Answers
One leg measures x.
One leg measures 13.5 cm.
The hypotenuse measures x + 8.45 cm.
With the lengths of the the 3 sides, we can use the Pythagorean theorem and solve for x.
[tex] x^2 + (13.5)^2 = (x + 8.45)^2 [/tex]
[tex] x^2 + 182.85 = x^2 + 16.9x + 71.4025 [/tex]
[tex] 182.25 = 16.9x + 71.4025 [/tex]
[tex] -16.9x = -110.8475 [/tex]
[tex] x = 6.559 [/tex]
Answer: x = 6.6 cm
Related Questions
Fred played golf and for the past 5 times had a score of 82, 79, 83, 71, and 80. What was his average score?
Answers
What is the equation of the function y=3/x translated 4 units to the right and 5 units down
Answers
y = 3/(x -4) -5
Answer:
The required equation is [tex]g(x)=\frac{3}{x-4}-5[/tex].
Step-by-step explanation:
The given function is
[tex]y=\frac{3}{x}[/tex]
It can be written as
[tex]f(x)=\frac{3}{x}[/tex]
The transformation of a function is defined as
[tex]g(x)=f(x+a)+b[/tex]
Where, a represents the horizontal shift and b represents the vertical shift.
If a>0, then the function f(x) shifts a units left and a<0, then the function f(x) shifts a units right.
If b>0, then the function f(x) shifts b units up and b<0, then the function f(x) shifts b units down.
Since the function translated 4 units to the right and 5 units down, therefore the value of a is -4 and bis -5.
[tex]g(x)=f(x-4)-5[/tex]
[tex]g(x)=\frac{3}{x-4}-5[/tex] [tex][\because f(x)=\frac{3}{x}][/tex]
Therefore the required equation is [tex]g(x)=\frac{3}{x-4}-5[/tex].
2.4 + 5.4q – 4.5q + 3.6
a.6+1.1q
b.9.9q+6
c.0.9q+6
d.9.9q-6
Answers
(5.4q - 4.5q) + (2.4 + 3.6) = 0.9q + 6
The answer is c. 0.9 +6
Answer:
c!
Step-by-step explanation:
i did the test loll <3
Which logarithmic equation is equivalent to the exponential equation below?
4c = 256
A. log256 c = 4
B. logc 256 = 4
C. log4 c = 256
D. log4 256 = c
Answers
The logarithmic equation is equivalent to the exponential equation is [tex]log_4[/tex] 256 = c
The correct option is (D).
What is Logarithm Function?Logarithms are useful for solving exponential equations and investigating the properties of exponential functions. They will also be incredibly useful in calculus, where they will be used to compute the slope of various functions and the area circumscribed by various curves.
Given:
[tex]4^c[/tex] = 256
Now, writing into Logarithmic Function we can write it as
[tex]log_4[/tex] 256 = c
If we further solve it we get
256 = [tex]4^c[/tex] (log become exponential we move from either side of Equal Sign.)
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Using the figure below, select the two pairs of alternate interior angles.
1 and 4
2 and 3
6 and 7
5 and 8
Answers
2 and 3
6 and 7
Answer
Options second and third
Reason
From the figure we get l and m are two parallel lines and t is the traversal.
There are two pairs of alternate interior angles
The pairs of alternate interior angles are equal
pairs of alternate interior angles
2 and 3
6 and 7
Similarly there are alternate exterior angles are there. Other two options are alternate exterior angles
An airline requires carry on luggage to weigh at most 40 pounds. Your suitcase currently weighs 10 pounds. How many pounds p are available for you to fill your suitcase with other items?
Answers
30 pounds is available to fill the suitcase with other items.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
An airline requires carry on luggage to weigh at most 40 pounds.
The Suitcase presently carry 10 pounds.
Let p be the pound available to fill your suitcase with other items.
So, p= 40- 10
p = 30 pounds
Hence, 30 pounds is available to fill the suitcase with other items.
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please help 1.Bryce started with $450 in a bank account that does not earn interest. In the middle of every month, he withdraws 1/2 of the account balance. Which recursive function rule models Bryce’s balance at the end of each month?
Answers
The following recursive function represents the Brye's balance at end of each month:
[tex] a_{n}= \frac{1}{2}* a_{n-1} [/tex]
where [tex] a_{n-1} [/tex] is the account balance of previous month. And [tex] a_{n} [/tex] is the account balance of current month.
Choose the correct sum of the polynomials (4x3 − 2x − 9) + (2x3 + 5x + 3). 6x3 − 3x − 6 2x3 − 7x − 12 6x3 + 3x − 6 2x3 + 3x − 3
Answers
= 4x^3 - 2x - 9 + 2x^3 + 5x + 3
= 6x^3 + 3x - 6 (Answer: C)
Answer:
[tex]6x^3+3x -6[/tex]
Step-by-step explanation:
(4x3 − 2x − 9) + (2x3 + 5x + 3)
[tex](4x^3 - 2x - 9) + (2x^3 + 5x + 3)[/tex]
To add two polynomials, we remove the parenthesis
[tex]4x^3 - 2x - 9+2x^3 + 5x + 3[/tex]
To add it , we combine like terms. we add the like terms
[tex]4x^3+2x^3- 2x+ 5x - 9+ 3[/tex]
[tex]6x^3+3x -6[/tex]
helppppppppppppppppppppppppppppppppppp
Answers
Justification:
1) For a function to have inverse function, the original function has to be one to one. This is for the original function two (or more) images cannot have different inputs. That condition is satisfied by the function m(x) = - 7x, since it is a straigh line.
2) the function b (x) = x^2 + 3 is a parabola. That means that, except by the vertex, every image is realated with two inputs.
For example, b(x) = 103 => x^2 = 103 - 3 = 100 => x = 10 and x = -10.
3) For the function d(x) = - 9, you cannot tell the input value for the image because it is the same image for any value of x.
4) The function p(x) = |x| also has a pair of images for the same value of x (excpet for the vertex).
For example, for x = - 100 and x = 100, p(x) = 100, so you cannot tell the x value given the p(x) value.
Y varies directly as x and inversely as the square root of w; write the sentence as an equation.
Answers
y = kx
Y varies inversely as the square root of w
y = [tex] \frac{k}{ \sqrt{w} } [/tex]
The relationship where y varies directly as x and inversely as the square root of w can be represented by the equation y = k * (x / sqrt(w)). Here, k is a constant of proportionality.
Explanation:From the statement given, we can deduce an equation representing a direct proportionality to x and an inverse proportionality to the square root of w.
In mathematics, direct and inverse proportionality relationships are commonly depicted as y = kx and y = k/x respectively, where k is a constant. For direct proportionality, as x increases, y also increases. Contrastingly, for inverse proportionality, as x increases, y decreases.
Given the statement, we can represent the relationship as follows: y = k * (x / sqrt(w)).
Here, y varies directly as x and inversely as the square root of w. The constant k is the constant of proportionality which can be determined based on specific values of x, y and w.
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a) Explain...
b) What is the probability that a person without HIV will have a test come out positive?
c) What is the probability that a person with HIV will have a test come out negative?
d) What is the probability that a person with HIV will have a test come out positive?
Answers
a) The cell corresponding to a positive diagnosis when the
person has antibodies present as well as the cell for a negative diagnosis when
the person has no antibodies present are the cells representing a CORRECT
diagnosis.
The cell corresponding to a negative diagnosis when you
actually have antibodies present is called a FALSE NEGATIVE and is considered
as a TYPE II error.
The cell corresponding to a positive diagnosis when you
actually don't have antibodies present is called a FALSE POSITIVE and is considered
as a TYPE I error.
For the tree diagram for the questions below, refer to the
picture attached.
b) To know the probability that a person without HIV will be diagnosed positive (false positive), we just trace the tree diagram from population to "antibodies not present" to "positive". The tree diagram will give us a value of 0.00588.
ANSWER: The probability of a false positive is 0.00588 or 0.588%.
c) We do the same thing as the previous subproblem to determine the probability that a person with HIV will be diagnosed as negative. We trace the tree diagram from population to "antibodies present" to "negative". The tree diagram will give us a value of 0.003.
ANSWER: The probability of a false negative is 0.003 or 0.3%.
d) Same thing for this subproblem. We trace the tree diagram from population to "antibodies present" to "positive" to know that the value is 0.01997.
ANSWER: The probability that a person with HIV will be diagnosed as positive is 0.01997 or 1.997%.
What is the range of the function graphed below?
Answers
We have then that in this case the values are:
from y = 3 (included)
up to y = -3 (not including it)
The range of the function is:
-3 <y <= 3
Answer:
the range of the function graphed below
-3 <y <= 3
what is 1000x - 1x?
A) 101x
B) 1001x
C) 99x
D) 999x
Answers
Let's think of what 1000x means.
We know that multiplication is repeated addition. For example, 5(5) = 5+5+5+5+5. It's 5 added five times.
It's no different here. That means we have x 1000 times. If we look at a simpler situation:
5x - 3x, we have (x + x + x + x + x) - (x + x + x)
That means we're getting rid of 3 x's, which means we have 2x. If we have different coefficients but the same variable, we can just subtract or add the coefficients but keep the variable. That means:
4x - 2x = 2x and 10x - 5x = 5x
Now, we can do this problem. We want:
(1000-1)x = 999x
Your answer is D.
Hope this helps!
A sample of n = 6 scores has a mean of m = 5. one person with a score of x = 12 is added to the distribution. what is the mean for the new set of scores?
Answers
Final answer:
To calculate the new mean after adding a score of 12 to the original 6 scores with a mean of 5, determine the total sum of the original scores, add 12, and divide by the new number of scores. The new mean for the 7 scores is 6.
Explanation:
To find the new mean when one person with a score of x = 12 is added to a sample of n = 6 scores with a current mean of m = 5, first calculate the total sum of the scores before the new score is added. This can be done by multiplying the mean by the number of scores. Then add the new score to this total and divide by the new number of scores.
Calculate the total sum of the original scores: Total sum = mean × number of scores = 5 × 6 = 30.Add the new score to the total sum: New total sum = 30 + 12 = 42.Calculate the new mean by dividing the new total sum by the new number of scores: New mean = New total sum ÷ new number of scores = 42 ÷ 7 = 6.So, the mean for the new set of scores is 6.
PLEASE SOMEONE HELP ON THIS !!!
BRAINLIEST WILL BE GIVEN TO CORRECT ANSWER
TRY TO EXPLAIN IT....
Answers
B and C are both 30cm of water, but B filled up 1 minute faster than C
Please help ASAP!!! 42 points and will mark brainliest for RIGHT answer!!!
Answers
Write an equation for the line that is parallel to the given line and that passes through the given point.
y =3/4 x – 9; (–8, –18)
Answers
Identify the slope : our slope is 3/4
Remember that parallel equations have the same slope, so both slopes are 3/4
Now, we have to find the y-intercept. Simply plug everything into the slope intercept form equation.
y = mx + b
(-18) = (3/4)(-8) + b
Simplify.
-18 = -6 + b
Add 6 to both sides.
-18 + 6 = b
Therefore, our y-intercept is -12.
Now plug everything into the slope intercept form.
y = mx + b
y = 3/4x - 12
~Hope I helped!~
To write an equation for a line that is parallel to a given line and passes through a given point, use the point-slope form of the linear equation. The slope of the parallel line is equal to the slope of the given line. Plug in the values and simplify to get the equation.
Explanation:To find an equation for a line that is parallel to the given line and passes through the given point, we need to use the fact that parallel lines have the same slope. The slope of the given line is 3/4, so the slope of the parallel line will also be 3/4. Using the point-slope form of a linear equation, we can write the equation:
y - y1 = m(x - x1)
where (x1, y1) is the given point and m is the slope. Plugging in the values, we get:
y - (-18) = 3/4(x - (-8))
Simplifying the equation gives:
y + 18 = 3/4(x + 8)
Next, we can distribute the 3/4 to both terms in the parentheses:
y + 18 = 3/4x + 6
To isolate y, we subtract 18 from both sides:
y = 3/4x - 12
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Using the information given, select the statement that can deduce the line segments to be parallel. If there are none, then select none.
Answers
Answer:
Option A. AB || DC
Step-by-step explanation:
In the given picture measurement of angle 2 = measurement of angle A
or m∠2 = m∠A (opposite angles)
This only possible only when m∠A = m∠2 = m∠C (Corresponding angles)
If these angles are equal then two lines AB and DC are parallel and two transverse AB and DC are intersecting them.
Therefore option A. AB || DC is the answer.
A waterfall has a height of 900 feet. A pebble is thrown upward from the top of the falls with an initial velocity of 12 feet per second. The height, h, of the pebble after t seconds is given by the equation h equals negative 16 t squared plus 12 t plus 900. How long after the pebble is thrown will it hit the ground?
Answers
_____
The quadratic formula tells you the time is
.. t = (-12 -√(12^2 +4*16*900))/(-32) = (3/8)*(1 +√401) . . . seconds
Final answer:
To find when the pebble hits the ground, solve for time using the quadratic equation from the given height function, resulting in around 6 seconds.
Explanation:
To find how long the pebble takes to hit the ground, we need to find the time t when its height h becomes 0. This means we need to solve the equation for t when h = 0:
-16t² + 12t + 900 = 0
This is a quadratic equation, and we can solve it using various methods like factoring, the quadratic formula, or completing the square. Here, we'll use the quadratic formula:
t = (-b ± √(b² - 4ac)) / 2a
where a = -16, b = 12, and c = 900:
t = (-12 ± √(12² - 4 × -16 × 900)) / (2 × -16)
t = (-12 ± √(614400)) / -32
t ≈ (-12 ± 247.88) / -32
There are two possible solutions:
t1 ≈ 25.50 seconds
t2 ≈ -5.50 seconds (we can discard this since time cannot be negative)
The pebble will hit the ground approximately 6 seconds after it is thrown.
the area of a rectangle is 20x^2-27x-8.the length is 4x+1. What is the width?
Answers
Explanation:
Let width be w
Then w(4x+1)=20x2−27x−8
So
(?x+?)(4x+1)=20x2−27x−8
Note that
5×4=20 and (−8)×(+1)=−8
⇒w(4x+1)
=(5x-8)(4x+1)=20x2+5x−32x−8
⇒w(5x−8)
Makhaya is required to spend more than 300 minutes to complete assignments, and he can use at most 20 paper sheets. Let W denote the number of writing assignments he completes and M the number of math assignments he completes.
Write an inequality that represents the condition based on the number of minutes.
Write an inequality that represents the condition based on the number of paper sheets.
Answers
.. 75W +15M ≥ 300 . . . . . . . minutes
The constraint on paper is
.. 3W +M ≤ 20 . . . . . . . . . . . sheets of paper
A nautical mile is a unit of distance frequently used in ocean navigation. It is defined as the length of an arc s along a great circle on the earth when the subtending angle has measure 1' = "one minute" = 1/60 of one degree. Assume the radius of the earth is 3,960 miles.
Find the length of one nautical mile to the nearest 10 feet.
Answers
s = rФ
Radius is given to be = 3960 miles
We are to find the arc length in feet, so we convert the miles to feet.
1 mile = 5280 feet.
So,
Radius = 3960 x 5280 feet = 20908800 feet
Angle = 1/60 degree
The angle must be in radians before, we use its value in the equation given above.
So, 1/60 degrees in radians will be:
[tex] \frac{1}{60} * \frac{ \pi }{180} = \frac{ \pi }{10800} [/tex]
Now we can use this value of angle in above equation to find the arc length.[tex]s = 20908800 * \frac{ \pi }{10800} = 6080 feet[/tex]
So, rounded of to nearest 10 feet, the length of one nautical mile is 6080 feet.
The value of one nautical mile to the nearest feet is [tex]\boxed{6080{\text{ feet}}}[/tex].
Further Explanation:
The arc, radius and the angle are related to each other.
The angle can be obtained as the ratio of an arc of the circle to the radius of the circle.
The formula for the angle can be expressed as,
[tex]\boxed{{\text{Angle = }}\frac{{{\text{length of an arc}}}}{{{\text{radius of circle}}}}}[/tex]
The length of an arc can be obtained as,
[tex]\boxed{{\text{Length of an arc}}=\left({{\text{radius}}\times{\text{angle}}}\right)}[/tex]
Given:
The angle is one minute represented by 1'.
One minute is equal to [tex]{\left({\frac{1}{{60}}}\right)^\circ}[/tex].
The radius of earth is 3960 miles.
Explanation:
One mile is equal to 5280 feet.
[tex]\boxed{1{\text{ mile}}=5280{\text{ feet}}}[/tex].
The radius in feet can be expressed as follows,
[tex]\begin{aligned}Radius&=3960\times5820\\&=20908800{\text{ feet}}\\\end{aligned}[/tex]
Convert the angle into radian.
[tex]\boxed{1{\text{ degree}} = \frac{\pi }{{180}}{\text{ radian}}}[/tex]
The value of [tex]\frac{1}{{{{60}^ \circ }}}[/tex] can be obtained as follows,
[tex]\begin{aligned}{\text{Angle}}&=\frac{1}{{60}}\times\frac{\pi }{{180}}\\&=\frac{\pi }{{10800}}\\\end{aligned}[/tex]
The length of an arc of the earth can be obtained as follows,
[tex]\begin{aligned}{\text{length of an arc}}&=20908800\times\frac{\pi }{{10800}}\\&=6080{\text{ feet}}\\\end{aligned}[/tex]
Learn more:
1. Learn more about inverse of the function https://brainly.com/question/1632445.
2. Learn more about equation of circle brainly.com/question/1506955.
3. Learn more about range and domain of the function https://brainly.com/question/3412497
Answer details:
Grade: High School
Subject: Mathematics
Chapter: Unit and Measurement
Keywords: Nautical mile, unit distance, earth, radius of earth, great circle, one degree, length of nautical unit, feet.
The length of a rectangle is 5 ft less than three times the width, and the area of the rectangle is 28 ft2 . find the dimensions of the rectangle.
Answers
Then the length is 3w - 5.
The area = LW = 28
w(3w - 5) = 28
3w^2 - 5w = 28
3w^2 - 5w - 28 = 0
(3w + 7)(w - 4) = 0
3w + 7 = 0 or w - 4 = 0
w = -7/3 or w = 4
The width of a rectangle cannot be a negative number, so we discard w = -7/3.
The width is 4 ft.
The length is 3w - 5 = 3(4) - 5 = 12 - 5 = 7
The length is 7 ft
Answer: The dimensions are length 7 ft and width 4 ft.
The rectangle has a width of approximately 4.18ft and a length of approximately 7.55ft. These are obtained by setting up and solving a system of equations based on the given information.
Explanation:Let's start by setting up equations based on the problem statement. Let's denote the width of the rectangle as
w and the length as l. From the problem, we know two things: one is that the length is 5 feet less than three times the width, which can be written as l = 3w - 5. The second thing we know is that the area of the rectangle, which is obtained by multiplying the length by the width, is 28 square feet, written as l*w = 28 . By substituting the first equation into the second, we can solve for w: (3w - 5)*w = 28
. This simplifies to a quadratic equation 3w^2 - 5w - 28 = 0 which can be solved to give w=~4.18 ft and w=-2.02ft. Because the width cannot be negative, we discard the second solution. Substituting w=~4.18ft into l = 3w -5 gives
l=~7.55 ft . Therefore, the dimensions of the rectangle are approximately 4.18ft (width) and 7.55ft (length).
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what is the value of z so that -9 and 9 are both solutipns fo x^2+z=103
Answers
[tex]\bf \begin{cases} x=-9\implies &x+9=0\\ x=9\implies &x-9=0 \end{cases} \\\\\\ (x+9)(x-9)=\stackrel{original~polynomial}{0}\implies x^2+0x-81=0 \\\\\\ x^2\underline{-81}=0\qquad \textit{and we can write }-81=\underline{-103+22} \\\\\\ x^2\underline{-103+22}=0\implies x^2+22=103[/tex]
Mario bought a shirt priced at $ 24.99 and a pair of pants priced at $ 39.99. For these items, he paid a total of $ 69.53 , sales tax included. What was the sales tax rate?
Answers
24.99 + 39.99 = 64.98
69.53-64.98 = 4.55
4.55/69.53 = 0.0654 = 6.5% sales tax
Which of the following is the solution of 5e^2x-4=11
Answers
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helpp me pleasweeee?!??!!
Answers
The 2nd selection completes the table.
The bear population increases at a rate of 3% each year. There are 1462 bears this year. How many bears will there be in 10 years?
Answers
Final answer:
The bear population will be approximately 1965 bears in 10 years.
Explanation:
To calculate the bear population in 10 years, we can use the formula for exponential growth:
P = P₀(1 + r)ⁿ
Where:
P is the final population
P₀ is the initial population
r is the growth rate as a decimal
n is the number of years
In this case, the initial population (P₀) is 1462, the growth rate (r) is 3% (0.03), and the number of years (n) is 10. Plugging these values into the formula, we get:
P = 1462(1 + 0.03)¹⁰ ≈ 1965.32
Therefore, there will be approximately 1965 bears in 10 years.
Can anyone help me with this math problem???
Answers
Selection A is appropriate.
Look at the picture below // 99 points // PLEASEE HELPP
Answers
area of rectangle = 21*18 = 378
area of shaded = 842 - 378 = 464
answer
A) 464 square units