Answer:
1) x = 12.2
3) x = 21.7
5) x = 17.9
7) x = 31.8
Step-by-step explanation:
Use Pythagorean Theorem (a^2 + b^2 = c^2 where a and b are bases and c is hypotenuse)
1) 10^2 + 7^2 = x^2
100 + 49 = x^2
149 = x^2
x = sqrt 149 which is about 12.2
3) 16^2 + x^2 = 27^2
256 + x^2 = 729
x^2 = 473
x = sqrt 473 which is about 21.7
5) 9^2 + x^2 = 20^2
(we know the other base is 9 because in an isosceles triangle, the altitude (the height) is the same as the median (which divides the base into half)
81 + x^2 = 400
x = sqrt 319 which is about 17.9
7) 16^2 + y^2 = 22^2 (y is the height of the triangle)
256 + y^2 = 484
x = sqrt 228
(sqrt 228)^2 + (44-16)^2 = x^2
228 + 784 = x^2
x^2 = sqrt 1012 which is about 31.8
I know how to do this but not with the fraction in it
•°|NO LINKS PLEASE, LOOKING FOR REAL ANSWERS|°•
What is the formula for finding the surface area of a square pyramid?
Answer:
a2 + 2al (or) a2 + √a24+h2 a 2 4 + h 2
Step-by-step explanation:
Answer:
SA=L²+2L√(L²/4+H²)
Step-by-step explanation:
Where H is the height and L is the length
find the radius if the circumference is 32 inches
Answer:
5.1 inches------------------
Use circumference formula:
C = 2πrFind the radius by rearranging the formula and substituting 32 for C:
r = C/(2π)r = 32/(2*3.14)r = 5.10 inches (rounded)Answer:
5.09 in
Step-by-step explanation:
We know that the formula to find the circumference of a circle is:
C = 2πr
Here,
C → Circumference → 32 in
r → radius
Let us find the radius of the circle by substituting the given values.
\(\sf C = 2\pi r\\\\\sf 32 = 2\pi r\\\\Divide\:both\:sides\:by\:2 \pi \:and\:make\:r\:the \:subject\\\\\dfrac{32}{2 \pi} =\dfrac{2 \pi r}{2 \pi} \\\\\red{5.09 \:in=r}\)
a restaurant gathers data about a new dish by providing free samples to parties of six or more diners. what does this scenario describe?
The scenario where restaurant gathers data about a new dish by providing free samples to parties of six or more is a sampling bias.
What is sampling bias?Sampling bias occurs when some members of a population are systematically more likely than others to be chosen for a sample. In the medical world, this is known as ascertainment bias. Because it threatens external validity, specifically population validity, sampling bias reduces the generalizability of findings.
Sampling bias occurs when some people in a community being surveyed are purposefully placed to be chosen or not chosen over others. If a sample process consistently favors some results over others, it is said to be biased. Ascertainment bias particularly in biological areas)/ and systematic bias are other terms for sampling bias. Bias can be intentional, but it is frequently unintentional.
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Solve for the value of n
Answer:
8
Step-by-step explanation:
Vertical angles are congruent, so 9n=8n+8. It follows that n=8.
don't mind the writings in pen, i didn't know what i was doing... PLS HELP ASAP
Answer:
(a) <AED=50°
(b) <DAB=65°
(c) <BCD=45°
(d) Reflex <ABC=225°
Step-by-step explanation:
(a) 180-65-65=50
(b) 180-115=65 (ADC is 115)
(c) 180-135-45
(d) Reflex <ABC 360-135=225
Find the Measurement indicated in each parallelogram
QY=2x-5
YS=5+x
FIND QY
Solving a linear equation we will see that x = 10, and with that we can see that:
QY = 15
How to find the length of QY?We can see that QY and YS are the two halfs of a diagonal on the quadrilateral, then these two have the same length, then we can write the linear equation:
QY = YS
2x - 5 = 5 + x
Now we can solve that for X to get:
2x - 5 = 5 + x
2x - x = 5 + 5
x = 10
Then the length of QY is:
QY = 2x - 5 = 2*10 - 5 = 15
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Which equation is the inverse of y = 16x² +1?
X
O Y=√16
O Y= 16
-1
0 У.
О У.
y=√x -1
±√√x-1
4
Answer:
\(x = + - \sqrt{ \frac{y - 1}{16} } \)
Step-by-step explanation:
\(y - 1 = 16 {x}^{2} \\ \frac{y - 1}{16} = {x}^{2} \\ + - \sqrt{ \frac{y - 1}{16} } = {x} \\ x = + - \sqrt{ \frac{y - 1}{16} } \)
Just answer the question thanks.
The distance in meters that was traveled is given as 300 meters
How to solve for distanceAcceleration = 60 / 40
= 3 / 2
When the velocity that we have in the graph is 30 m/s the time in seconds is twenty seconds
We have to use the formula s = 1 / 2 a t ^2
= 1 / 2 x 3 / 2 x 20^2
= 1200 / 4
= 300 meters
Hence the train traveled for a distance of 300 meters
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Use the original price and the markdown to find the retail price. Original price: $100; Markdown: 28%. What is retail price ?
Answer:
$72 is the retail price
Step-by-step explanation:
100 x (100-28)/100
Completing the square........... (+25 points+!) Someone please help:)
Answer:
D)
\(5 \times {10}^{ - 12} \)
Step-by-step explanation:
velocity(v) = distance/time
but distance =
\(3 \times {10}^{ - 4} \)
and velocity =
\(6 \times {10}^{7} \)
\(6 \times {10}^{7} = \frac{3 \times {10}^{ - 4} }{time} \)
\(time = \frac{3 \times {10}^{ - 4} }{6 \times {10}^{7} } \)
\(time = 5 \times {10}^{ - 12} \)
Without multiplying, is 4 × 0.36 less
than or greater than 4? Explain its for my little sis oof
Answer:
Less
Step-by-step explanation:
Think of it like this:
Four times of 0.36
0.36 + 0.36 + 0.36 + 0.36 = 1.44
So 4 × 0.36 is less than 4
Hope I helped your little sista :)
NEED HELP! with these 2?
Step-by-step explanation:
answer,
first one is -5 and the second is 5
hope it helps
Answer: first one is -5
Second one is 5
Step-by-step explanation:
an item is regularly priced at $91 . it is on sale for 35% off the regular price. use the aleks calculator to find the sale price.
The sale price of an item that is regularly priced at $91 and is on sale for 35% off the regular price using the aleks calculator is $59.15.
To calculate the sale price of an item that is regularly priced at $91 and is on sale for 35% off the regular price using the aleks calculator we will follow these steps:
Step 1: Calculate the amount of discount = Regular Price × Discount rate
Discount rate = 35/100
Simplifying the value we have:
Discount rate = 0.35
Amount of discount = 91 × 0.35
Amount of discount = $31.85
Step 2: Calculate the sale price
Sale price = Regular price − Amount of discount
Sale price = $91 − $31.85
Sale price = $59.15
Hence, the sale price of an item that is regularly priced at $91 and is on sale for 35% off the regular price using the aleks calculator is $59.15.
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Determine the intervals for which the function shown below is increasing
The function is increasing in the intervals: (-∞, -3) and (2, 5)
the surface area of a cube is 2400 yd^2. what will be the new surface area if all the dimensions are multiplied by 1/4
The original surface area of the cube is 2400 yd^2. If all the dimensions are multiplied by 1/4, the new surface area of the cube can be found by multiplying the original surface area by (1/4)^2 = 1/16. The new surface area of the cube would be 2400 yd^2 * (1/16) = 150 yd^2.
The surface area of a cube is given by the formula 6s^2, where s is the length of one edge of the cube. So, if the surface area of a cube is 2400 yd^2, then we can write:
6s^2 = 2400
Dividing both sides by 6, we get:
s^2 = 400
Taking the square root of both sides, we get:
s = 20
So, each edge of the original cube is 20 yards long.
If we multiply each dimension by 1/4, then the new edge length will be (1/4)*20 = 5 yards. Therefore, the new surface area of the cube can be found by plugging in 5 for s in the surface area formula:
6(5^2) = 150
Therefore, the new surface area of the cube is 150 yd^2.
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Find the slope-intercept equation of the line that passes through (1,-2) and has an undefined slope.
The slope - intercept equation of a line that would pass through (1,-2) and has an undefined slope, is y = -2 x
How to find the slope intercept equation?The slope - intercept equation takes the form:
y = mx + b
m = slope
b = y - intercept
When the slope is undefined, it means that there is no y - intercept as the slope is a vertical line which crosses the x - axis alone. The slope would therefore be :
y = mx
- 2 = 1 x
m = - 2
The slope - intercept form is:
y = -2 x
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I need help with this question. Select the exclusion that fits best with this problem. 13x^6/51x^4
Answer:
Last option e : X=0
Step-by-step explanation:
X=0
Answer:
x = 0
Step-by-step explanation:
I got it correct on Odyssey. : )
helllllllllllllllppppppppppppp WILL MARKBRIANLIST
Answer:
4(25) + 6(-5) -2 = 100 - 30 -2 = 70 - 2= 68
is the equation 2x+y=4 and 2x^2+y=6 linear.. if so, how do i graph them?
Answer:
No, but you can graph them by converting to mx+b form
Step-by-step explanation:
The procedure for solving simultaneous linear equations now called Gaussian elimination appears in the ancient Chinese mathematical text Chapter Eight: Rectangular Arrays of The Nine Chapters on the Mathematical Art. Its use is illustrated in eighteen problems, with two to five equations.[4]
Systems of linear equations arose in Europe with the introduction in 1637 by René Descartes of coordinates in geometry. In fact, in this new geometry, now called Cartesian geometry, lines and planes are represented by linear equations, and computing their intersections amounts to solving systems of linear equations.
The first systematic methods for solving linear systems used determinants, first considered by Leibniz in 1693. In 1750, Gabriel Cramer used them for giving explicit solutions of linear systems, now called Cramer's rule. Later, Gauss further described the method of elimination, which was initially listed as an advancement in geodesy.[5]
In 1844 Hermann Grassmann published his "Theory of Extension" which included foundational new topics of what is today called linear algebra. In 1848, James Joseph Sylvester introduced the term matrix, which is Latin for womb.
Linear algebra grew with ideas noted in the complex plane. For instance, two numbers w and z in {\displaystyle \mathbb {C} }\mathbb {C} have a difference w – z, and the line segments {\displaystyle {\overline {wz}}}{\displaystyle {\overline {wz}}} and {\displaystyle {\overline {0(w-z)}}}{\displaystyle {\overline {0(w-z)}}} are of the same length and direction. The segments are equipollent. The four-dimensional system {\displaystyle \mathbb {H} }\mathbb {H} of quaternions was started in 1843. The term vector was introduced as v = x i + y j + z k representing a point in space. The quaternion difference p – q also produces a segment equipollent to {\displaystyle {\overline {pq}}.}{\displaystyle {\overline {pq}}.} Other hypercomplex number systems also used the idea of a linear space with a basis.
Arthur Cayley introduced matrix multiplication and the inverse matrix in 1856, making possible the general linear group. The mechanism of group representation became available for describing complex and hypercomplex numbers. Crucially, Cayley used a single letter to denote a matrix, thus treating a matrix as an aggregate object. He also realized the connection between matrices and determinants, and wrote "There would be many things to say about this theory of matrices which should, it seems to me, precede the theory of determinants".[5]
Benjamin Peirce published his Linear Associative Algebra (1872), and his son Charles Sanders Peirce extended the work later.[6]
The telegraph required an explanatory system, and the 1873 publication of A Treatise on Electricity and Magnetism instituted a field theory of forces and required differential geometry for expression. Linear algebra is flat differential geometry and serves in tangent spaces to manifolds. Electromagnetic symmetries of spacetime are expressed by the Lorentz transformations, and much of the history of linear algebra is the history of Lorentz transformations.
The first modern and more precise definition of a vector space was introduced by Peano in 1888;[5] by 1900, a theory of linear transformations of finite-dimensional vector spaces had emerged. Linear algebra took its modern form in the first half of the twentieth century, when many ideas and methods of previous centuries were generalized as abstract algebra. The development of computers led to increased research in efficient algorithms for Gaussian elimination and matrix decompositions, and linear algebra became an essential tool for modelling and simulations.[5]
Vector spaces
Main article: Vector space
Until the 19th century, linear algebra was introduced through systems of linear equations and matrices. In modern mathematics, the presentation through vector spaces is generally preferred, since it is more synthetic, more general (not limited to the finite-dimensional case), and conceptually simpler, although more abstract.
A vector space over a field F (often the field of the real numbers) is a set V equipped with two binary operations satisfying the following axioms. Elements of V are called vectors, and elements of F are called scalars. The first operation, vector addition, takes any two vectors v and w and outputs a third vector v + w. The second operation, scalar multiplication, takes any scalar a and any vector v and outputs a new vector av. The axioms that addition and scalar multiplication must satisfy are the following. (In the list below, u, v and w are arbitrary elements of V, and a and b are arbitrary scalars in the field F.)[7]
Mr stoves is investing $1500 on a bank account that would give him 3. 7% compounded monthly. What would be his final balance after 10 years?
Mr stove's final balance after 10 years if he invested 1500 on a bank account that would give him 3. 7% compounded monthly is $2,170.37
What would be his final balance after 10 years?A = P(1 + r/n)^nt
Where
P = $1500
r = 3.7% = 0.037
n = monthly = 12
t = 10 years
So,
A = P(1 + r/n)^nt
A = 1,500.00(1 + 0.037/12)^(12×10)
A = 1,500.00(1 + 0.0030833333333333)¹²⁰
A = $2,170.37
Ultimately, Mr stove will have $2,170.37 as his balance after 10 years.
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Solve the exponential equation
4^x = 7(3^x)
The solution to the given exponential equation is; x = 6.48
What is the solution to the exponential equation?
We want to solve the exponential equation;
4^(x) = 7 - (3^x)
We can use logarithm or inverse of logarithm to solve this but in this case we will use the logarithm to get;
x log 4 = 7 - (x log 3)
x log 4 + x log 3 = 7
x(log 4 + log 3) = 7
1.08x = 7
x = 7/1.08
x = 6.48
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HELPPPPP
7 8 ÷ 1 4
A) 3 1 2
B) 4
C) 7 16
D) 7 32
Answer:
A) 3 1/2
Explanation:
\(\hookrightarrow \sf \dfrac{7}{8} \div \dfrac{1}{4}\)
rewrite the following
\(\hookrightarrow \sf \dfrac{7}{8} * \dfrac{4}{1}\)
join both fractions
\(\hookrightarrow \sf \dfrac{7*4}{8}\)
multiply
\(\hookrightarrow \sf \dfrac{28}{8}\)
simplify the following
\(\hookrightarrow \sf \dfrac{7}{2}\)
turn into mixed fraction
\(\hookrightarrow \sf 3\dfrac{1}{2}\)
Answer:
\(\dfrac{7}{2}\)
Step-by-step explanation:
Given expression:
\(\dfrac{7}{8} \div \dfrac{1}{4}\)
Simplify the expression:
\(\implies \dfrac{7}{8} \div \dfrac{1}{4}\)
\(\implies \dfrac{7 \div 1}{8 \div 4}\)
\(\implies \dfrac{7}{2}\)
Find the mean, median, mode and range 28,45,53,28, 47 show work please
Value of mean is, 40.2
Value of median is, 45
Value of mode is, 28
Value of range is, 25
Given that;
Data set is,
⇒ 28, 45, 53, 28, 47
Now, We can arrange into ascending order as;
⇒ 28, 28, 45, 47, 53
Hence, Value of mean is,
⇒ (28 + 28 + 45 + 47 + 53) / 5
⇒ 40.2
And, The value of median is,
⇒ (5 + 1) / 2
⇒ 6/2
⇒ 3rd term
⇒ 45
The value of mode =28
And, The value of range is,
⇒ 53 - 28
⇒ 25
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a study of a local high school tried to determine the mean number of text messages that each student sent per day. the study surveyed a random sample of 82 students in the high school and found a mean of 193 messages sent per day with a standard deviation of 55 messages. determine a 95% confidence interval for the mean, rounding all values to the nearest whole number.
Rounding all values to the nearest whole number, the 95% confidence interval for the mean number of text messages sent per day is approximately:
Confidence Interval = (181, 205)
To determine the 95% confidence interval for the mean number of text messages sent per day, we can use the formula:
Confidence Interval = Sample Mean ± Margin of Error
The margin of error depends on the sample size, standard deviation, and desired level of confidence. Since the sample size is relatively large (n = 82), we can use the Z-score for a 95% confidence level, which corresponds to a Z-score of approximately 1.96.
First, let's calculate the margin of error:
Margin of Error = Z * (Standard Deviation / sqrt(Sample Size))
Z = 1.96 (for a 95% confidence level)
Standard Deviation = 55
Sample Size = 82
Margin of Error = 1.96 * (55 / sqrt(82))
Calculating this value, we find:
Margin of Error ≈ 12.49
Now, we can construct the confidence interval:
Confidence Interval = Sample Mean ± Margin of Error
Sample Mean = 193
Confidence Interval = 193 ± 12.49
Rounding all values to the nearest whole number, the 95% confidence interval for the mean number of text messages sent per day is approximately:
Confidence Interval = (181, 205)
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For the complex number z = (5sqrt(3))/4 - 5/4 * i what is the polar form
Answer: 3
Step-by-step explanation:
The required polar form of the equation is \(Z = 5/2cos30 - 5/2sin30i.\)
For the complex number z = (5sqrt(3))/4 - 5/4 * i the polar form is to be determined.
The number that constitutes real and imaginary numbers are called complex numbers. The standard form of complex number = a + bi
\(z = 5\sqrt{3}/4 - 5/4i\)
the polar form complex numbner can be given as
\(z = rcos\theta +rsin\theta i\) - - - - - -(1)
where r = \(\sqrt{a^2+b^2}\)
and \(\theta=tan^-\frac{b}{a}\)
Since a = 5√3/4 and b = -5/4
\(r = \sqrt{(5\sqrt{3}/4)^2+(5/4)^2}\)
r = 10/4
r = 5/2
Now,
\(\theta=tan^-\frac{b}{a}\)
\(\theta=tan^-\frac{-5/4}{5\sqrt{3}/4 }\\\theta=tan^-\frac{1}{\sqrt{3} }\\\theta=tan^-(-tan30)\\\theta=-30\)
Now the polar form is given by substituting the values of r and \(\theta\) in equation 1
Here,
\(z = 5/2cos30 +5/2sin(-30)i\\z = 5/2cos30-5/2sin30 i\)
Thus, the required polar form of the equation is \(Z = 5/2cos30 - 5/2sin30i.\)
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hep me out with this question i will give you brainly!
Answer:
c because have great day
The graph of an exponential function is shown on the grid. Which dashed line is an asymptote for the graph?
Answer:
It’s line S
Step-by-step explanation:
Don’t ask how Ik, just trust the process...Nd quizzez
The asymptote for the given exponential function shown in the graph is line r. Option b is correct.
What is an asymptote?An asymptote is a straight line or curve that a graph approaches but never touches. Asymptotes can occur in various types of graphs, including functions, equations, and curves. In a function, an asymptote can occur when the function approaches a certain value as the input variable approaches infinity or negative infinity.
Here,
Asymptotes can be vertical, horizontal, or slanted, and they can occur on either side of the graph. Asymptotes are important in mathematical analysis, as they can help determine the behavior of a function or equation as the input variable increases or decreases without bounds.
So, the asymptote for the given exponential function shown in the graph is line r. Option b is correct.
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A math tutor charges a flat traveling fee plus an additional fee per hour of tutoring. The graph shows the linear
relationship between the number of hours spent tutoring and the total amount of money earned by the tutor,
including the traveling fee.
70-
D60
£50-
40
30
20-
10
1 2 3 4 5 6 7 X
Hours
Which statement is true?
O a The additional fee per hour of tutoring is $10.
Ob The traveling fee is $20.
Oc The traveling fee is $10.
Od The additional fee per hour of tutoring is $15.
Money Earned
Answer:
\(\bigodot\:a \:\) The additional fee per hour of tutoring is $10
Step-by-step explanation:
Option a is the correct answer.
In circle d, which is tangent to the circle? line g h line segment a b cd ef
The line that is tangent to the circle D is: line segment AB.
What does a circle tangent mean?The straight line that "just touches" the curve at a particular location is known as the tangent line (or simply tangent) to a plane curve in geometry. It was described by Leibniz as the path connecting two points on a curve that are infinitely near together.
At any given location, a line that is tangent to a circle contacts the curve of the circle.See image 1 below, which explains what a tangent is.
According to the second diagram's representation of circle D, line segment AB touches circle D's curve at point B.
As a result, line segment AB is the line that is perpendicular to the circle D.
Your question is incomplete but most probably your full question was
Circle D is shown. Line segment F E goes through point D. Line segment C D is shown. Line segment G H goes from one side of the circle to the other side. Line segment A B is outside of the circle and intersects the circle at point B. In circle D, which is tangent to the circle? Line G H Line segment A B CD EF
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Answer:
B
Step-by-step explanation:
Line segment AB