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Trigonometric Ratios
The figure is a triangle with hypotenuse of h = 25 feet. The angle of elevation is 35°.
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please help me thank you
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Triangle MNO has its vertices at the following coordinates:M(2, 2) N(-1,3) O(1,5)Give the coordinates of the image triangle M'N'O' after a 90° counterclockwise rotation about the origin.
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The counter clockwise rotation of any point X(x,y) about origin results in change of coordinates as,
[tex]X(x,y)\rightarrow X^{\prime}(-y,x)[/tex]Determine the coordinates of the vertices of the triangle M'N'O'.
[tex]M(2,2)\rightarrow M^{\prime}(-2,2)[/tex][tex]N(-1,3)\rightarrow(-3,-1)[/tex][tex]O(1,5)\rightarrow(-5,1)[/tex]So coordinates of triangle M'N'O' are;
M'(-2,2)
N'(-3,-1)
O'(-5,1)
Is the point (-2, 2) a solution for the equation y-4 = 3(x + 1)?
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Remember that ordered pairs are written in the form:
[tex](x,y)[/tex]To find it (-2,2) is a solution for the given equation, substitute x=-2 and y=2:
[tex]\begin{gathered} y-4=3(x+1) \\ \Rightarrow2-4=3(-2+1) \\ \Rightarrow-2=3(-1) \\ \Rightarrow-2=-3 \end{gathered}[/tex]Since the expression -2=-3 is false, then the point (-2,2) is not a solution for the given equation.
You are a landscaper working on the design of a parking lot in a new shopping center. You are measuring the length of a grass median that will be exactly as long as four parking spots and their dividing lines. One of these spots is a handicapped spot, which is 1018 feet wide and next to the curb. The other three spots are 838 feet wide. There are four dividing lines between the spots, and each measures 18 foot. What is the length of the grass median, D?
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SOLUTION
From the given information:
one of the spots is
[tex]10\frac{1}{8}ft[/tex]Other three spots are
[tex]8\frac{3}{8}ft\text{ wide}[/tex]There are four dividing line of
[tex]\frac{1}{8}\text{foot}[/tex]The total length of the grass median is:
[tex]10\frac{1}{8}+3(8\frac{3}{8})+4(\frac{1}{8})[/tex]Calculate the value
[tex]\begin{gathered} \frac{81}{8}+3(\frac{67}{8})+\frac{4}{8} \\ =\frac{81}{8}+\frac{201}{8}+\frac{4}{8} \\ =\frac{81+201+4}{8} \\ =\frac{286}{8} \end{gathered}[/tex]Reduce the fraction
[tex]\frac{286}{8}=35\frac{6}{8}=35\frac{3}{4}[/tex]Therefore the length of the grass median is
[tex]35\frac{3}{4}[/tex]Write the inequality shown by the shaded region in the graph with the boundary line 2x + 2y = -6
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The Solution:
Given the equation of a line below:
[tex]2x+2y=-6[/tex]Step 1:
We shall determine the x-intercept and y-intercept of the given line.
x-intercept: The value of x when y=0
[tex]\begin{gathered} \text{When y=0} \\ 2x+2(0)=-6 \\ 2x=-6 \end{gathered}[/tex]Dividing both sides by 2, we get
[tex]\begin{gathered} x=\frac{-6}{2}=-3 \\ \text{ So,} \\ \text{ The x-intercept = (-3,0)} \end{gathered}[/tex]Similarly,
y-intercept: the value of y when x=0
[tex]\begin{gathered} 2(0)+2y=-6 \\ \\ 2y=-6 \end{gathered}[/tex]Dividing both sides by 2, we get
[tex]\begin{gathered} y=\frac{-6}{2}=-3 \\ \text{ hence,} \\ \text{ The y-intercept = (0,-3)} \end{gathered}[/tex]Determine the inequality symbol that will be used to replace the equality sign.
If the straight line is unbroken, it means the points on the line are inclusive. So, the inequality symbol will not be a strict inequality. It will be one of these two inequalities:
[tex]\leq\text{ or }\ge[/tex]Determine the exact inequality symbol that will represent the shaded region.
If the shaded region is below the line, the correct inequality will be:
[tex]\leq[/tex]But where the shaded region is above the line, the correct inequality symbol will be:
[tex]\ge[/tex]From the given graph, it is clear that the shaded region is above the line. So, it follows that the correct inequality is:
[tex]\ge[/tex]Therefore, the correct answer is:
[tex]2x+2y\ge-6[/tex]5-3/2x>1/3what is x?
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Coco, this is the solution to the inequality:
5 - 3x/2 ≥ 1/3
Subtracting 5 at both sides:
5 - 3x/2 - 5 ≥ 1/3 - 5
-3x/2 ≥ 1/3 - 15/3
-3x/2 ≥ -14/3
LCD (Least Common Denominator) between 2 and 3 : 6
-9x/6 ≥ -28/6
Dividing by -9/6 at both sides:
-9x/6 / -9/6 ≥ -28/6 / -9/6
x ≥ 28/9
In consequence, the correct answer is C. x ≥ 28/9
A polynomial function with degree 5 can have a maximum of how many turning points? It would be 5 right?
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In this case, we'll have to carry out several steps to find the solution.
Step 01:
data:
polynomial function
Step 02:
turning points:
The maximum number of turning points of a polynomial function is always one less than the degree of the function.
5th degree polynomial function and has 4 turning points.
The answer is:
5th degree polynomial function and has 4 turning points.
It's in the photo, it's a bit to hard to type out.
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Perpendicular lines have slopes that are negative reciprocals.
If two perpendicular lines have slopes m1 and m2, then we have the following equation:
[tex]m_1=-\frac{1}{m_2}[/tex]Then, we can analyze each pair.
a) In this case, both lines have the same slope (m = 1/5). They are parallel, not perpendicular.
b) In this case, the slopes are different. They are reciprocals (m1 = 1/m2), but they are not negative reciprocals, so they are not perpendicular.
c) In this case the slopes are the negative of each other (2/3 and -2/3), but they are not negative reciprocals. Then, they are not perpendicular.
d) In this case, the slopes are negative reciprocals:
[tex]-\frac{1}{m_2}=-\frac{1}{-\frac{3}{2}}=\frac{1}{\frac{3}{2}}=\frac{2}{3}=m_1[/tex]Then, this lines are perpendicular.
Answer: Option d.
(Solve the problem & round to four decimal places as needed.)
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SOLUTION
Given:
[tex]ln0.0664=-2.7121[/tex]Final answer:
-2.7121
Question 37?Find the indicated function and state its domain in interval notation?
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Given the functions:
[tex]\begin{gathered} f(x)=-\sqrt[]{x-3} \\ g(x)=3x \end{gathered}[/tex]You need to multiply them, in order to find:
[tex](f\cdot g)(x)[/tex]Then, you get:
[tex]\begin{gathered} (f\cdot g)(x)=(-\sqrt[]{x-3})(3x) \\ (f\cdot g)(x)=-3x\sqrt[]{x-3} \end{gathered}[/tex]In order to find the Domain, you need to remember that the Domain of a Radical Function are those input values (x-values) for which the Radicand is positive. Then, in this case, you need to set up that:
[tex]x-3\ge0[/tex]Now you have to solve for "x":
[tex]x\ge3[/tex]Therefore:
[tex]Domain\colon\lbrack3,\infty)[/tex]Hence, the answer is:
[tex]\begin{gathered} (f\cdot g)(x)=-3x\sqrt[]{x-3} \\ \\ Domain\colon\lbrack3,\infty) \end{gathered}[/tex]• 5th 3230 [] What would be the slope of a line perpendicular to the line graphed above? -2 2 1/2 -1/2 Zoom in Double Jeop 3:39
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When two lines are perpendicular to each other, their slopes would be a negative inverse of each other. This simply means the slope of a line perpendicular to the one in the question should be equal to the negative inverse of the one we have here. Let us begin by calculating the slope of this line.
When you are given two endpoints, the slope is derived as;
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]When the coordinates are (0, 3) and (-1.5, 0)
That is, when x = 0 then y = 3 (observe the point where the line touches the vertical axis), and when x = -1.5, then y = 0 (observe the point where the line touches the horizontal axis)
Therefore, the coordinates (0, 3) and (-1.5, 0) are now your (x1, y1) and (x2, y2)
[tex]\begin{gathered} m=\frac{0-3}{-1.5-0} \\ m=\frac{-3}{-1.5} \\ m=2 \end{gathered}[/tex]Therefore the slope of a line perpendicular to the one on the graph is -1/2.
Is y = 8 a solution to the inequality below?
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Answer:
Yes
Step-by-step explanation:
136/8 = 17
17 +3 = 20
20 is less than or equal to 123 so 8 does work as a solution
X+27+32 = 8
X+ 3y +32 = 10
X + 2y +42 = 9
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Value of x and y are -51 and 8 respectively
What is Algebra?
One of the many branches of mathematics is algebra. Algebra, which is a common thread throughout practically all of mathematics, is broadly defined as the study of mathematical symbols and the rules for using these symbols in formulas.
Let,
X+27+32 = 8
X+ 3y +32 = 10
X + 2y +42 = 9
Be, equation 1, 2 and 3 respectively
X+27+32 = 8 -----(1)
X+ 3y +32 = 10 -----(2)
X + 2y +42 = 9 -----(3)
From equation we can find the value of x
X+27+32 = 8
X + 59 = 8
X = 8 - 59
X = - 51
Substituting the value of x in equation 3
X + 2y +42 = 9
(-51) + 2y + 42 = 9
-51 + 42 + 2y = 9
-9 + 2y = 9
2y = 9 + 9
2y = 18
y = 18/2
y = 9
Hence, the value of x = -51 and y = 9
To learn more about Algebra click on the link
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A hot chocolate recipe calls for 2.5 gallons of milk. How many quarts of milk are needed for the recipe
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Answer: 10
Step-by-step explanation: a gallon has 4 quarts, 4x2.5=10
10 quarts is 2.5 gallons.
There are no solutions to the system of inequalities shown below. y< 4X-6 y > 4x + 2 A.true B. false
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The graphs of both inequalities is shown below;
Please note that the red region with the broken lines represents y < 4x - 6
The blue blue region with the broken lines represent y > 4x + 2
Observe carefully that both graphs run parallel to each other and there is no point of intersection. This means there is no values of x and y that can satisfy both inequalities.
Simply put, there are no solutions to the system of inequalities shown.
The answer is
A: TRUE
Which of the following lists of data has the smallest standard deviation? Hint: you should not need to compute the standard deviation for each list.Select the correct answer below:11, 17, 9, 4, 4, 6, 6, 9, 8, 1829, 21, 21, 28, 28, 26, 24, 24, 17, 236, 8, 10, 6, 8, 8, 10, 7, 10, 1023, 19, 12, 19, 17, 18, 16, 10, 12, 2117, 12, 6, 6, 15, 16, 20, 20, 5, 17
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Standard deviation is an important measure of spread or dispersion. It tells us how far, on average the results are from the mean.
The smallest standard deviation belongs to the dataset with the smallest range and almost no outliers. Closer the values are to the mean, less the value of the standard deviation.
Comparing those datasets, the one that fits this description is the third one.
[tex]\lbrace6,8,10,6,8,8,10,7,10,10\rbrace[/tex]By using the substitution u = 4 + 3x^2, or otherwise, find
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Solution
We have the following integral:
[tex]\int \frac{2x}{(4+3x^{2})^{2}}dx[/tex]We can use the substitution u= 4 +3x² and we have du= 6x dx, then we have this:
[tex]\int \frac{2x}{(u^{})^2}\cdot\frac{du}{6x}=\frac{1}{3}\int u^{-2}du=\frac{1}{3}\cdot\frac{u^{-1}}{-1}+C=-\frac{1}{3u}+C=-\frac{1}{3(4+3x^{2})}+C[/tex]in the sophomore class at Summit High School the number of students taking French is 2/3 of the number taking Spanish. how many students are studying each language if the total number of students in French and Spanish is 310 ?This is Homework
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From the information given in the statement let be
[tex]\begin{gathered} f=\frac{2}{3}s\text{ (1)} \\ f+s=310\text{ (2)} \end{gathered}[/tex]Where
*f: number of students taking a French class
*s: number of students taking a Spanish class
So, you have a system of linear equations, which you can use the substitution method.
To do this, replace the value of the first equation in the second equation and solve for s
[tex]\begin{gathered} f+s=310\text{ (2)} \\ \frac{2}{3}s+s=310 \\ \frac{5}{3}s=310 \\ \text{ Multiply by }\frac{3}{5}\text{ on both sides of the equation} \\ \frac{3}{5}\cdot\frac{5}{3}s=310\cdot\frac{3}{5} \\ s=186 \end{gathered}[/tex]Now,
while exploring a volcano zane heard somerumbling, so he decided to climb up out of there as quicklyas he could zane's elevation relative to the edge of the inside of the volcano (in meter) as a function time (in seconds) is graphed. PLEASE HELP ME WITH THIS How long did it take Zane to reach the edge of the volcano?
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We have to find the time it took for Zane to be in the same elevation as the edge of the Volcano, that is, when his relative elevation is 0 on the graphic.
This happens at a time of 35 seconds. So:
It took Zane 35 seconds to reach the edge of the volcano.
Rigid Transformations: Question 3A military compound is located in a city where the streetsare arranged in a grid. The compound is going to be movedto a new location in the same city. The new compound willbe exactly the same as the old one and in the sameorientation. The existing location is represented on thecoordinate grid shown, where each unit represents one cityblock. Which of the following best describes the situation?14B1210CDD'C6 4AB2-14 12 10 86226 8 10 12 142D4С6 8N10Wm12s141
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In this question, we are given two locations of a military compound.
Let's take the coordinates of point A from the graph,
A = (-3, 2)
The new coordinates of A' = (5, 13)
translation in x-axis = 5 - (-3) = 5 + 3 = 8
translation in y-axis = 13 - 2 = 11
hence, each point of the figure will be translated to 8 units on the x-axis and 11 units on the y-axis.
in a classroom there are 28 tablets which includes 5 that are defective. if seven tablets are chosen at random to be used by student groups. 12. how many total selections can be made? a. 140 b. 98280 c. 11793600 d. 4037880 e. 1184040 13. how many selections contain 2 defective tablets? a. 10 b. 21 c. 336490 d. 706629 e. 33649
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Using the combination formula, it is found that:
The number of total selections that can be made is: e. 1184040.The number of selections that contain two defective tablets is: c. 336490.Combination formula[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula, involving factorials. It is used when the order in which the elements are chosen does not matter.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In the context of this problem, we have that seven tablets are chosen from a set of 28 tablets, hence the number of selections that can be made is given by:
[tex]C_{28,7} = \frac{28!}{7!21!} = 1,184,040[/tex]
For two defective tablets, the selections are given as follows:
Two defective from a set of five.Five non-defective from a set of 23.Hence the number of selections is calculated as follows:
[tex]C_{23,5}C_{5,2} = \frac{23!}{5!18!} \times \frac{5!}{2!3!} = 336,490[/tex]
A similar problem, also about the combination formula, is given at https://brainly.com/question/25821700
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Michael and Ashley each buy x pounds of turkey and y pounds of ham. Turkey costs $3 per pound at Store A and $4.50 per pound at Store B. Ham costs $4 per pound at Store A and $6 per pound at Store B. Michael spends $18 at Store A, and Ashley spends $27 at Store B. Could Michael and Ashley have bought the same amount of turkey and ham?
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Step 1
Michael spends $18 at store A
He buys x pounds of turkey and y pounds of ham.
But turkey costs $3 in-store A and ham costs $4 in-store A
Therefore, we will have the following equation for Michael
[tex]3x+4y=18---(1)[/tex]Step 2
Ashley spends $27 in-store B
She buys x pounds of turkey and y pounds of ham.
But turkey costs $4.50 in-store B and ham costs $6 in-store B.
Therefore, we will have the following equation for Ashley
[tex]4.5x+6y=27----(2)[/tex]Step 3
Solve the equations graphically
If the graphs of the equations are the same, then there are an infinite number of solutions that are true for both equations. Since the graphs are the same, then there are infinitely many solutions true for both equations.
For instance, the points if we test for the points on the graph, we will conclude if both Michael and Ashley bought the same amount of turkey and ham.
[tex]\begin{gathered} 3x+4y=18_{} \\ 4.5x+6y=27 \\ At\text{ x =2 and y=3} \\ we\text{ have,} \\ 3(2)+4(3)=18_{} \\ 6+12=18 \\ 18=18 \\ 4.5(2)+6(3)=27 \\ 9+18=27 \\ 27=27 \\ \text{At x=6, y=0} \\ we\text{ have} \end{gathered}[/tex][tex]\begin{gathered} 3(6)+4(0)=18 \\ 18=18 \\ 4.5(6)+6(0)=\text{ 27} \\ 27=27 \end{gathered}[/tex]Therefore yes, Michael and Ashley could have bought the same amount of turkey and ham.
Graph the equation. y = 2x 20 N 18 16 14 12 10 8 6 4 N. 0 1 2 3 4 ул 6 10 2. y = 2x
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Make a table, and give values to x.
Solve the equation and obtain y values.
Graph the points and join them:
x = 0
y= 2x = 2 (0) = 0
x= 2
y= 2(2) = 4
x= 4
y= 2(4) = 8
Graph:
A 65 ft tree casts a 13 ft shadow. At the same time of day, how long would the shadow of a 20 ft building be? (Draw a diagram to help you set up a proportion)
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height of tree = 65 ft
length of shadow = 13 ft
Let draw a diagram to illustrate the question effectively
The proportion can be set up below
[tex]\begin{gathered} \frac{65}{20}=\frac{13}{x} \\ \text{cross multiply} \\ 65x=260 \\ x=\frac{260}{65} \\ x=4\text{ ft} \end{gathered}[/tex]Th shadow will be 4 ft. do you
find the explict formula for 15, 12, 9, 6
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Given:
15, 12, 9, 6
To write the explicit formula, use the form:
[tex]a_n=a_1+d(n-1)[/tex]Where
a1 = first term = 15
d = common difference = 12 - 15 = -3
n = number of terms
Therefore, the explicit formula is:
[tex]\begin{gathered} a_n=15-3(n-1) \\ \\ a_n=15-3n+3 \\ \\ a_n=18-3n \end{gathered}[/tex]ANSWER:
[tex]a_n=18-3n[/tex]Ashley can text 60 words in 45 seconds. At this rate, how many words can she text in 60 seconds?
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Let Ashley can text x words in 60 minutes. Then equation for x is,
[tex]\begin{gathered} \frac{60}{45}=\frac{x}{60} \\ x=\frac{60\cdot60}{45} \\ =80 \end{gathered}[/tex]Thus, Ashley text 80 words in 60 seconds.
Solve the system of two equations in two variables.6x - 7y = 282x + 4y = -16
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Answer:
Explanation:
Given the system of equations
[tex]\begin{gathered} 6x-7y=28 \\ 2x+4y=-16 \end{gathered}[/tex]We intend to use the elimination method to solve it.
• Multiply the first equation by 2
,• Multiply the second equation by 6
This gives us:
[tex]\begin{gathered} 12x-14y=56 \\ 12x+24y=-96 \end{gathered}[/tex]We eliminate x by subtracting.
[tex]undefined[/tex]Painter charges $20 every hour that he paints let H represent the number of hours he paints & E represent his earnings select all statements that are trueA. The equation H equals 20 E shows the correct relationship between the earnings and hours worked B. With this hourly rate the painter must work more than 12 hours to earn 500C. With this hourly rate the painter earns 20h dollars for each hour worked.D. With this hourly rate if the painter works 10 hours he earns 20.E. Is the painter raises his hourly rate by two dollars the new equation is e=22h
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Answer:
No.
Yes.
Yes.
No.
Yes...
Use the x and y intercepts to sketch a graph of each equation.
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The given equation is expressed as
x + 4y = 8
4y = 8 - x
y = 2 - x/4
The first step is to input values for x into the equation and determine the corresponding y values. These values are then plotted on the graph.
For x = 0, y = 2 - 0/4 = 2
For x = 1, y = 2 - 1/4 = 1.75
For x = 2, y = 2 - 2/4 = 1.5
We would plot these points on the graph
When 80% of a number is added to the number, the result is 162.
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Given:
80% of a number is added to the number, the result is 162.
Required:
To find the number.
Explanation:
80% of a number is added to the number
[tex]\begin{gathered} \frac{80}{100}x+x \\ \\ =0.8x+x \end{gathered}[/tex]The result is 162, so
[tex]\begin{gathered} 0.8x+x=162 \\ \\ 1.8x=162 \\ \\ x=\frac{162}{1.8} \\ \\ x=90 \end{gathered}[/tex]Final Answer:
The number is 90.
