Answers
The measure of the hypotenuse n is 5√3
Hypotenuse
Hypotenuse refers the longest side of a right-angled triangle, the side opposite the right angle. And the length of the hypotenuse can be found using the Pythagorean theorem, which states that the square of the length of the hypotenuse equals the sum of the squares of the lengths of the other two sides.
Given,
Here we have the triangle with some measures on it.
Here we need to find the value of n.
While we looking into the diagram, we have identified that, n is the hypotenuse of the triangle,
So, the value of n is the root of the product of the two hypotenuse segments it touches:
=> n = √(5·15)
=> n = √75
It can be simplified as,
=> n = √(3 x 25)
=> n = 5√3
Therefore, the value of n is 5√3.
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Related Questions
Find z_1 x z_2 for z_1 = 9(cos225° + isin225°) and z_2 = 3(cos45° + isin45°).The 'z' is all subscript.
Answers
Using Euler's Formula:
[tex]re^{i\theta}=r(\cos (\theta)+i\sin (\theta))[/tex]Since:
[tex]\begin{gathered} z1=9(\cos (225)+i\sin (225)) \\ z2=3(\cos (45)+i\sin (45)) \\ \end{gathered}[/tex]We can rewrite them as:
[tex]\begin{gathered} z1=9e^{225i} \\ z2=3e^{45i} \end{gathered}[/tex]So:
[tex]\begin{gathered} z1\times z2=(9e^{225i})(3e^{45i})=27e^{225i+45i}=27e^{270i} \\ so\colon \\ z1\times z2=27(\cos (270)+i\sin (270)) \end{gathered}[/tex][tex]\begin{gathered} a=r\cos (\theta) \\ b=r\sin (\theta) \\ where \\ r=27 \\ \theta=270 \end{gathered}[/tex]So:
[tex]undefined[/tex]
b. A family of four went to see a live concert in Vancouver. Each family member bought
a commemorative concert T-shirt, which cost 1/5 of the price of a ticket. The total bill
for 4 tickets and 4 T-shirts was $384. How much did each ticket and each T-shirt cost?
Answers
The cost of 1 ticket is $80 and the cost of 1 T-Shirt is $16 .
In the question ,
it is given that ,
a family of four people went to see a live concert in Vancouver ,
and the price of T-shirt is 1/5 of the price of the ticket .
let the price of 1 ticket be = x ,
so , the price of 1 T-Shirt be = x/5 .
also given that the bill for 4 tickets and 4 T-Shirts was $384 ,
that means
4x + 4x/5 = 384
taking LCM as 20 and solving further ,
we get,
20x/5 + 4x/5 = 384
24x/5 = 384
24x = 384*5
24x = 1920
x = 1920/24
x = 80
the cost for T-Shirt = 80/5 = 16
Therefore , The cost of 1 ticket is $80 and the cost of 1 T-Shirt is $16 .
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Write the equation of the line in fully simplified slope-intercept form.
pls helpp me
Answers
Answer:
y= 1/5x -7
Step-by-step explanation:
1/5 is the slope
-7 is the y-intercept
help please, do working outs too i don’t understand it
Answers
1.) The line with the greatest slope.
The greater the slope of the line, the more upright it is. Observing the given graph, the line with the greatest slope is line a.
2.) Lines that are parallel.
Two lines are parallel if they do not have an intersection with each other at any point in the graph. We can see that line b and line d, do not intersect at any point in the graph and are thus parallel lines.
3.) Line with a negative slope
A line with a negative slope is a line that goes downwards from left to right, in the graph we can see that line e and line f goes downwards from left to right.
4.) Line that is perpendicular to the y-axis.
A line that is perpendicular to the y-axis, is a line that is parallel to the x-axis. Looking at the graph, line c is perpendicular to the y-axis.
119° 100° 88° 116° 11. Determine the value of x. A. 117° B. 59° C. 63° D. 90°
Answers
We have that the shape is a pentagon of sorts, and we will have that the sum of the internal angles of a pentagon equals 540°.
Knowing this, we will find the missing interior angle in the shape:
100° + 119° + 88° + 116° + a = 540°
Then, we will have that the missing side we named a, will have a measure of 117°.
Now, by supplementary angles, we will have the following:
117° + x = 180°
When we solve for x, we will have that is has a measure of 63°
***
You can determine the total sum of interior angles by the function:
[tex](n-2)\cdot180[/tex]Where n is the number of sides the shape has.
-2/3 (x-7) = 1/6 (x+1) -3
Answers
Answer: x = 9
Step-by-step explanation:
We will isolate the variable x to solve this equation.
Given:
-2/3 (x-7) = 1/6 (x+1) -3
Distribute:
-2/3x + 14/3 = 1/6 (x+1) -3
-2/3x + 14/3 = 1/6x + 1/6 -3
Combine like terms on the right side using subtraction:
-2/3x + 14/3 = 1/6x - 17/6
Subtract 1/6x from both sides of the equation:
-5/6x + 14/3 = - 17/6
Subtract 14/3 from both sides of the equation:
-5/6x = -15/2
Divide both sides of the equation by -5/6:
x = 9
Geometry! Just the first question:)
Answers
Hi your answers would be
a) 30 degrees
b) 65 degrees
c) 115 degrees
d) 85 degrees
e) 150 degrees
f) 30 degrees
Hope these answers help.
Answer:
5 round table pizza and amen and amen and amen and amen
Step-by-step explanation:
the program I think the banner side effects
What is the solution to the missing side of the figure, rounded to the nearest tenths place?A) 16.2.B.) √261C) 16.1D.) 261
Answers
The figure appears to be a triangle with the following measures:
Opposite Side = a = 6
Adjacent Side = b = 15
Hypotenuse = c = unknown
To be able to find the measure of the unknown side, since it appears to be a right triangle, we will be using the Pythagorean Formula:
[tex]\text{ c}^2=a^2+b^2[/tex][tex]\text{ c = }\sqrt[]{a^2+b^2}[/tex][tex]\begin{gathered} \text{ c = }\sqrt[]{(6)^2_{}+(15)^2} \\ \end{gathered}[/tex][tex]\text{ = }\sqrt[]{36\text{ + 225}}[/tex][tex]\text{ = }\sqrt[]{261}[/tex][tex]\text{ c = }\sqrt[]{261}\text{ = 16.1554944214}[/tex]Which situation could be represented by the graph
Answers
Answer:
what graph
Step-by-step explanation:
What is the value of x?
Answers
Answer:
75 degree
Step-by-step explanation:
We know that a straight angle is 180 degree
and in the picture we can see an angle of 105 degree
so we get 180-105= 75 degree
1. If Rocco makes 18 out of 25 free throws and Graham makes 14 out of 20 free throws, who has the better free
throw record? Show why using comparable rates.
Answers
write an equation in slope intercept form for the lines that passes through (-2,-8) and is parallel to y=-9x-81
Answers
The general form of an equation in slope intercept form is ;
y= mx + c where m is the gradient and c is the y-intercept
The equation given is : y = -9x-81 ------this means the slope is -9
This is determined from the general equation ;
y = m x + c
y= -9 x - 81
where -9 is the gradient
Because the two lines are parallel, it means the other equation should have a slope of -9, thus apply the formula for slope give point {-2,-8}
m= change in y-coordinates value / change in x coordinate values
-9 = y --8/x--2
-9 = y+8 /x+2
-9 {x+2} = y+8
A pack of cinnamon-scented pencils sells for $8.00. What is the sales tax rate if the total cost of the pencils Is $8.56 The sales tax rate is ___%
Answers
To find the tax rate we can use the rule of three.
[tex]\begin{gathered} 8\rightarrow100 \\ 8.56\rightarrow x \end{gathered}[/tex]Then,
[tex]x=\frac{8.56\cdot100}{8}=107[/tex]Now, since 8.56 dollars represents 107% of the prices, this means that the tax rate is 7.
Leah is buying titles for her bathroom. Each tile is 3/8 foot wide and covers an area that is 7/3 square feet. The bathroom floor is in the shape of a rectangle. She is putting 8 tiles along the longer wall of the bathroom and 5 tiles along the shorter wall of the bathroom. What is the perimeter of the bathroom? The bathroom and one tile are pictured below.
Answers
The perimeter of the rectangular floor is 103 feet.
What are rectangles?With four sides, four corners, and four right angles (90°), a rectangle is a closed 2-D object. A rectangle's opposing sides are equal and parallel.Since a rectangle is a two-dimensional form, it has two dimensions: length and width. The rectangle's length is its longer side, while its width is its shorter side.So, the perimeter of the bathroom floor will be:
First, let the length of the tiles be 'x'.Now,
7/3 = x × 3/8x = 7/3 ÷ 3/8x = 7/3 × 8/3x = 56/9So, the length of the tile is 56/9.
Now, the l and b of the rectangular floor will be:
56/9 × 8 + 3/8 × 5448/9 + 15/88(448) + 9(15)/723584 + 135/723719/7251.65Formula is: 2(l+b)
Now,
2 × 51.65103.3Rounding off: 103 feet
Therefore, the perimeter of the rectangular floor is 103 feet.
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For the point P(-24,-24) and Q(-19,-19), find the distance d(P,Q) and theof the midpoint M of the segment PQ,coordinates
Answers
Solution:
Given;
[tex]P(-24,-24),Q(-19,-19)[/tex]The distance d(P,Q) is;
[tex]\begin{gathered} d=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2} \\ \\ x_1=-24,y_1=-24,x_2=-19,y_2=-19 \\ \\ d=\sqrt{(-19-(-24))^2+(-19-(-24))^2} \\ \\ d=\sqrt{50} \\ \\ d=5\sqrt{2} \end{gathered}[/tex]Also, the midpoint, M, is;
[tex]\begin{gathered} M=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}) \\ \\ M=(\frac{-24+(-19)}{2},\frac{-24+(-19)}{2}) \\ \\ M=(-\frac{43}{2},-\frac{43}{2}) \end{gathered}[/tex]Voters in Arizona in 2020 passed Prop 207, legalizing the sale of recreational marijuana. At the time the industry estimated that the Arizona Department of Revenue would collect $135 million in taxes. In the first year, the state has generated approximately $200 million in tax revenue.State the absolute difference in the estimated amount of tax revenue generated and the actual amount received by the AZ Department of Revenue. Be sure to answer in a complete sentence.
Answers
The estimated amount of tax is 135 million
The actual amount received is 200 million
The difference means subtraction
Taking the absolution value means when we subtract, we find the positive value of the result
| estimated - actual |
| 135 million - 200 million |
| -65 million|
Taking the positive result
65 million
The absolute value of the difference in the estimate amount of the tax revenue generated and the actual amount received by the AZ department of Revenue is 65 million dollars.
Can someone please explain to me why -4² = -16?
Answers
Answer:
-4 x -4 = -16
4 x 4 = 16
^2 or to the power of 2 basely means 4 times itself, because 2.
I need help with this problems please I need a huge explanation
Answers
In this case we must apply the properties of supplementary angles and opposite angles.
1 .
opposite angles
∠ 1 = 120 °
supplementary angles
∠ 1 + ∠ 2 = 180
120 + ∠ 2 = 180
∠ 2 = 180 - 120
∠ 2 = 60 °
The same properties can be applied in the other exercises to solve them.
The solution is:
∠ 1 = 120 °
∠ 2 = 60 °
Suppose a 95% confidence interval for the average amount of weight loss on a diet program for males is between 13. 4 and 18. 3 pounds. These results were based on a sample of 42 male participants who were deemed to be overweight at the start of the 4-month study. What is the standard error of the sample mean?.
Answers
The standard error of the sample mean is 1.213
How to calculate the standard error of the sample mean?
Given,
c = 95% = 0.95
n = 42
lower limit = 13.4
upper limit = 18.3
Since standard deviation population is unknown, we use this formula to calculate standard error.
standard error = margin of error / [tex]t_{\alpha/2,d.f.}[/tex]
First, we calculate the t distribution value
[tex]t_{\alpha/2,d.f.}[/tex] = [tex]t_{(1-c)/2,n-1}[/tex]
= [tex]t_{(1-0.95)/2,42-1}[/tex]
= [tex]t_{0.025,41}[/tex]
To find the value use t table. So, [tex]t_{0.025,41}[/tex] = 2.0195
Next, we calculate the margin of error
margin of error = (upper limit - lower limit)/2
= (18.3 - 13.4)/2
= 4.9/2
= 2.45
Now, we can calculate the standard error. So,
standard error = 2.45 / 2.0195
= 1.213
Thus, the standard error of the sample mean is 1.213
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The number of infected
zombies triples every
hour. How many
zombies are there after 6
hours if one zombie was
initially infected?
Answers
Answer:
f(x) = 4(1.15)6.
Step-by-step explanation:
84 points + brainliest if well explained and correct:
During a thunderstorm at a sports event, a detector goes off to let participants know there is lightning in the area so people can seek shelter. The accuracy of the lightning detector is summarized in the table.
Lightning detector activates Lightning detector does not activate Row Totals
Lightning in area 88% 2% 90%
No lightning in area 7% 3% 10%
Column Totals 95% 5% 100%
What is the ratio of false positives to false negatives in this scenario? Round your answer to one decimal place.
0.1
1.5
2.3
3.5
Answers
The ratio of false positives to false negatives is (d) 3.5
How to determine the ratio?The table of values is given as
Activates. Does not activate Row Totals
Lightning in area 88% 2% 90%
No lightning in area 7% 3% 10%
Column Totals 95% 5% 100%
The false negative is when there is lighting and it does not activate
So, we have
False negative = 2%
The false positive is when there is no lighting and it activates
So, we have
False positive = 7%
When represented as ratio, we have
Ratio = 7% : 2%
So, we have
Ratio = 7 : 2
This gives
Ratio = 7/2
Evaluate
Ratio = 3.5
Hence, the ratio is (d) 3.5
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Which of the following terms is defined as a set of all points in a planethat are a given distance from a point?O CircleO Line segmentO RayO Parallel line
Answers
Given:
A set of all points in a plane that are a given distance from a point.
Required:
To choose the correct option for the given definition.
Explanation:
A circle is the set of all points in a plane that are equidistant from a given point called the center of the circle.
Final Answer:
A set of all points in a plane that are a given distance from a point is called circle.
The measures of two complementary angles are described by the expressions (11x−11)° and (16x−7)°. Find the measures of the angles.I know complementary when their measures add to 90 degrees. but I'm not to sure where to plug the numbers in
Answers
Given:
[tex](11x-11)^{\circ}and(16x-7)^{\circ}\text{ forms an complementary angles.}[/tex][tex]\begin{gathered} 11x-11+16x-7=90 \\ 27x-18=90 \\ 27x=90+18 \\ 27x=108 \\ x=\frac{108}{27} \\ x=4 \end{gathered}[/tex]This table gives a few (x,y) pairs of a line in the coordinate plane.
x y
40 -30
61 -45
74 -60
What is the x-intercept of the line?
( , )
its on khan academy
Answers
The x-intercept of the line is found to be -38 from the given table data using the slope-point form.
What exactly is the slope-point form?The equation of a straight line that is inclined at a specific angle to the x-axis and passes through a specific point may be found using the slope-point form. Only when the line's slope and a particular point are known can the point slope formula be applied. The slope-point form's equation is as follows: y - y₁ = m(x - x₁)Take a look at any two points, such as (40, -30), and (61, -45).
The line connecting them must have the following slope:
(y₂ - y₁)/(x₂ - x₁) = (-45 -(- 30))/(61 - 40) = -15/21.
Since they are on the same line, any combination of (48,30) and (74,60) will have the same answer.
The slope-point form is given as follows:
y - y₁ = m(x - x₁)
y -(- 30) = (-15/21) (x - 40)
21(y + 30) = -15(x - 40)
-15x + 21y = 570
Now, we can convert the above equation in intercept form to find x-intercept.
The intercept form is given as:
x/a + y/b = 1, where a and b are x and y intercepts.
-15x + 21y = 570
Dividing by 570 we get,
(-15x)/570 + (21y/570) = 1
x/-38 + y/27 = 1
Compare this to x/a + y/b = 1, where a and b are the x and y intercepts, respectively.
In this case, the x intercept is -38.
Therefore, the x-intercept of the line is found to be -38 from the given table data.
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The difference of a number and 6 is the same as 5 times the sum of the number and 2. What is the number?A 4B. -2C -1D. 1
Answers
You need to know the following:
1. The "difference" is the result of a subtraction.
2. The word "times" indicates a multiplication.
3. The sum is the result of an addition.
Let be "n" the number mentioned in the exercise.
Knowing the explained above, you know that "the difference of a number and 6" can expressed as:
[tex]n-6[/tex]And "5 times the sum of the number and 2" can be expressed as:
[tex]5(n+2)[/tex]Therefore, "the difference of a number and 6 is the same as 5 times the sum of the number and 2" can be written as the following equation:
[tex]n-6=5(n+2)[/tex]Now, in order to find the number, you must solve for "n":
[tex]undefined[/tex]14. You buy a package that contains 10 1/2 cups of fruit and nut mix. How many snack bags each with 3/4 cup of fruit and nut mix can you fill from the package?
Answers
Given:
The package contains 10 1/2 cups of fruit and nut mix
When need to snack bags, each bag contain 3/4 cup
So, to find the number of bags, divide 10 1/2 by 3/4
so, the number of bags =
[tex]10\frac{1}{2}\div\frac{3}{4}=\frac{21}{2}\div\frac{3}{4}=\frac{21}{2}\cdot\frac{4}{3}=7\cdot2=14[/tex]So, the answer is: the number of bags = 14
3.152 written as an improper fraction or a mixed number and explained how it was done.
Answers
Answer: 3.152 as an improper fraction would be: 394 / 125
Step-by-step explanation: You can take any number, such as 3.152, and write a 1 as the denominator to make it a fraction and keep the same value, like this:
3.152 / 1
To get rid of the decimal point in the numerator, we count the numbers after the decimal in 3.152, and multiply the numerator and denominator by 10 if it is 1 number, 100 if it is 2 numbers, 1000 if it is 3 numbers, and so on.
Therefore, in this case we multiply the numerator and denominator by 1000 to get the following fraction:
3152 / 1000
Then, we need to divide the numerator and denominator by the greatest common divisor (GCD) to simplify the fraction.
The GCD of 3152 and 1000 is 8. When we divide the numerator and denominator by 8, we get the following:
394 / 125
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3. The equation 11a +8s = 4752 represents the ticket sales at last night's football game for a
adult tickets and s student tickets.
a. How much money was collected in total from all ticket sales?
b. What is the price of an adult ticket? What is the price of a student ticket?
c. If the ticket booth sold only adult tickets, how many would they have sold?
d. If the ticket booth sold only student tickets, how many would they have sold?
Answers
Step-by-step explanation:
The equation 11a +8s = 4752 represents the ticket sales at last night's football game for a adult tickets and s student tickets.
a. How much money was collected in total from all ticket sales? $4,752
________________________
b. What is the price of an adult ticket? $11 What is the price of a student ticket? $8
________________________
c. If the ticket booth sold only adult tickets, how many would they have sold?
if only adults:
11a = 4752
a = 432 tickets
________________________
d. If the ticket booth sold only student tickets, how many would they have sold?
if only students:
8a = 4752
a = 594 tickets
-. Write an equation in slope-intercept form that
describes the line through the points (2,7) and
(-1,-5).
Answers
The slope-intercept form equation of the line is y=(-2/3)x-(17/3) when the line is passing through the points (2,7) and (-1,-5).
What is meant by slope?Finding the ratio of vertical change to horizontal change between any two distinct points on a line yields the slope. Occasionally, the ratio is written as a quotient, which produces the same number for every two distinct points on the same line. A negative rise refers to a diminishing line. The line could be functional, set by a road surveyor, or depicted in a diagram that represents a road or a roof as a description or a plan.
The absolute value of the slope is used to determine how steep, incline, or grade a line is. The steeper the line, the larger the absolute magnitude of the slope.
The slope-intercept form is y=mx+c
Given points are (2,7) and (-1,-5)
Slope m= (y₂-y₁)/(x₂-x₁)
m=(-5+7)/(-1-2)
m=-2/3
By substituting m value in the above equation we get,
y=(-2/3)x + c
Given that, the above equation is passing through the point (-1,-5)
-5=(-2/3)(-1)+c
c=-5-(2/3)
c=-17/3
y=(-2/3)x-(17/3)
Therefore, the equation of the slope-intercept form is y=(-2/3)x-(17/3)
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12)50 students took a quiz with five questions. The frequency table below shows the results of the quiz. Use the frequency table to answer the following questions. ValueFrequencyRelative FrequencyCumulative Frequency040.084180.1612260.1218320.04204150.3355150.350a)How many students answered exactly 3 questions correctly?Number of students answered exactly three questions = 2b)How many students answered less than 3 questions correctly?c)What proportion (percent) of students answered exactly 4 questions correctly?
Answers
From the table, we have:
• The first column (Value),: indicates the # of correct answers,
,• The second column (Frequency),: indicates the # of students that answer the # of correct answers to the left in the table,
,• The third column (Relative Frequency),: indicates the proportion of the # of students to the total,
,• The fourth column (Cumulative Frequency),: gives the sum of the previous frequencies up to that row.
Using these data, we answer the questions:
a) Looking at the column Frequency for Value = 3, we find that 2 students answered exactly 3 answers correct.
b) Looking at the column Cumulative Frequency for Value = 2 (the previous value to 3), we find that 18 students answered less than 3 questions correctly.
c) Looking at the column Relative Frequency for Value = 4, we find that 0.3 = 0.3 * 100% = 30% of the students answered exactly 4 questions correctly.
Answera) 2
b) 18
c) 30%