Answers
Since we are dealing with a right triangle, we can use trigonometric identity below
[tex]\begin{gathered} sin\theta=\frac{O}{H} \\ \theta\rightarrow\text{ interior angle} \\ O\rightarrow\text{ opposite side to}\theta \\ H\rightarrow\text{ hypotenuse} \end{gathered}[/tex]Therefore, in our case,
[tex]\begin{gathered} sin(45\degree)=\frac{5}{x} \\ \Rightarrow x=\frac{5}{sin(45\degree)}=\frac{5}{\frac{1}{\sqrt{2}}}=5\sqrt{2} \end{gathered}[/tex]Thus, the answer is x=5sqrt(2), the second optionRelated Questions
If reciangle ABCD is in quadrant II, and rotated 270 degrees counterciockwise around the origin, then what quadrant will rectangle A'B'C'D' be in ? Quadrant l Quadrant II Quadrant lll Quadrant IV
Answers
Quadrant IV.
1) Let's Draw this to give us a better idea.
In a 270º CCW Rotation, the rule is every coordinate to be translated
(x.y) ---(y,-x)
2) Let's give to our quadrilateral
A(-2,3) ---- A'(3,2)
B(-4, 3) -----B'(3,4)
C(-6, 4) -----C' (4,6)
D( -8, 4) ---- D' (4, 8)
And so forth
So Quadrant IV is the answer.
Evaluate the left hand side to find the value of aa in the equation in simplest form. 4
Answers
Given
[tex]\frac{x^{\frac{1}{2}}}{x^{\frac{1}{6}}}[/tex]Solution
Apply exponent rule
[tex]\begin{gathered} x^{\frac{1}{2}-\frac{1}{6}}=x^{\frac{3-1}{6}} \\ \\ \\ x^{\frac{2}{6}}=x^{\frac{1}{3}} \end{gathered}[/tex][tex]a=\frac{1}{3}[/tex]We have
[tex]\frac{x^{\frac{1}{2}}}{x^{\frac{1}{6}}}=x^{\frac{1}{3}}[/tex]a. A random sample of 43 cars in the drive-thru of a popular fast food restaurant revealed an average bill of $18.58 per car. The population standard deviation is $6.22. Estimate the mean bill for all cars from the drive-thru with 97% confidence. Round intermediate and final answers to two decimal places.
Answers
Given
[tex]\begin{gathered} n=43 \\ Mean\text{ = \$18.58} \\ \sigma=\text{ \$6.22} \end{gathered}[/tex]Solution
Formula
[tex]\text{Confident interval =M }\pm\frac{Z\sigma}{\sqrt[]{n}}[/tex]where
[tex]\begin{gathered} M=\text{ mean or Average} \\ Z-score=Z_{97}=2.17 \\ n=43 \end{gathered}[/tex]Substitute the parameters into the Confident Interval formula
[tex]\text{Confident interval =18.58}\pm\frac{2.17\times6.22}{\sqrt[]{43}}[/tex]Then we calculate the Addition and subtraction
First the Addition
[tex]\begin{gathered} \text{Confident interval =18.58+}\frac{2.17\times6.22}{\sqrt[]{43}} \\ \\ \text{Confident interval =18.58+}\frac{13.4974}{\sqrt[]{43}} \\ \\ \text{Confident interval =18.58+}\frac{13.4974}{6.5574} \\ \text{Confident interval =18.58+}2.05833 \\ \text{Confident interval =}20.63833342 \\ \\ \text{Confident interval =}20.64\text{ two decimal places} \end{gathered}[/tex]Then now for subtraction
[tex]\begin{gathered} \text{Confident interval =18.58-}\frac{2.17\times6.22}{\sqrt[]{43}} \\ \\ \text{Confident interval =18.58-}\frac{13.4974}{\sqrt[]{43}} \\ \\ \text{Confident interval =18.58-}\frac{13.4974}{6.5574} \\ \text{Confident interval =18.58-}2.05833 \\ \text{Confident interval =}16.5216658 \\ \\ \text{Confident interval =16.52 two decimal places} \end{gathered}[/tex]The final answer
[tex](16.52,\text{ 20.64)}[/tex]I am confused on my geometry test review and need help.
Answers
4/3 = ? /12
Multiply both-side of the equation by 12
4/3 x12 = ?
48 / 3 = ?
16 = ?
WX = 16
Evaluate the expression xy - 3x when x = 4 and y = 5
Answers
Answer:
xy - 3x = 8
when x = 4 and y = 5
Explanation:
Given the expression
xy - 3x
When x = 4 and y = 5, the equation becomes
(4)(5) - 3(4)
= 20 - 12
= 8
3. Determine the missing length in the following triangle. Round to thenearest tenth. (2 points: 1 point for correct answer, 1 point for showingyour work) *1214Your answer
Answers
7.2
1) Examining the picture, we can assume this is a Right Triangle, and then use the Pythagorean Theorem
a²=b² +c²
14² = 12² +c² The hypotenuse is the larger side a
196=144 +c²
196-144 = c²
52 =c²
√52 =√c²
c= √52
2) Rounding off to the nearest tenth we can write
c= √52 is approximately 7.2
what is the value of the square root of -25+10
Answers
Celeste, this is the solution to the exercise:
Let's recall that √-1 = i, therefore:
The first term of the sum is √-25 = √25 * -1 = 5i
The second term remains the same. + 10
Thus, the correct answer is D. 5i + 10
Is A= {9000, 5, 8, 119} a finite set?
Answers
ANSWER
Yes, it is.
EXPLANATION
A finite set is a set that contains a finite number of elements. That is, the number of elements in a finite set are countable.
The set given is:
A = {9000, 5, 8, 119}
There are 4 elements in this set and hence, it is countable.
According to the definition of a finite set, this set is a finite set.
if x-1/x = 20, then x =
Answers
Given
[tex]\frac{x-1}{x}=20[/tex]Solution
[tex]\begin{gathered} \frac{x-1}{x}=\frac{20}{1} \\ \text{cross multiply} \\ 1(x-1)=20(x)_{} \\ we\text{ have} \\ x-1=20x \\ \text{collect the like terms} \\ -1=20x-x \\ -1=19x \\ \text{rewrite} \\ 19x=-1 \\ \text{Divide both sides by 19} \\ \frac{19x}{19}=-\frac{1}{19} \\ \\ x=-\frac{1}{19} \end{gathered}[/tex]The final answer
[tex]x=-\frac{1}{19}[/tex]Solve the inequality -2d < 5
Answers
Answer:
d> -5/2
Step-by-step explanation:
-2d<5
divide both sides by -2
d>-5/2
Answer:
d > - [tex]\frac{5}{2}[/tex]
Step-by-step explanation:
- 2d < 5
divide both sides by - 2, reversing the symbol as a result of dividing by a negative quantity.
d > [tex]\frac{5}{2}[/tex] or d > 2.5
Given the system below. What is the x value of the solution? 3x + 5y = 8 y = x + 8
Answers
We are given the following system of equations:
3 x + 5 y = 8
y = x + 8
So we can use the "substitution method" to solve it, since the second equation is already giving us a possible substitution to make:
Replace y with x + 8 in the other equation.
We proceed as shown below:
3 x + 5 y = 8
3 x + 5 (x + 8) = 8
Use distributivr property to remove the parenthesis:
3 x + 5 x + 40 = 8
8 x + 40 = 8
subtract 40 from both sides to isolate the term in "x"
8 x = 8 - 40
8 x = - 32
divide both sides by 8 to isolate "x"
x = - 32 / 8
x = - 4
We found the requested x value
We are also asked to find y , so we use the value for x in the substitution equation:
y = x + 8
y = -4 + 8 = 4
Then y = 4
The pair that satisfies this system is x = -4 and y = 4 or in pair form: (-4, 4)
I need help with the third question where it says segment addition
Answers
ANSWER
EXPLANATION
We have that the line EG = 71.
We are given that
EF = 8x - 17
and
FG = 5x - 3
We see from the diagram that:
EF + FG
The price to mail a letter at the post office is $0.51 for the first ounce, and $0.20 for each additional ounce. Stephanie paid $1.31 to mail her letter. How much did the letter weigh?A. 7 ounces B.6 ouncesC.4 ounces D.5 ounces
Answers
The cost of sending mail is given as $0.51 for the first ounce and then every ounce after that costs $0.20.
For each letter, the cost would be expressed as;
[tex]\begin{gathered} C=0.51+0.20x \\ \text{Where x is the weight in ounces} \\ \text{For Stephanie's letter,} \\ 1.31=0.51+0.20x \\ \text{Subtract 0.51 from both sides} \\ 1.31-0.51=0.51-0.51+0.20x \\ 0.8=0.20x \\ \text{Divide both sides by 0.20} \\ \frac{0.8}{0.2}=x \\ 4=x \\ \text{Note that she paid \$0.51 for the first ounce} \\ \text{This means she paid for 1 ounce plus another 4 ounces} \\ \text{Stephanie's letter weighs 5 ounces} \end{gathered}[/tex]Therefore, Stephanie's letter weighs 5 ounces.
The correct answer is option D
Which x value is in the domain of the function f(x)=2cot(3x)+4?A. pi/4B. pi/3C. piD. 2pi
Answers
Solution:
Given:
[tex]f(x)=2cot(3x)+4[/tex]The domain of the function is;
[tex]\frac{\pi }{3}nHence, the x-value that is in the domain of the function is;[tex]\begin{gathered} any\text{ value that is not a multiple of }\frac{\pi}{3} \\ \\ Hence,\text{ } \\ \frac{\pi}{3},\pi,2\pi\text{ will be multiples of 3x and will make the function undefined.} \\ \\ Therefore,\text{ the x-value in the domain is }\frac{\pi}{4}\text{ because putting x = }\frac{\pi}{4}\text{ makes the function defined} \end{gathered}[/tex]Therefore, OPTION A is correct.
Which equation represents a line which is perpendicular to the line y =- +522x - 5y = -302x + 5y = 152y-53 = 10O 5x + 2y 12
Answers
Answer:
The equation that represents the perpendicular line is;
[tex]2y-5x=-10[/tex]Explanation:
We want to find the equation of a line perpendicular to the line;
[tex]y=-\frac{2}{5}x+5[/tex]Recall that for two lines to be perpendicular to each other, their slope must be a negative reciprocal of one another.
[tex]m_1.m_2=-1_{}_{}[/tex]so;
[tex]m_2=-\frac{1}{m_1}[/tex]For the given equation, the slope of the given line is;
[tex]m_1=-\frac{2}{5}[/tex]To get the slope of the perpendicular line, let us substitute m1 to the equation above;
[tex]\begin{gathered} m_2=-\frac{1}{m_1} \\ m_2=-\frac{1}{(-\frac{2}{5})_{}} \\ m_2=\frac{5}{2_{}} \end{gathered}[/tex]So, the equation of the perpendicular line would be of the form;
[tex]\begin{gathered} y=m_2x+c \\ y=\frac{5}{2}x+c \\ mu\text{ltiply through by 2} \\ 2y=5x+c \\ 2y-5x=c \end{gathered}[/tex]The equation of the perpendicular line will be of the form;
[tex]2y-5x=c[/tex]Where c is a constant;
From the options, the only equation that is similar to the derived equation is;
[tex]2y-5x=-10[/tex]Therefore, the equation of the perpendicular line is;
[tex]2y-5x=-10[/tex]A math teacher said that 18 out of 25 students passed the test. What percent of the students did NOT pass the test?can you please show me the work for this?
Answers
Given:
A math teacher said that 18 out of 25 students passed the test.
So,
Total number of students = 25 student
Number of students who passed the test = 18
Number of students who did not pass the test = 25 - 18 = 7
So, the percent of the students who did NOT pass the test =
[tex]\frac{7}{25}\times100=28\%[/tex]So, the answer will be 28%
What is the image of (−9,−12) after a dilation by a scale factor of 1/3
centered at the origin?
Answers
By dilation with a scale factor of 1 / 3 centered at the origin, the image of the resulting point is (- 3, - 4).
How to determine the location of the image of a point by using a dilation formula
In this problem we find the coordinates of a point set on Cartesian plane, whose image is the result of using a dilation centered at the origin, whose definition is introduced below:
P'(x, y) = O(x, y) + k · [P(x, y) - O(x, y)]
Where:
O(x, y) - Center of dilationP(x, y) - Original pointP'(x, y) - Resulting pointk - Scale factorIf we know that O(x, y) = (0, 0), k = 1 / 3 and P(x, y) = (- 9, - 12), then the image of the original point is:
P'(x, y) = (0, 0) + (1 / 3) · [(- 9, - 12) - (0, 0)]
P'(x, y) = (- 3, - 4)
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Please help me with this geometry problem. i don’t understand.
Answers
Tangent theorem states that when two tangents intersect out a circle they are said to be equal
Therefore,
Tangent 2x+13 is equal to tangent 4x-8
[tex]\begin{gathered} 4x-8=2x+13_{} \\ by\text{ collecting like terms we will have that,} \\ 4x-2x=13+8 \\ 2x=21 \\ to\text{ find x we will dive both sides by the coefficent of x which is 2} \\ \frac{2x}{2}=\frac{21}{2} \\ x=10\frac{1}{2} \\ x=10.5 \end{gathered}[/tex]Hence,
The value of x =10.5
Jakayla is thinking of a number. The number includes the digits 3,7 and 8 and rounds to 700 when rounding to the nearest hundred. what number could Jakayla be thinking of?
Answers
According to given data we have numbers 3,7,8
So the possible numbers starting from 7 are 738 and 783.
But the nearest to 700 is 738.
So Jakayla is thinking about 738
)) Rick has decided to examine his checking account statements. The account balance was $2,010 last month, and 50% less this month. What is the account balance this month?
Answers
The account balance this month is $4020
Let the account balance this month = x
From the question, we have
The account balance was $2,010 last month.
∴x* 50%= $2,010
⇒x* 50/100= $2,010
⇒x* 1/2= $2,010
⇒x = $4020
Multiplication:
Finding the product of two or more numbers in mathematics is done by multiplying the numbers. It is one of the fundamental operations in mathematics that we perform on a daily basis. Multiplication tables are the main use that is obvious. In mathematics, the repeated addition of one number in relation to another is represented by the multiplication of two numbers. These figures can be fractions, integers, whole numbers, natural numbers, etc. When m is multiplied by n, either m is added to itself 'n' times or the other way around.
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how are rational munbers written as decimalsfYI:I was listening but I just don't understand
Answers
We have 4 rational numbers which we are asked to express in decimal numbers.
To do this, we divide the numerator of each rational number by its denominator, when we do that, we get the following results:
[tex]undefined[/tex]The equation of the line is y=_. The slope indicates that the temperature decreases by 3.5 F for each 1000 foot increase in altitude
Answers
The slope of the function is m = -3.5, which indicates that the temperature decreases by 3.5 degrees for each 1000 feet increase in elevation.
The temperature at Sea level is 87 °F
What is the slope of a function?The slope of a straight line function is the ratio of the rise to the run of the function.
Parts of the question that appear missing includes; The slope and the temperature at Sea level is required.
A point on the table of the graph is that at 4 feet, the temperature is 73 °F
The rate at which the the temperature changes = -3.5 °F per 1,000 feet
The slope of the equation is therefore;
y - 73 = -3.5·(x - 4)
y = -3.5·x + 14 + 73 = -3.5·x + 87
y = -3.5·x + 87
The equation of the the line of the temperature above Sea level is an equation of a straight line, which is of the form; y = m·x + c
Where;
m = The slope of the function
By comparison, the slope of the equation of the line the function is; m = -3.5
The temperature at Sea level, which is the y-intercept is found at the point where x = 0, which gives;
y = -3.5 × 0 + 87 = 87
The temperature at Sea level is 87 °F
The slope of line of the graph of the function, m = -3.5
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Writing an equation in slope intercept form for the line passing through each pair of point . (0, 3) and ( 1, -2)
Answers
Data:
• Point ,A( 0, 3 )
,• Point ,B( 1, -2 )
,• Equation in slope-intercept form:
[tex]y=mx+b[/tex]Procedure:
0. Finding the slope ( ,m ,):
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{-2-3}{1-0}=\frac{-5}{1}[/tex][tex]m=-5[/tex]2. Finding the intersection with y-axis ( b ) using point A:
[tex]\begin{gathered} y=mx+b \\ 3=(-5)\cdot0+b \\ b=3 \end{gathered}[/tex]Answer:
[tex]y=-5x+3[/tex]Summary:
0. We found the slope of the equation ( ,m ,)
,1. We found the intersection with the ,y-axis ,( ,b ,)
,2. We displayed the values in the correct position of the equation.
Find the slope vx and the distance Ay for this pair of coordinates. (-2,-4) (3,-1) Change in y Change in x
Answers
The slope and the distance of two points (a,b), (c,d) is given by
[tex]\begin{gathered} m\text{ = }\frac{d-b}{c-a} \\ d=\sqrt[]{\mleft(c-a\mright)^2+(d-b)^2} \end{gathered}[/tex]Replacing our original points, we have
[tex]\begin{gathered} m=\frac{-1-(-4)}{3-(-2)}=\frac{-1+4}{3+2} \\ m=\frac{3}{5} \\ d=\sqrt[]{(3-\mleft(-2)\mright)^2+(-1}-(-4))^2 \\ d=\sqrt[]{5^2+3^2} \\ d=5.83 \end{gathered}[/tex]In your own words describe an exponential function. Are there restrictions on the domain why or why not? Are exponential and logarithmic function inverse. why or why not?(this is all one question, from the same page i just am on my laptop so cant provide picture)
Answers
Answer:
An exponential function is a mathematical function, which is used in many real-world situations. It is mainly used to find the exponential decay or exponential growth or to compute investments, model populations, and so on. In this article, you will learn about exponential function formulas, rules, properties, graphs, derivatives, exponential series, and examples.
An example of an exponential formula is given below as
[tex]y=ab^x[/tex]The following figure represents the graph of exponents of x. It can be seen that as the exponent increases, the curves get steeper and the rate of growth increases respectively. Thus, for x > 1, the value of y = fn(x) increases for increasing values of (n).
Are there restrictions on the domain why or why not?
For any exponential function, f(x) = ab^x, the domain is the set of all real numbers. For any exponential function, f(x) = ab^x, the range is the set of real numbers above or below the horizontal asymptote, y = d, but does not include d, the value of the asymptote.
Hence,
The domain of exponential functions is equal to all real numbers since we have no restrictions with the values that x can take.
Are exponential and logarithmic function inverse. why or why not?
Logarithmic functions are the inverses of exponential functions. The inverse of the exponential function y = a^x is x = a^y. The logarithmic function y = logx base a is defined to be equivalent to the exponential equation x = a^y
Hence,
Exponential functions and logarithmic functions are inverses of each other
Line t is graphed in the xy-plane. Line t does not have a y-intercept. Which of the following equations couldrepresent a line parallel to line t?
Answers
when a graph doesn't have a y intercept it means that its y value is zero.
The constants in the equations are all intercepts. The only equation whose y is zero and has no constant ( intercept ) is x = 2
Thus, the solution to the question is x = 2 ( because y=o at this point and it has no constant )
Simplify -7(-5+3x)-4x
Answers
Solution:
Given:
[tex]-7(-5+3x)-4x[/tex]Expanding the bracket,
[tex]\begin{gathered} -7(-5+3x)-4x \\ (-7)(-5)+(-7)(3x)-4x \\ 35-21x-4x \end{gathered}[/tex]Simplifying further,
[tex]35-21x-4x=35-25x[/tex]Therefore, the solution is;
[tex]-7(-5+3x)-4x=35-25x[/tex]Which graph was created using a table of values calculated from the equation y=(2/5)^x+1
Answers
Usually, an important point to verify the graph is the point:
[tex](0,f(0))[/tex]It's when the function touches the y-graph, then, let's evaluate the function at x = 0
[tex]\begin{gathered} y=\left(\frac{2}{5}\right)^{x+1}\text{ , \lparen x =0\rparen} \\ \\ y=\left(\frac{2}{5}\right)^{0+1} \\ \\ y=\left(\frac{2}{5}\right)^1 \\ \\ y=\frac{2}{5}=0.4 \end{gathered}[/tex]Therefore the point should be
[tex](0,0.4)[/tex]Therefore any graph that does not include that point is not correct!
We can also eliminate all graph that shows a crescent curve, but, in fact, only the point we calculated can eliminate all graphs and gives us the correct answer:
What are 2 numbers that are exactly the same are said to be?
Answers
When two numbers are exactly the same, we say that they're equal. Is denoted by the sign '='
a/b = c/d is equivalent to b/a = d/c. in other words, if two fractions are in proportion, their _____ are also in proportion
Answers
If two fractions are in proportion, their inverse ratio are also in proportion.
Proportion:
Proportion means an equation in which two ratios are set equal to each other.
Given,
a/b = c/d is equivalent to b/a = d/c. in other words, if two fractions are in proportion, their _____ are also in proportion.
Here we need to fill the blank with the correct answer.
According to Invertendo Property,
For the four numbers a, b, c, d,
Consider if a : b = c : d, then b : a = d : c; which means
if two ratios are equal, then their inverse ratios are also equal.
It can be written as,
If a : b :: c : d then b : a :: d : c.
Then it can be written as,
=> a : b :: c : d
⟹ a/b= c/d
When take the inverse, then we get,
⟹ b/a= d/c
Which implies the following,
⟹ b : a :: d : c
Therefore, the answer is inverse ratio.
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