{1-\sin^2\theta} \end{gathered}[/tex]Given value of sin is:
[tex]\begin{gathered} \sin\theta=0.47 \\ \\ \sin^2\theta=(0.47)^2 \\ \\ \sin^2\theta=0.2209 \end{gathered}[/tex]So, the value is:
[tex]\begin{gathered} \cos\theta=\sqrt{1-\sin^2\theta} \\ \\ \cos\theta=\sqrt{1-0.2209} \\ \\ \cos\theta=\sqrt{0.7791} \\ \\ \cos\theta=0.883 \end{gathered}[/tex]So, the value is 0.883
Using the vertex point(-2.5, -6.25), write the equation of this function in vertex form.
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Form of the parabola:
Standard form:
y = ax² + bx + c
Vertex form:
y = a(x-h)² + k
The vertex is a point, V(h,k), on the parabola. Where:
h = -b/(2a) ; k = (4ac-b²)/4a
If the vertex point is :
V(h,k) = (-2.5, -6.25)
the equation of this function in vertex form is:
y = a(x - (-2.5))² + (-6.25)
y = a(x + 2.5)² - 6.25
Find the greatest common factor of thefollowing monomials:6m3n2 m5 n52mn3
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So we have the following set of terms:
[tex]6m^3n,2m^5n^5,2mn^3[/tex]The greatest common factor (from now on, GCF) is a term that meets the following:
- All the three terms are multiples of it.
- It's the greatest number with the greatest power of each variable that meets the condition above.
One way to find it is looking for the GCFs of the integers, the powers of m and the powers of n separately. For example, the integers present in the set of three terms are 6, 2 and 2. If we factor each of them we get:
[tex]2\cdot3,2,2[/tex]The only number that appears in the 3 factored numbers is 2 so the GCF of the integers is 2.
Then we have to find the GCF among the powers of m. When you look for the GCF of a set of powers of the same variable the result is the power with the smallest exponent so if the powers we have are:
[tex]m^3,m^5,m[/tex]Then the GCF is m because its exponent is 1 whereas the other two exponents 3 and 5 are greater.
If we do the same for the powers of n we have:
[tex]n,n^5,n^3[/tex]Again, the GCF is the power of n with the lowest exponent, in this case n.
Now that we have found the GCFs of the integers, the powers of m and the powers of n we can find the GCF of all the terms. This is given by the product of those 3. Then the answer is:
[tex]2mn[/tex]Translate the following into an inequality:What number divided by five, is less than 8?m ÷ 5 < 85 ÷ m ≤ 8m ÷ 5 > 85 ÷ m > 8
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The phrase "number divided by five" can be expressed as
[tex]m\div5[/tex]"is less than 8" is expressed as
[tex]<8[/tex]Putting it together, the inequality is
[tex]m\div5<8[/tex]