Answer:
7
Step-by-step explanation:
8+3³/12-7
8+27/5
35/5
7
How far is a chord of length 8 cm from the centre of a circle of radius 5 cm
Answer:
3 cm
Step-by-step explanation:
A line from the centre of the circle at right angles to the chord is a perpendicular bisector.
Thus a right triangle is formed with legs d , the line from centre to chord and 4 , half the length of the chord. The radius 5 is the hypotenuse.
Using Pythagoras' identity in the right triangle.
4² + d² = 5², that is
16 + d² = 25 ( subtract 16 from both sides )
d² = 9 ( take the square root of both sides )
d = [tex]\sqrt{9}[/tex] = 3
Thus the chord is 3 cm from the centre of the circle.
OB = 3 cm
Step-by-step explanation:AO = radius = 5 cm
AB = 8cm/2 = 4 cm
Pythagora
OB² = AO² - AB²
= (5cm)² - (4cm)²
= 25cm² - 16cm²
= 9 cm²
OB = √9cm²
= 3 cm
Find the midpoint of the segment with the given endpoints.
(10,5) and (-2, -10)
Answer:
The answer is
[tex] (4, - \frac{ 5}{2} )[/tex]Step-by-step explanation:
The midpoint M of two given points is given by
[tex]M = ( \frac{x1 + x2}{2} , \: \frac{y1 + y2}{2} )[/tex]where
(x1 , y1) and (x2 , y2) are the points
From the question the points are
(10,5) and (-2, -10)
The midpoint of points is
[tex]M = (\frac{10 - 2}{2} , \frac{5 - 10}{2} ) \\ = ( \frac{8}{2} , - \frac{5}{2} )[/tex]We have the final answer as
[tex]M = (4, - \frac{ 5}{2} )[/tex]Hope this helps you
Carl, Caitlyn, and Daryl are comparing their ages. Carl is two years older than Caitlyn. Daryl is five years older than Carl. The product of Carl and Daryl's ages is at least 160. If x represents Caitlyn's age, which inequality represents this situation?
Answer:
Step-by-step explanation:
If x represents Caitlyn's age, then can be used to represent Carl's age, and can be used to represent Daryl's age.
The product of Caitlyn and Daryl's ages is at least 160. Use this information to set up an inequality to represent this situation.
The answer is x squared +9x+14 is greater than or equal to 160.
The inequality that represents the given situation where x is the age of Caitlyn will be (X+2) (x+7) ≥ 160.
The inequality equation is a representation of the relation between two or more expressions that are not equal, not equal to, less than, or greater than.
Represented by:
greater than as >less than as <not equal to as ≠at least or, either equal or greater than as ≥Solution:
It is given that,
Caitlyn's age = x,
Carl's is two years older than Caitlyn, therefore,
Carl's age = x + 2
And, Daryl is 5 years older than Carl, therefore,
Daryl's age = Carl's age + 5
= (x + 2) + 5
= x + 7
The last condition is that the product of Carl and Daryl's age is at least 160, at least is represented as ≥ which mean that value either equal or greater than.
Therefore, the inequality would be (x+2) (x+7) ≥ 160
Learn more about inequality:
https://brainly.com/question/16826399
Hector is flying a kite. He has let out 86 feet of string and is holding it 4 feet off the ground. If the string is at an angle of elevation of 42°15'30", how high is the kite?
Answer:
h = 61.83 feet
Step-by-step explanation:
length of string from Hector to kite = c = 86 feet.
and 4 feet off the ground.
angle A = 42° 15' 30"
req'd: how high is the kite?
angle A = 42° + 15' (1° / 60') + 30"(1° / 3600'')
angle A = 42.26
to get the side a (height of kite) 4 feet above ground: use Sin(A) = opp / hyp
Sin(A) = a / c
Sin(42.26) = a / 86
a = Sin(42.26) * 86
a = 57.83 feet
therefore, the height of the kite from the ground = h = 57.83 + 4
h = 61.83 feet
simplify the expression 10(7+7g)+4
Answer:
70g+74
Step-by-step explanation:
Answer:
= 70g + 74
Step-by-step explanation:
10 (7 + 7g) + 4
= 10(7g + 7) + 4
= 70 + 70g + 4
= 70g + 74
Find the smallest positive integer x which is greater than 1 and relatively prime to 120 (recall that relatively prime means that the GCD of x and 120 is 1)
Answer: 7
Explanation:
List out the factors of 120 until we hit a gap
1,2,3,4,5,6,8
Note that 7 is not shown above. We can see that 120/7 = 17.14 approximately meaning that 7 doesn't go evenly into 120. So this is why 7 isn't a factor. Something like 3 is a factor because 120/3 = 40 is a whole number result.
Also, 7 is prime. The only factors of 7 are 1 and itself. This means that 7 and 120 do not have any common factors other than 1. The GCF of 7 and 120 is 1, leading to the two numbers being relatively prime
Side note: The term "coprime" is sometimes used in place of "relatively prime"
Solve your equation from the first problem and pick the BEST interpretation for the solution. a \large h\approx2.9; The solution shows that it will take about three more hours to fill the pool. b \large h\approx1.8, The solution show that it will take two more hours to fill the pool. c \large h\approx2.9; The solution shows that it will take about 2 more hours to fill the pool. d \large h\approx4.2, The solution shows that it will take 4 more hours to fill the pool.
Answer:
The correct option is (a).
Step-by-step explanation:
The complete question is:
A hose can fill a swimming pool in 6 hours. Another hose needs 3 more hours to fill the pool than the two hoses combined. How long would it take the second hose to fill the pool.
Solution:
The first hose takes 6 hours to fill the pool.
So, work done per hour by the first hose is, 1/6.
Suppose the second hose takes x hours to fill the pool.
So, work done per hour by the second hose is, 1/x.
The work done per hour by the two hoses together is, [1/6 + 1/x] = (x + 6)/6x.
Together the two hoses can fill the pool in, 6x/(x + 6) hours.
It is provided that, the second hose needs 3 more hours to fill the pool than the two hoses combined.
That is:
6x/(x + 6) = x - 3
6x = (x - 3)(x + 6)
6x = x² + 3x - 18
x² - 3x - 18 = 0
x² - 6x + 3x - 18 = 0
x (x - 6) + 3 (x - 6) = 0
(x + 3)(x - 6) = 0
x = 6
Then the time taken by the two hoses together is,
6x/(x + 6) = x - 3 = 6 - 3 = 3 hours
So, each hose takes 6 hours and together they take 3 hours to fill the pool.
This implies that the second hose takes 3 hours more than the 3 hours together to fill the pool.
Thus, the correct option is (a).
PLEASEEEE HELP ME!!!!!!! Write the quotient as a mixed number.
14 divided by 9 =1 R5
Answer:
1 5/9
Step-by-step explanation:
Divide using long division. The whole number portion will be the number of times the denominator of the original fraction divides evenly into the numerator of the original fraction, and the fraction portion of the mixed number will be the remainder of the original fraction division over the denominator of the original fraction.
Which expression does not represent "the sum of n and 6"?
1. 6+n
2. n+6
3. 6n
anyone please help surds questions
Answer:
[tex]2\sqrt{21}[/tex]
Step-by-step explanation:
We can multiply the two irrational terms, getting [tex]\sqrt{84}[/tex].
We see that 4 is a factor of 84, so we can rewrite [tex]\sqrt{84}[/tex] as [tex]\sqrt{4 (21) }[/tex]. We can take the 4 out, getting [tex]2\sqrt{21}[/tex].
Simplify 9^-8 × 1/9^3
Answer:
1/31381059609
Step-by-step explanation:
A least squares regression line a. can be used to predict a value of y if the corresponding x value is given. b. implies a cause-and-effect relationship between x and y. c. can only be determined if a good linear relationship exists between x and y. d. ensures that the predictions of y outside the range of the values of x are valid.
Answer:
The correct option is (a).
Step-by-step explanation:
The general least square regression line is given by,
[tex]\hat Y=a+bX[/tex]
Here,
X = independent variable
Y = dependent variable.
b = slope (or regression) coefficient
a = intercept
The main purpose of the least square regression line is to predict the value of the dependent variable when the independent variable is known.
So, the correct interpretation is:
A least squares regression line can be used to predict a value of y if the corresponding x value is given.
The correct option is (a).
-2/3 + 4/5 + 5/8 Please help me :/
Answer:
91/120
Step-by-step explanation:
It might be convenient to use the form ...
(a/b) +(c/d) = (ad +bc)/(bd)
__
-2/3 +4/5 +5/8 = (-2/3 +4/5) +5/8
= (-10 +12)/15 +5/8
= 2/15 +5/8
= (16 +75)/120
= 91/120
PLEASE HELP !!! Find the measure of y A. 43 B. 90 C. 53 D. 47
===============================================
Explanation:
Notice how inscribed angles x and y subtend (or cut off) the same minor arc measure. This means that x = y. So if we find x, we found y also.
The vertical line is a diameter of the circle. The blue angle marked in the diagram below is a right angle due to Thales Theorem, which is a special case of the inscribed angle theorem. Thales Theorem says that any inscribed angle in a semicircle is 90 degrees.
Therefore the triangle marked in red (same diagram) is a right triangle, allowing us to say
x+47+90 = 180
x+137 = 180
x = 180-137
x = 43
So y = 43 as well.
MOD Pizza purchased a new brick-fired oven for $14,500. If they make a profit of $3 for every pizza they sell, how many pizzas must be in order to make their money back on the purchase of the oven?
Answer:
4,834
Step-by-step explanation:
$14,500/($3 / pizza) = 4833.3 pizzas
MOD Pizza must sell 4,834 pizzas to cover the cost of the oven.
7. Write the power as a product of factors: 97
What is the slope of the line given by the equation y = 4x +12?
Answer:
4
Step-by-step explanation:
The equation of a line can be written as y = mx + b where m is the slope.
In this case, m = 4 since the equation is y = 4x + 12.
Answer: The slope is 4
Step-by-step explanation:
The slope of a y intercept form equation which uses the formula y=mx+b is the number acting as the coefficient.
Write an equation of the line that passes through the origin and
is parallel to the line whose equation is y = 3x - 7.
Answer:
y = 3x
Step-by-step explanation:
Parallel lines have the same slope, so the slope of this new line will be the same as the given one.
For a line to pass through the origin it needs to have a y intercept of 0, because the origin is the point (0,0).
Answer:y = 3x
Step-by-step explanation:
2[tex]\sqrt{2}[/tex] ×[tex]\frac{1}{2}[/tex]
Answer:
[tex] \sqrt{2} [/tex]
Step-by-step explanation:
[tex]2 \sqrt{2} \times \frac{1}{2} = \frac{ 2\sqrt{2} }{1} \times \frac{1}{2} = \frac{2 \sqrt{2} }{2} = \sqrt{2} [/tex]
Hope this helps ;) ❤❤❤
8. 1 Write a complex number to represent the impedance of each element. The voltage, V, is the real part, and the current, I, is the multiple of the imaginary unit i.
9. V = 34 volts: I = 3 milliamperes
10. V = 13 volts; I = 2.4 milliamperes
Given that,
Voltage = 34 volt
Current = 3i mA
We need to calculate the complex number to represent the impedance
Using ohm's law
[tex]V=IR[/tex]
[tex]R=\dfrac{V}{I}[/tex]
Where, V = voltage
I = current
R = impedance
Put the value into the formula
[tex]R=\dfrac{34}{0.003i}[/tex]
[tex]R=\dfrac{34}{0+0.003i}\times\dfrac{0-0.003i}{0-0.003i}[/tex]
[tex]R=\dfrac{0.102i}{0.9\times10^{-5}}\ \Omega[/tex]
(b). Given that,
Voltage = 13 volts
Current = 2.4 mA
We need to calculate the complex number to represent the impedance
Using ohm's law
[tex]R=\dfrac{V}{I}[/tex]
Put the value into the formula
[tex]R=\dfrac{13}{0.00024i}[/tex]
[tex]R=\dfrac{13}{0.00024i}\times\dfrac{-0.00024i}{-0.00024i}[/tex]
[tex]R=\dfrac{0.00312i}{5.76\times10^{-8}}\ \Omega[/tex]
Hence, (a). The complex number to represent the impedance is [tex]\dfrac{0.102i}{0.9\times10^{-5}}\ \Omega[/tex]
(b). (a). The complex number to represent the impedance is [tex]\dfrac{0.00312i}{5.76\times10^{-8}}\ \Omega[/tex]
The table below shows the amount paid for different numbers of items. Determine if this relationship forms a direct variation. Verify your answer.
Direct variation occurs when a variable varies directly with another variable. That is, as the x-variable increases, the y-variable also increases.
The ratio of between y-variable and x-variable would be constant.
Direct variation can be represented by the equation, [tex] y = xk [/tex], where k is a constant. Thus,
[tex] \frac{y}{x} = k [/tex]
From the table given, it seems, as x increases, y also increases. Let's find out if there is a constant of proportionality (k).
Thus, ratio of y to x, [tex] \frac{0.50}{1} = 0.5 [/tex]
k = 0.5.
If the given table of values has a direct variation relationship, then, plugging in the values of any (x, y), into [tex] \frac{y}{x} = k [/tex], should give us the same constant if proportionality.
Let's check:
When x = 2, and y = 1:
[tex] \frac{y}{x} = k [/tex],
[tex] \frac{1}{2} = 0.5 [/tex],
When x = 3, y = 1.5:
[tex] \frac{1.5}{3} = 0.5 [/tex],
When x = 5, y = 2.50:
[tex]\frac{2.5}{5} = 0.5[/tex],
The constant of proportionality is the same. Therefore, the relationship forms a direct variation.
Answer:
Direct variation occurs when a variable varies directly with another variable. That is, as the x-variable increases, the y-variable also increases.
Step-by-step explanation:
You are painting your bedroom wall which is 9 feet high and 12 feet long, using paint that covers 50 square feet per gallon. How many gallons do you need to paint the wall?
Answer:
2.16 gallons
Step-by-step explanation:
Area to be painted:
9 ft × 12 ft = 108 ft²
Pain required:
50 ft² = 1 gallon ⇒ 1 ft² = 1/50 gallon108 ft² = ?108 × 1/50 = 2 8/50 = 2.16 gallonsHow much of a circle does a 100-degree angle turn through?
help pls
1. 1
2. 100/180
3. 50/360
4. 100/360
pls help!!!
Answer:
100/360
Step-by-step explanation:
A complete turn of a circle is 360 degrees
Therefore, 100 degrees turn is 100 out of 360
Piz look at the pic
[tex]piz \: help \:me \: thx[/tex]
Answer:
-12a²+9a-5
Step-by-step explanation:
-7a²+3a-9 - (5a²-6a-4)=
-7a²+3a-9-5a²+6a+4=
-12a²+9a-5
Which step is the same when constructing an inscribed square and an inscribed equilateral triangle?
Answer: Constructing a circle of any arbitrary radius.
Step-by-step explanation:
When trying to construct an inscribed square and also an inscribed equilateral triangle, one step which is same for both procedures is the construction of a circle with an arbitrary radius because both shapes would be inscribed inside the circle been drawn. So the step involving the drawing of the circle is same for both.
Answer: Set the compass width to the radius of the circle.
Step-by-step explanation:
PLZ HELP I CANT DO THIS QUESTION!!!!
Step-by-step explanation:
(A) (In the fig. triangle represented by small triangle with angle of elevation 30° and height h1 ) ( Using this explanation since the figure is not marked)
[tex]tan30 = \frac{h1}{40} [/tex]
[tex]h1 = \frac{40}{\sqrt{3} } m[/tex]
(B) (In the fig. triangle represented by small triangle with angle of depression 58° and height h2 )
[tex]tan58 = \frac{h2}{40} [/tex]
[tex]h2 = 64m[/tex]
(C)
[tex]Height \: of \: Building \: A = h2 = 64m[/tex]
[tex]Height \: of \: Building \: B = h1+h2 = (64 + \frac{40}{ \sqrt{3} } )= 87m[/tex]
Translate
Solve the equation.
3m= 5(m + 3)-3
HELP
Answer:
m = -6
Step-by-step explanation:
3m= 5(m + 3)-3
Distribute
3m = 5m +15 -3
Combine like terms
3m = 5m +12
Subtract 5m
3m-5m = 5m+12-5m
-2m = 12
Divide by -2
-2m/-2 = 12/-2
m = -6
2 less than the sum of x and y
Answer:
(x + y) - 2 or x + y - 2
Step-by-step explanation:
"sum of x and y"
may be expressed mathematically as (x + y)
"two less than sum of x and y", can thus be written:
(x + y) - 2 or x + y - 2
4. (x+ 2)(2x2 + 9x+8)
A.
2x3 + 13x2 + 26x+ 16
B.
16x3 + 728 + 46x - 16
C.
2x3 + 17x2 + 22x+ 16
D.
2x3 + 13x2 - 26x+ 16
Answer:
2x3+9x2+8x+4x2+18x+16
2x3+13x2+26x+16
Which of the following is true of the data represented by the box plot
Answer:
The data is skewed to the bottom and contains an outlier.
Step-by-step explanation:
1. Test for outlier
An outlier is a point that is more than 1.5IQR below Q1 or above Q3.
IQR = Q3 - Q1 = 74 - 51 = 23
1.5 IQR = 1.5 × 23 = 34.5
51 - 15 = 36 > 1.5IQR
The point at 15 is an outlier.
2. Test for normal distribution
The median is not in the middle of the box.
Rather, it cuts the box into two unequal parts, so the data does not have a normal distribution.
3. Test for skewness
The longer part is to the left of the median, so the data is skewed left.