Find the measurement of each deferment. assume that each figure is not drawn to scale
Answers
From the present figure, we can conclude that the distance from W to Y must be equal the sum of the distance from W to X with the disctance from X to Y, because it is a straight line. From this, we can write a math relation as follows:
[tex]WY=WX+XY[/tex]We know the distance from X to Y (XY) and from W to Y (WY). Substituting these values into the relation we have, we cansolve it as follows:
[tex]\begin{gathered} 100\operatorname{cm}=WX+89.6\operatorname{cm} \\ WY=100\operatorname{cm}-89,6\operatorname{cm} \\ \\ WY=10.4\operatorname{cm} \end{gathered}[/tex]From the above solution, we conclude that the correct answer is the second option: 10.4 cm
Related Questions
Find the sample variance and standard deviation 5, 57, 10, 51, 34, 24, 29, 28, ,29 , 31
Answers
SOLUTION
Write out the data given, we have
[tex]5,57,10,51,34,24,29,28,29,31[/tex]Write out the formula
[tex]\begin{gathered} \\ s^2=\frac{\sum_{i=1}^n\left(x_i-\bar{x}\right)^2}{n-1} \\ \text{Where } \\ s^2=\text{varaince} \\ n=10,\bar{x}=\operatorname{mean}=29.8 \end{gathered}[/tex]Hence
[tex]\text{sum of squares=}2253.6[/tex]Hence, Sample variance will be
[tex]s^2=\frac{ss}{n-1}=\frac{2253.6}{10-1}=\frac{2252.6}{9}=250.4[/tex]The sample variance is 250. 4
The standard deviation is the square root of the variance
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17374474747477484×92929292
Answers
EXPLANATION:
ANSWER:
17374474747477484x 92929292=1.61x10^24
IMPORTANT NOTE ;
To solve long multiplications there are two methods vertically and horizontally, the answers will always be significantly long, so we must know how to round significant figures.
What is the value of the expression below when x = 2? 2x + 6
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The equation is:
[tex]2x+6[/tex]If x = 2 then then we replace the value of x
[tex]\begin{gathered} 2(2)+6 \\ 4+6 \\ 10 \end{gathered}[/tex]A square red placement has a gold square in the center. The side length of the gold square is (x+2) inches and the width of the red region is 4 inches. What is the area of the red part of the placement?
Answers
A square red placement has a gold square in the center.
The side length of the gold square = (x+2) inches
and the width = 4 inches
Thus the area if the red part of the placement is the product od width and the dimension of square
[tex]\begin{gathered} (x+2)^2-4^2 \\ x^2+4+4x-16 \\ x^2+4x-12 \end{gathered}[/tex]Area of the p;ace is x^2+4x-12
Simplify the rational expression below. When typing your numerator and denominators be sure to but the term with the variable first and do not put spaces between your characters. \frac{\left(12n^2-29n-8\right)}{\left(28n^2-5n-3\right)} The numerator is AnswerThe denominator is Answer
Answers
Given the rational expression below:
[tex]\frac{12n^2-29n-8}{28n^2-5n-3}[/tex]The simplification is as shown below:
[tex]\begin{gathered} \frac{12n^2-29n-8}{28n^2-5n-3}=\frac{12n^2-32n+3n-8}{28n^2-12n+7n-3} \\ \frac{12n^2-32n+3n-8}{28n^2-12n+7n-3}=\frac{4n(3n-8)+1(3n-8)}{4n(7n-3)+1(7n-3)} \\ \frac{4n(3n-8)+1(3n-8)}{4n(7n-3)+1(7n-3)}=\frac{(3n-8)(4n+1)}{(7n-3)(4n+1)} \end{gathered}[/tex]It can be observed from the simplification that (4n+1) is common to both the numerator and denominator. To simplify further we will cross (4n+1) out in the numerator and denominator as shown below:
[tex]\begin{gathered} \frac{(3n-8)(4n+1)}{(7n-3)(4n+1)}=\frac{3n-8}{7n-3} \\ Hence,\frac{12n^2-29n-8}{28n^2-5n-3}=\frac{3n-8}{7n-3} \end{gathered}[/tex]Hence, after the simplification,
the numerator is 3n - 8, and
The denominator is 7n - 3
[tex] \frac{x}{3} \times \frac{x}{7 } = \frac{5}{3} [/tex]solve for x please
Answers
Answer:
x=
x=5.92 or -5.92
Explanation:
Given the equation:
[tex]\frac{x}{3}\times\frac{x}{7}=\frac{5}{3}[/tex]Combine the fractions on the left-hand side by multiplying:
[tex]\implies\frac{x^2}{21}=\frac{5}{3}[/tex]Next, multiply both sides by 21:
[tex]\begin{gathered} \frac{x^2}{21}\times21=\frac{5}{3}\times21 \\ \implies x^2=35 \end{gathered}[/tex]Finally, find the square root of both sides:
[tex]\begin{gathered} \sqrt{x^2}=\pm\sqrt{35} \\ x=\pm\sqrt[]{35} \\ x=\sqrt[]{35}\text{ or x=-}\sqrt[]{35} \\ x\approx5.92\text{ or }-5.92 \end{gathered}[/tex]The area of a rectangle can be represented by the expression 4x^2+8x+9 If the area of the rectangle is 69 square inches, what is the value of x, the width of the rectangle, in inches?
Answers
Explanation
[tex]A=4x^2+8x+9[/tex]Step 1
Let
A=96 (square inches)
so,replacing
[tex]\begin{gathered} A=4x^2+8x+9 \\ 69=4x^2+8x+9 \\ \text{now, to set the equation equal to zero subtract 69 in both sides} \\ 69-69=4x^2+8x+9-69 \\ 0=4x^2+8x-60\Rightarrow equation\text{ (1)} \end{gathered}[/tex]Step 2
now, we need to solve the quadratic equation,we can use the quadratic formula
[tex]\begin{gathered} 4x^2+8x-60=0\Rightarrow ax^2+bx+c \\ thus \\ a=4 \\ b=8 \\ c=-60 \\ x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ \text{replace} \\ x=\frac{-8\pm\sqrt[]{8^2-4(4)(-60)}}{2(4)} \\ x=\frac{-8\pm\sqrt[]{1021}}{8} \\ x=\frac{-8\pm32}{8} \end{gathered}[/tex]therefore, the solutions are
[tex]\begin{gathered} x=\frac{-8\pm32}{8} \\ x_1=\frac{-8+32}{8}=\frac{24}{8}=3 \\ x_2=\frac{-8-32}{8}=\frac{-40}{8}=-5 \end{gathered}[/tex]as we are looking for a distance, the ONLY valid answer must be positive
so, the answer is
x=3
I hope this helps you
x
Hi, can you help me to solve this exercise, please !
Answers
We have to find the length of AC.
As we have a right triangle of which we know the length of the hypotenuse and one angle measure, we can use a trigonometric ratio to find AC:
[tex]\begin{gathered} \sin (B)=\frac{\text{Opposite}}{\text{Hypotenuse}}=\frac{AC}{BC} \\ AC=BC\cdot\sin (B) \\ AC=18\cdot\sin (30\degree) \\ AC=18\cdot\frac{1}{2} \\ AC=9 \end{gathered}[/tex]Answer: AC = 9
#2). A train averaging 50mph leaves San Francisco at 1pm for Los Angeles 440 miles away. At the same time a second train leaves Los Angeles headed for San Francisco on the same track and traveling at an average rate of 60 mph. At what time does the accident occur?
Answers
Identify the pair ofexpressions belowthat are equivalent.7x + 1lyA and1ly + 7xB3x + 3yand 6xy12x – Yc) and6(2x - y)7 + 7 + 7
Answers
Pair A:
[tex]7x+11y,11y+7x[/tex]Remember that characteristic of the numbers is that, in general:
[tex]a+b=b+a[/tex]For any numbers a and b, this is always true. So, in our case:
[tex]\begin{cases}a=7x \\ b=11y\end{cases}\Rightarrow7x+11y=11y+7x[/tex]So the pair A is equivalent
As for pair B:
We are going to it by contradiction: if we suppose that the two equations are the same (one is equal to the other) and we found a pair of numbers (x,y) that produce a contradiction, then the two equations cannot be equivalent. Let me show you:
Suppose pair B is equivalent, then:
[tex]3x+3y=6xy[/tex]Now, suppose that x=0 and y=1, then:
[tex]3(0)+3(1)=6(0)(1)\Rightarrow3=0!![/tex]And of course, 3 is not equal to 0!
So, by supposing that the 2 equations are equivalent we reach a false implication, which means that the pair is NOT equivalent
As for pair C:
We can expand the expression 6(2x-y):
[tex]6(2x-y)=6(2x)-6(y)=12x-6y[/tex]Which is exactly the first expression! So the pair is equivalent!
A particular country has 55 total states. If the areas of 35 states are added and the sum is divided by 35, the result is 191,374 square kilometers. Determine whetherthis result is a statistic or a parameter.Choose the correct answer below.O A. The result is a statistic because it describes some characteristic of a sample.B. The result is a parameter because it describes some characteristic of a sample.OC. The result is a parameter because it describes some characteristic of a population.D. The result is a statistic because it describes some characteristic of a population.
Answers
Lets reminde the differences between parameter and statitics:
A parameter is a number describing a whole population (e.g., population mean), while a statistic is a number describing a sample (e.g., sample mean).
In our case, we took a sample of 35 states and fond the average area of each state, so this number describe our sample of 35 states, so is a "statistic".
Find fractional notation. Simplify 450%
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
450%
fractional notation = ?
Step 02:
fractional notation:
450% = 450 / 100 = 45 /10
The answer is:
The fractional notation is 45 /10
what's 2 + 2 1 take away 3 divided by 5 * 2
Answers
2+21 = 23
we are ask to take away 3, this implies we are to subtract 3 from 23
That is;
23 - 3 = 20
Then we are to divide by 5 x2
5 x2 = 10
20 ÷ 10 = 2
Hence;
2 + 2 1 take away 3 divided by 5 * 2 =
If the xy- plane The graph of the equation (x-6)^2+ (y+5^2)= 16 is a circle. point p is on the circle and has coordinates (10, -5). If PQ is a diameter of the circle, what are the coordinates of Q?
Answers
(x - 6)² + (y + 5)² = 16 is a circle centered at (6, -5) with a radius of 4 units.
The point P(10, -5) has the same y-coordinate as the center of the circle and it is placed 4 units to the right of it.
Then, the point Q must have the same y-coordinate and must be placed 4 units to the left of the center, therefore its x-coordinate is 6 - 4 = 2. In consequence, point Q is placed at (2, -5), as can be seen in the next graph:
Which of the following piecewise functions best describes the graph below ?The answer
Answers
To answer this question, we need to be careful with the domain (x values) and the slope of the lines.
From left to right we have the following functions:
For values less than or equal to -3, we have a line with a positive slope. We have two lines, y = x - 2, and y = x - 3.
If we make:
x = -3, and y = -5, then we have:
1. For y = x - 2
[tex]-5=-3-2\Rightarrow-5=-5[/tex]2. For y = x - 3
[tex]-5=-3-3\Rightarrow-5\ne-6[/tex]Then, we have that the second option is a possible candidate to solve the question.
We can also see that the first option is not an option since the domain is given for x less than -3 (and the graph is for x less or equal to -3 - see the solid circle of the line).
We also have that for the interval from x greater than -3 and less or equal to 5, the value for the function is equal to 8.
We also have that the line has a negative slope for values greater than 6, and the given equation is y = -x + 10.
Therefore, the answer to this question is the second option:
[tex]undefined[/tex]Solve for < ABC. First you will have to find the value of x
Answers
We know that the sum of the angles is 360 degrees:
[tex]80+90+40+x+x-10=360[/tex]Now, we solve for x
[tex]\begin{gathered} 2x+200=360 \\ 2x=160 \\ x=80 \end{gathered}[/tex]describe the lines of symmetry in the word kid if there is one
Answers
The line of symmetry divides a shape into 2 equal halves. The line of symmetry can be describe as an imaginary line that passes through the center of a figure and create a mirror image of the figure. An example of a line of symmetry is a line dividing a shape into two equal halves .
The imaginary line is the green line and it divide the square into 2 equal halves . Therefore, the word kid has no line of symmetrry
Springfield, and Capital City form a right triangle. The distance between Centerville and Springfield is 913 kilometers and the distance between Springfield and Capital City is 976 kilometers. View the map.What is the direct distance between Centerville and Capital City? Round to the nearest kilometer.
Answers
To the nearset kilometer, the distance between Centerville and Capital City is 1,336 km
Here, we want to find the distance between Centerville and Capital city
From what we have in the diagram, we can see a right-angled triangle
Thus, we can use Pythagoras' theorem here
It states that the square of the hypotenuse equals the sum of the squares of the two other sides
The distance between Centerville and Capital city is the hypotenuse as it is the side that faces the right-angle
Let us call the distance h
Thus, according to Pythagoras' theorem, we have it that;
[tex]\begin{gathered} h^2=913^2+976^2 \\ h^2\text{ = 833,569+952,576} \\ h^2=\text{ 1,786,145} \\ h\text{ = }\sqrt[]{1,786,145} \\ h\text{ = 1,336.47 } \end{gathered}[/tex]the table above gives the annual ales (in billions of dollars) of Pepsico, which operates two major businesses: beverages (including Pepsi) and snack foods. The table shows Pepsico ales in billions of dollars for the 11 years.A) What was the change of annual ales between the first year, 2010, and the 2015 year?B) What is the average rate of change in sales for the 2015 years beginning in 2010?billion dollars per year
Answers
Answer:
A) 5.92 billion dollars
B) 1.184 billion dollars per year
Explanation:
Part A)
The change in annual sales between 2010 and 2015 is calculated as the difference between the sales of 2015 and 2010. So, taking into account the table, we get:
59.42 - 53.5 = 5.92 billions of dollars
Because 59.42 billion are sales in 2015 and 53.5 billion are sales in 2010.
Therefore, the answer is 5.92 billion dollars
Part B)
The average rate of changes in sales from 2010 to 2015 is equal to the change in the annual sales divided by the number of years, so it is calculated as
[tex]\frac{59.42-53.5}{2015-2010}=\frac{5.92}{5}=1.184[/tex]Therefore, the average rate of change is 1.184 billion dollars per year.
I need help with 14 I need answer and a explanation
Answers
Step 1
Like terms in an expression are terms that are exactly alike. Either they are constants(for example 8), variables( for example x ) or a combination of variables and constants ( for example 3x)
Step 2
Draw a conclusion from step 1
The given expression is 3x + 8 + 8x
The like terms here are therefore 3x and 8x because they are alike, consisting of a variable and a coefficient or constant.
Use synthetic division to determine whether the first expression is a factor of the second X-2, 4x^3-3x^2-4x+12(X-2)(__)
Answers
The expression is given as,
[tex]4x^3-3x^2-4x\text{ + 12}[/tex]The given factor is ( x - 2 ) .
Applying the synthetic division method ,
As the remainder is not zero in the last column .
Therefore ( x - 2 ) is not a factor of the given expression .
find the domain of g(x)= x/x^2-49.answer in interval notation
Answers
Explanation
Given
[tex]g(x)=\frac{x}{x^2-49}[/tex]The domain of the function is the set of x values that will make the function defined. This is given below.
Using the denominator, we will find the point of singularity.
[tex]\begin{gathered} x^2-49=0 \\ x^2=49 \\ x=7,x=-7 \end{gathered}[/tex]Therefore, the points of singularities are 7 and -7. Hence we will exclude those points from the set of real numbers.
Answer:
[tex](-\infty-7)\cup(-7,7)\cup(7,\infty)[/tex]-/2 Points]DETAILS OSELEMALG1 1.4.328.Translate to an algebraic expression, but do not simplify.the product of -18 and the difference of c and d
Answers
Answer:
[tex]\begin{gathered} -18(c-d) \\ =\text{ 18d-18c} \end{gathered}[/tex]Explanation:
Here, we want to translate the given statement into an algebraic expression
The product of -18 and the difference between c and d
The difference between c and d will be:
[tex]c-d[/tex]Then, we multiply -18 with this. That would give:
[tex]-18(c-d)[/tex]Simplifying the above, we have:
[tex]-18c\text{ + 18d = 18d-18c}[/tex]the measure of angle is 16 what is the measure of a complementary angle
Answers
Two angles are called complementary when their measures add to 90 degrees
Let the two angles are x and y
[tex]x\text{ + y =90}[/tex]one angle is given , x = 16
substitute the value of x=16 and solve for y
[tex]\begin{gathered} x+y=90 \\ 16+y=90_{} \\ y=90-16 \\ y=74 \end{gathered}[/tex]So, the measure of another angle is 74 degree which makes angle 16 to complementary angles
Answer : Measure of complementary angle = 74 degree
3) By how many zeros do the following numbers end:a) 7^2 × 2^4 × 5^4 b) 3^5 × 2^7 × 11^2 × 5^6
Answers
SOLUTION
(3). (a) We want to find the number of zeros the number
72 × 24 × 54 end.
To do this, what we have to do is count how many times did 2 and 5 occurred in the question as factor. Number of zeros is equal to the one (2 or 5) which occurred less times.
From7^2 × 2^4 × 5^4, we have
[tex]\begin{gathered} 7^2\text{ there are no 5's or 2's} \\ 2^4,\text{ there are four 2's} \\ 5^4,\text{ there are four 5's } \\ Altogether,\text{ we have four 2's and four 5's} \\ So,\text{ since the number of 2's and 5's are equal, we choose one} \end{gathered}[/tex]Hence the answer is 4 zeros
(b) 3^5 × 2^7 × 11^2 × 5^6
[tex]\begin{gathered} 3^5,\text{ there are no 2's or 5's } \\ 2^7,\text{ there are seven 2's} \\ 11^2,\text{ there are no 2's or 5's} \\ 5^6,\text{ there are six 5's} \\ Making\text{ a total of seven 2's and six 5's. So we go for the lesser} \\ which\text{ is six 5's } \end{gathered}[/tex]Hence the answer is 6 zeros
The pair of equations 3x + y + 4 = 0 and -3x - 6y + 1 = have * A unique solution*exactly two solutions*infinitely many solutions*no solutions
Answers
Given:
3x + y + 4 = 0
-3x - 6y + 1 = 0
Required:
To calculate which option is correct
Explanation:
The given equations are
3x + y + 4 = 0
3x - 6y + 1 = 0
a1=3; b1=1 ; c1=4
a2=-3;b2=-6 ; c2=1
[tex]\frac{a1}{a2}=\frac{3}{-3}=-1[/tex][tex]\frac{b1}{b2}=\frac{1}{-6}=-\frac{1}{6}[/tex][tex]\frac{c1}{c2}=\frac{4}{1}=4[/tex][tex]\frac{a1}{a2}\ne\frac{b1}{b2}\ne\frac{c1}{c2}[/tex]which means it is A unique solution
Required answer:
Option A
If a figure has been dilated by a scale factor of one third, which transformation could be used to prove the figures are similar using the AA similarity postulate?
Answers
SOLUTION:
If a figure has been dilated by a scale factor of one third, the transformation that could be used to prove the figures are similar using the AA similarity postulate is;
Answer:
A translation because it can map one angle onto another since dilations preserve angle measures of triangles.
Step-by-step explanation:
I believe this is the answer
Find the probability of z occurring in the indicated region of the standard normal distribution.P(0
Answers
To find the probability:
[tex]P(0we need to remember that:[tex]P(0No we need to find each of the probabilities in a standard table, then we have:[tex]\begin{gathered} P(0Therefore:[tex]P(0graph the line passing through -1 and -5 whose slope is m equals 1/5
Answers
Expanation:
FIrst we have to locate point (-1, -5) in the coordinate plane (in red).
Then we have to use the slope to find another point from there. The slope is:
[tex]m=\frac{\Delta y}{\Delta x}[/tex]If the slope is 1/5 it means that we have to move 5 units to the right (in orange) from the point and then 1 unit up (in light blue). That's the second point (in dark green). Now we just have to draw a line passing through those two points:
Answer:
The graph of the line is:
find x to the nearest 100th if sin x = 7/8
Answers
Answer:
x = 61.04°
Explanation:
Given:
[tex]\sin x=\frac{7}{8}[/tex]Take the arcsin of both sides of the equation.
[tex]\begin{gathered} \arcsin(\sin x)=\arcsin(\frac{7}{8}) \\ \implies x=61.04\degree \end{gathered}[/tex]The value of x is 61.04° to the nearest 100th.