given that triangle DEF is a right triangle with acute angles D and F and right angle E, which trigonometric function would be equal to Sin(F).
Answers
EXPLANATION
We can represent this situation as shown as follows:
The expression of Sin(F) is equal to Sin F = Opposite/Hypotenuse = DE/DF
[tex]\sin F=\frac{Opposite}{\text{Hypotenuse}}=\frac{DE}{DF}[/tex]The equivalent expression would be:
[tex]Cos\text{ D=}\frac{Adjacent}{\text{Hypotenuse}}=\frac{DE}{DF}[/tex]
Related Questions
Patricia keeps apples in 3 bins and 2 crates in her store. Each bin can hold no more than 200 pounds. Each crate can hold no more than 50 pounds. Which number line represents all of the possible weights, in pounds, of apples Patricia can keep in her store?
Answers
Given:
The bins can hold no more than w(b) < 200 pounds.
The crate can hold no more than w(c) < 50 pounds.
The number of bins is n(b) = 3.
The number of crates is n(c) = 2.
The objective is to find the correct number line for the graph.
Explanation:
The maximum quantity of bins can be calculated as,
[tex]\begin{gathered} Q(b)The maximum quantity of crate can be calculated as,[tex]\begin{gathered} Q(c)To find the maximum store capacity:The maximum store capacity can be calculated as,
[tex]undefined[/tex]Translate this sentence into an equation.The product of 5 and Julie's height is 80.Use the variablej to represent Julie's height.
Answers
ANSWER:
5 x j = 80
STEP-BY-STEP EXPLANATION:
The sentence as an equation would be the multiplication of j and 5 equal to 80, just like this:
[tex]5\times j=80[/tex]A freight train is carrying goods across the country. The distance it has traveled directly with the number of gallons of fuel it has used. See the graph below
Answers
1) To find how many miles per gallon that freight train makes is to find a rate. We can find it in two ways, either by setting a proportion or by finding the slope.
2) Note that this direct variation depicted by the graph is proportional. Therefore, let's find the slope by picking two points:
[tex]\begin{gathered} (200,50),(400,100) \\ \\ m=\frac{y_2-y_1}{x_2-x_1}=\frac{100-50}{400-200}=\frac{50}{200}=\frac{1}{4} \end{gathered}[/tex]3) Thus, the answers are:
As we learn more about lines, we will occasionally have to consider perfectly vertical lines as a special case and treat them differently. Think about applying what you have learned in the last couple of activities to the case of vertical lines. What is the same? What is different?
Answers
If the line of the graph is vertical then the slope of the graph is zero. The coordinate of the y-value will never change on vertical lines.
What are vertical lines?The vertical line is a line that is parallel to the y-axis. A vertical line can be defined as a line on the coordinate plane where all the points on the line have the same x-coordinate. A form of test employed in relation is the vertical line test. Any kind of vertical line equation lacks a y-intercept. The vertical line test is used to determine whether or not the given relation is a function. The vertical line is another name for the vertical bar. A mathematical sign is an upright slash. Depending on the context, it may be used to represent a certain kind of logic or an operation. The vertical line is the line that runs along the y-axis.
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Use the value of x to find the measure of Angle 1.x=25 5x-5 2x+10
Answers
Given:
• x = 25
,• ∠1 = 5x - 5
,• ∠2 = 2x + 10
Let's find the measure of angle 1.
To find the measure of angle 1, substitute 25 for x in (5x - 5) and evaluate.
We have:
m∠1 = 5x - 5
m∠1 = 5(25) - 5
m∠1 = 125 - 5
m∠1 = 120
Therefore, the measure of angle 1 is 120 degrees.
ANSWER:
∠1 = 120°
A committee must be made up of two students from grades 9, 10, or 11, and another two students from grade 12. How many different committees can be made? Explain and show all of your work.
Answers
to make the committee
what is 8q= 96 what is it?
Answers
To find the value of q, divide both sides of the equation by 8:
[tex]\begin{gathered} 8q=96 \\ \Rightarrow\frac{8q}{8}=\frac{96}{8} \end{gathered}[/tex]Simplify both members of the equation:
[tex]\begin{gathered} \Rightarrow q=\frac{96}{8} \\ \Rightarrow q=12 \end{gathered}[/tex]Therefore:
[tex]q=12[/tex]. Compare: what is greater 5/3 or 9/16
Answers
hello
between 5/3 and 9/16, 5/3 is greater than 9/16
[tex]\frac{5}{3}>\frac{9}{16}[/tex]The midpoint of AB is M(5,1). If the coordinates of A are (3,6), what are thecoordinates of B?
Answers
We have a segment AB of which we know the coordinates of A(3,6) and the midpoint M(5,1).
We have to find the coordinates of B.
We know that the coordinates of the midpoint M are the average of the coordinates of the endpoints A and B, so we can write:
[tex]\begin{gathered} x_M=\frac{x_A+x_B}{2} \\ 2\cdot x_M=x_A+x_B \\ x_B=2x_M-x_A \end{gathered}[/tex]Now we have the x-coordinate of B in function of the x-coordinates of A and M.
The same can be calculated for the y-coordinate:
[tex]y_B=2y_M-y_A[/tex]Then, we can replace and calculate:
[tex]\begin{gathered} x_B=2x_M-x_A \\ x_B=2\cdot5-3 \\ x_B=10-3 \\ x_B=7 \end{gathered}[/tex][tex]\begin{gathered} y_B=2y_M-y_A \\ y_B=2\cdot1-6 \\ y_B=2-6 \\ y_B=-4 \end{gathered}[/tex]Then, the coordinates of B are (7,-4).
Answer: B = (7,-4)
write an equation of the line that satisfies the given conditions. give the equation (a) in slope intercept form and (b) in standard form. m=-7/12 ,(-6,12)
Answers
Given the slope of the line:
[tex]m=-\frac{7}{12}[/tex]And this point on the line:
[tex](-6,12)[/tex](a) By definition, the Slope-Intercept Form of the equation of a line is:
[tex]y=mx+b[/tex]Where "m" is the slope and "b" is the y-intercept.
In this case, you can substitute the slope and the coordinates of the known point into that equation, and then solve for "b", in order to find the y-intercept:
[tex]12=(-\frac{7}{12})(-6)+b[/tex][tex]12=\frac{42}{12}+b[/tex][tex]\begin{gathered} 12=\frac{42}{12}+b \\ \\ 12=\frac{7}{2}+b \end{gathered}[/tex][tex]\begin{gathered} 12-\frac{7}{2}=b \\ \\ b=\frac{17}{2} \end{gathered}[/tex]Therefore, the equation of this line in Slope-Intercept Form is:
[tex]y=-\frac{7}{12}x+\frac{17}{2}[/tex](b) The Standard Form of the equation of a line is:
[tex]Ax+By=C[/tex]Where A, B, and C are integers, and A is positive.
In this case, you need to add this term to both sides of the equation found in Part (a), in order to rewrite it in Standard Form:
[tex]\frac{7}{12}x[/tex]Then, you get:
[tex]\frac{7}{12}x+y=\frac{17}{2}[/tex]Hence, the answers are:
(a) Slope-Intercept Form:
[tex]y=-\frac{7}{12}x+\frac{17}{2}[/tex](b) Standard Form:
[tex]\frac{7}{12}x+y=\frac{17}{2}[/tex]3. If the mZLKI - 174º and KR bisects LLKI, then find the mLLKR.
R
E
K
87°
1740
0740
90°
Answers
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1:
[tex]undefined[/tex]Answer:
87°
Step-by-step explanation:
Angle bisector:Angle bisector is a ray that divides an angle into two congruent angles.
∠LKR = ∠LKJ ÷ 2
= 174° ÷ 2
= 87°
according to a census, there were 66 people per square mile (population density) in a certain country in 1980. By 2000, the # of people per square mile had grown to 76. This information was used to develop a linear equation in slope intercept form, given below, where x is the time in years and y is the population density. Think of 1980 as year zero. what is the population density expected to be in 2018? y = 1/2x + 66
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Determine the value of x for taking 1980 as 0.
[tex]\begin{gathered} x=2018-1980 \\ =38 \end{gathered}[/tex]The equation is y = 1/2x + 66.
Substitute the value of x in the equation to determine the population density in 2018.
[tex]\begin{gathered} y=\frac{1}{2}\cdot38+66 \\ =19+66 \\ =85 \end{gathered}[/tex]So population density in year 2018 is 85.
Answer: 85
Find the X-Intercept and the y-intercept of 4x- 5y = 15X-Intercept:???Y-intercept: ???help
Answers
The y-intercept is (0,-3) while the x-intercept is (18.75,0)
Here, we want to find the x and y-intercepts of the given line
Firstly, we have to rewrite the equation of the line in the standard form
We have this as;
[tex]\text{y = mx + b}[/tex]m is the slope and b is the y-intercept
Rewriting the given equation, we have this as;
[tex]\begin{gathered} 5y\text{ = 4x-15} \\ y\text{ =}\frac{4}{5}x-\frac{15}{5} \\ \\ y\text{ = }\frac{4}{5}x\text{ - 3} \end{gathered}[/tex]We have the y-intercept as -3
In the coordinate form, this is (0,-3)
To get the x-intercept, we set the y value to zero
We have this as;
[tex]\begin{gathered} 0\text{ = }\frac{4}{5}x-15 \\ 15\text{ = }\frac{4x}{5} \\ \\ 4x\text{ = (15}\times5) \\ 4x\text{ = 75} \\ x\text{ = }\frac{75}{4} \\ x\text{ = 18.75} \end{gathered}[/tex]The x-intercept is 18.75 which in the coordinate form is (18.75,0)
How to solve this problem step by step in depth. I have no idea how to solve this
Answers
Answer
[tex]f^{-1}(x)=\frac{-1}{5}x-\frac{4}{5}[/tex]Explanation
The given function is
[tex]f(x)=-5x-4[/tex]Let y = f(x), this implies
[tex]y=-5x-4[/tex]Now, make x the subject of the formula
[tex]\begin{gathered} y=-5x-4 \\ 5x=-y-4 \\ \text{To get x, we divide both sides by 5} \\ \frac{5x}{5}=\frac{-y-4}{5} \\ \\ x=\frac{-y-4}{5} \end{gathered}[/tex]Since f(x) = y, then x = f⁻¹(y)
[tex]\begin{gathered} f^{-}^{1}\mleft(y\mright)=\frac{-y-4}{5} \\ \therefore f^{-1}(x)=\frac{-x-4}{5} \end{gathered}[/tex]The above inverse function can be rewritten as follows
[tex]\begin{gathered} f^{-1}(x)=\frac{-x}{5}-\frac{4}{5} \\ f^{-1}(x)=\frac{-1}{5}x-\frac{4}{5} \end{gathered}[/tex]Some roads in the Rocky Mountains have a rise of 7 feet for every 100 horizontal feet.What is the slope of such roads?
Answers
Let's begin by listing out the information given to us:
The road rises by 7 feet every 100 horizontal feet
The equation becomes:
Slope (m) = Δy/Δx = 7/100 = 0.07
Slope (m) = 0.07
Suppose the booster club is raising money to help offset the cost of a trip.You make $10 per door wreath sold and $2 per candy bar sold. The clubwants to raise at least $400.00. Write an inequality to represent thissituation.
Answers
Let the number of door wreath sold is x.
Let the number of candy bar sold is y.
The inequality can be represented as,
[tex]10x+2y\ge400[/tex]Thus, the above inequation gives the required inequality.
1/ (gg^2 e^5)^2 Write your answer with only positive exponents
Answers
ANSWER
[tex]\frac{1}{g^6e^{10}}[/tex]EXPLANATION
In the denominator, we have the product of g and g². The product of two powers with the same base is the base raised to the sum of the exponents,
[tex]\frac{1}{(gg^2e^5)^2}=\frac{1}{(g^{2+1}e^5)^2}=\frac{1}{(g^3e^5)^2}[/tex]Now, we also have the power of a product. The exponents can be distributed into the multiplication,
[tex]\frac{1}{(g^3e^5)^2}=\frac{1}{(g^3)^2(e^5)^2}[/tex]And finally, for both g and e, we have the power of a power. The result is the base raised to the product of the exponents,
[tex]\frac{1}{(g^3)^2(e^5)^2}=\frac{1}{g^{3\cdot2}e^{5\cdot2}^{}}=\frac{1}{g^6e^{10}}[/tex]Hence, the simplified expression is,
[tex]\frac{1}{g^6e^{10}}[/tex]differentiatey = 3x√x⁴-5
Answers
Given:
[tex]y=3x\sqrt{x^4-5}[/tex]Required:
We need to differentiate the given expression.
Explanation:
Consider the given expression.
[tex]y=3x\sqrt{x^4-5}[/tex][tex]y=3x(x^4-5)^{\frac{1}{2}}[/tex]Differentiate the given expression with respect to x.
[tex]Use\text{ }(uv)^{\prime}=uv^{\prime}+vu^{\prime}.\text{ Here u=3x and v=}(x^4-5)^{\frac{1}{2}}.[/tex][tex]y^{\prime}=3x(\frac{1}{2})(x^4-5)^{\frac{1}{2}-1}(4x^3)+(x^4-5)^{\frac{1}{2}}(3)[/tex][tex]y^{\prime}=\frac{3x(4x^3)}{2\left(x^4-5\right)^{\frac{1}{2}}}+3(x^4-5)^{\frac{1}{2}}[/tex][tex]y^{\prime}=\frac{6x^4}{\left(x^4-5\right)^{\frac{1}{2}}}+3(x^4-5)^{\frac{1}{2}}[/tex][tex]y^{\prime}=\frac{6x^4}{\left(x^4-5\right)^{\frac{1}{2}}}+\frac{3(x^4-5)^{\frac{1}{2}}(x^4-5)^{\frac{1}{2}}}{(x^4-5)^{\frac{1}{2}}}[/tex][tex]y^{\prime}=\frac{6x^4}{\left(x^4-5\right)^{\frac{1}{2}}}+\frac{3(x^4-5)}{(x^4-5)^{\frac{1}{2}}}[/tex][tex]y^{\prime}=\frac{6x^4}{\left(x^4-5\right)^{\frac{1}{2}}}+\frac{3x^4-15}{(x^4-5)^{\frac{1}{2}}}[/tex][tex]y^{\prime}=\frac{6x^4+3x^4-15}{\left(x^4-5\right)^{\frac{1}{2}}}[/tex][tex]y^{\prime}=\frac{9x^4-15}{\left(x^4-5\right)^{\frac{1}{2}}}[/tex][tex]y^{\prime}=\frac{3(3x^4-5)}{\left(x^4-5\right)^{\frac{1}{2}}}[/tex][tex]y^{\prime}=\frac{3(3x^4-5)}{\sqrt{x^4-5}}[/tex][tex]y^{\prime}=\frac{3(3x^4-5)}{\sqrt{x^4-5}}\times\frac{\sqrt{x^4-5}}{\sqrt{x^4-5}}[/tex][tex]y^{\prime}=\frac{3(3x^4-5)\sqrt{x^4-5}}{x^4-5}[/tex]Final answer:
[tex]y^{\prime}=\frac{3(3x^4-5)\sqrt{x^4-5}}{x^4-5}[/tex]5. Determine the value of each variable for parallelogram INDY that has diagonals that intersect at P.IP = 3x, DP = 6x-2, NP = 3y, and YP = 7x - 2.
Answers
Given the INDY
The diagonals has intersected at the point P
IP = 3x, DP = 6x - 2
NP = 3y , YP = 7x - 2
So, IP = DP
[tex]6x-2=3x[/tex]Solve for x :
[tex]\begin{gathered} 6x-2=3x \\ 6x-3x=2 \\ 3x=2 \\ \\ x=\frac{2}{3} \end{gathered}[/tex]And : NP = YP
[tex]3y=7x-2[/tex]substitute with the value of x :
[tex]\begin{gathered} 3y=7\cdot\frac{2}{3}-2=\frac{23}{3}-2=\frac{17}{3} \\ \\ y=\frac{17}{9} \end{gathered}[/tex]So, the answer is :
[tex]\begin{gathered} x=\frac{2}{3} \\ \\ y=\frac{17}{9} \end{gathered}[/tex]solve equation 10 - 25x = 5 what is the value of x
Answers
ANSWER
x = 1/5
EXPLANATION
We are given the equation:
10 - 25x = 5
To find the value of x, first we subtract 10 from both sides of the equation:
10 - 25x - 10 = 5 - 10
10 - 10 - 25x = 5 - 10
-25x = -5
Now, divide both sides by 5:
=> x = -5 / -25
x = 1/5
That is the value of x.
the first drop down answers are 18,10,7,14the second drop down box options are 16.5,30.5,44.5the third options are 2.5, 1.5, 1,3 the fourth options are 14n, 18n, 7n, 10nthe fifth options are each movie tickets cost the same amount, there is a service fee for buying tickets online, the cost increase as tge number of tickets increase, the leaste amount of tickets you cab buy is 1
Answers
Answer:
Recursive formula:
a_n = a_n-1 + 14,
a_1 = 16.5
Explicit formula: a_n = 14(n - 1) + 16.5
Each movie costs the same amount.
Explanation:
Looking at the numbers we see that each next term a_n is 14 added to the previous term, a_n-1 and the first term a_1 is 16.5; therefore, we can say
[tex]\begin{gathered} a_n=a_{n-1}+14, \\ a_1=16.5 \end{gathered}[/tex]
find the shaded area to the nearest tenth, use 3.14 for pi. help pls due tmrw
Answers
The area of the shaded region inside the circle is 49.04cm².
What is a circle?All points in a plane that are at a specific distance from a specific point, the center, form a circle.
In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant.
So, the shaded area is:
We can easily tell that the diameter of the circle here is 12cm.
So, the radius will be 6cm.
Now, calculate the area of a circle as follows:
A = πr²
A = 3.14(6)²
A = 3.14(36)
A = 113.04cm²
Now, the area of the smaller square:
A = s²
A = 2²
A = 64²
Area of the shaded region:
113.04 - 64
49.04 cm²
Therefore, the area of the shaded region inside the circle is 49.04cm².
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Sketch vector v. Be sure to number your axes. Then find the magnitude of vector v. Show all work.
Answers
Step 1
Sketch the vector V.
[tex]v=-2i\text{ +5j}[/tex]Step 2
Find the magnitude of the vector. The magnitude of a vector is given as;
[tex]\begin{gathered} |v|=\sqrt{(i)^2+(j)^2} \\ i=-2 \\ j=5 \\ \left|a+bi\right|\:=\sqrt{\left(a+bi\right)\left(a-bi\right)}=\sqrt{a^2+b^2} \end{gathered}[/tex][tex]\begin{gathered} |v|=\sqrt{(-2)^2+(5)^2} \\ |v|=\sqrt{4+25} \\ |v|=\sqrt{29} \end{gathered}[/tex]Therefore, the magnitude is given as;
[tex]|v|=\sqrt{29}[/tex]3.What are the coordinates of the center and the length of the radius of the circle whose equation is(x + 1)^2 + (-5)^2 = 16?
Answers
The general equation of circle with centre (h.k) and radius r is,
[tex](x-h)^2+(y-k)^2=r^2[/tex]Simplify the equation to obtain the centre and radius of circle.
[tex]\begin{gathered} (x+1)^2+(y-5)^2=16 \\ (x-(-1))^2+(y-5)^2=(4)^2 \end{gathered}[/tex]So center of circle is (-1,5) and radius 4.
If Rosa is at most 27 years old. What symbol does at most refer to less than greater than less than or equal to greater than or equal to
Answers
The correct answer is less than or equal to because at most 27 years means that Rosa's highest age is 27.
evaluate the expression 0.03^3
Answers
The given expression is,
[tex]0.03^3[/tex]So, expanding we have,
[tex]0.03^3=0.03\times0.03\times0.03=\text{0}.000027[/tex]Hello, I need help writing a recursive formula for these I’m struggling bad
Answers
1) Notice that:
[tex]\begin{gathered} 3=\frac{30}{10}, \\ \frac{3}{10}=\frac{3}{10}, \\ \frac{3}{100}=\frac{\frac{3}{10}}{10}. \end{gathered}[/tex]Therefore the recursive formula for the first sequence is:
[tex]\begin{gathered} a_1=30, \\ a_n=\frac{a_{n-1}}{10}\text{ for }n\geq2. \end{gathered}[/tex]2) Notice that:
[tex]\begin{gathered} 11=14-3, \\ 8=11-3, \\ 5=11-3. \end{gathered}[/tex]Therefore the recursive formula for the second sequence is:
[tex]\begin{gathered} a_1=14, \\ a_n=a_{n-1}-3\text{ for }n\geq2. \end{gathered}[/tex]Answer:
Left sequence:
[tex]\begin{gathered} a_1=30, \\ a_n=\frac{a_{n-1}}{10}\text{ for }n\geq2. \end{gathered}[/tex]Right sequence:
[tex]\begin{gathered} a_1=14, \\ a_n=a_{n-1}-3\text{ for }n\geq2. \end{gathered}[/tex]
solve the equation. check your solution 1/3 (2b+9) =2/3 (b+9/2)
Answers
The equation to solve is:
[tex]\frac{1}{3}(2b+9)=\frac{2}{3}(b+\frac{9}{2})[/tex]We use distributive property [a(b+c)=ab+ac], simplify and solve for b:
[tex]\begin{gathered} \frac{1}{3}(2b+9)=\frac{2}{3}(b+\frac{9}{2}) \\ \frac{2}{3}b+3=\frac{2}{3}b+3 \end{gathered}[/tex]From here, we can't solve.
It is the same equation.
No Solution.
What is the missing reason for The third step in the proof below
Answers
Solution
The image below contain the solution
which portion must be true?
Answers
The two figures are similar
Using the similarity theorem
The only true proportion is
[tex]\frac{8}{2}\text{ = }\frac{x}{y}[/tex]