Answer:
x = 6
Step-by-step explanation:
.16x + 2 * .02 = (x + 2) * .17
.16x + .4 = .17x + .34
.06 = .01x
6 = x
X^2 + y^2 = 169 and y = -5 as a graph and where are the coordinates of intersection
Step-by-step explanation:
please mark me as brainlest
only a genius can solve it !!
[tex] \frac{ \cos(A) }{1 - \sin(A) } + \frac{ \sin(A) }{1 - \cos(A) } + 1 = \frac{ \sin(A) \cos(A) }{(1 - \sin(A)(1 - \cos(A)} [/tex]
[tex]\text{L.H.S}\\\\=\dfrac{\cos A}{1-\sin A} + \dfrac{\sin A}{1-\cos A} +1\\\\\\=\dfrac{\cos A(1-\cos A) + \sin A(1-\sin A) + (1-\sin A)(1 - \cos A)}{(1-\sin A)(1 -\cos A)}\\\\\\=\dfrac{\cos A - \cos^2 A + \sin A - \sin^2 A + 1 - \cos A - \sin A + \sin A \cos A}{(1 -\sin A)(1 - \cos A)}\\\\\\=\dfrac{-(\sin^2 A + \cos^2A) +1 + \sin A \cos A}{(1 - \sin A)(1 - \cos A)}\\\\\\=\dfrac{-1 + 1 + \sin A \cos A }{(1 - \sin A)((1 - \cos A)}\\\\\\=\dfrac{0+ \sin A \cos A}{(1 - \sin A)(1 - \cos A)}\\[/tex]
[tex]=\dfrac{\sin A \cos A}{(1 - \sin A)(1 - \cos A)}\\\\\\=\text{R.H.S}\\\\\text{Proved.}[/tex]
A rational expression simplifies to 3. the denominator of the original expression is given. which polynomial is the numerator?
The polynomial within the numerator is 9x²+45x+54.
Given the denominator of the initial expression is [tex]\frac{?}{3x^2+15x+18}[/tex] and also the rational expression simplifies to three.
A mathematical expression which will be rewritten to a rational fraction, an algebraic fraction specified both the numerator and therefore the denominator are polynomials. and a polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables.
Let's take the polynomial within the numerator is k.
So, rewrite the given expression as
[tex]\frac{k}{3x^2+15x+18}=3[/tex]
or it also can be written as
[tex]\frac{k}{3x^2+15x+18}=\frac{3}{1}[/tex]
Cross multiply either side as a×d=b×c where a=k, b=3x²+15x+18, c=3 and d=1 and acquire
k=3(3x²+15x+18)
Simplify the above expression,
k=9x²+45x+54
Hence, the polynomial within the numerator within the given expression [tex]\frac{?}{3x^2+15x+18}[/tex] which is simplified to 3 is 9x²+45x+54.
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Answer:a
Step-by-step explanation:
Find all solutions of the equation in the interval [0, 2π).
Answer:
x=0
Step-by-step explanation:
[tex]4 \cos(x) = - \sin {}^{2} (x) + 1[/tex]
[tex]4 \cos(x) = 1 - \sin {}^{2} (x) [/tex]
[tex]4 \cos(x) = \cos {}^{2} (x) [/tex]
[tex]4 \cos(x) - \cos {}^{2} (x) = 0[/tex]
[tex] \cos(x) (4 - \cos(x) ) = 0[/tex]
[tex] \cos(x) = 0[/tex]
[tex]x = 0[/tex]
[tex]4 - \cos(x) = 0[/tex]
[tex] \cos(x) = 4[/tex]
There is no solution here because cosine is undefined it the range is not between -1 and 1 so the only answer is 0.
What is the factored form of the following expressions?
x2 – x – 42
Answer:
(x-7)(x+6)
Step-by-step explanation:
Can someone look at this image ?
Answer:
3x-2y=13
Step-by-step explanation:
Find the measure of x.
Answer:
25.99
Step-by-step explanation:
SOH CAH TOA
(sin = opposite / hypotenuse
cos = adjacent / hypotenuse
tan = opposite / adjacent)
For the angle measurement provided (38 degrees), we know the opposite leg value, and we need to find the hypotenuse
the measurement of sin (opposite / hypotenuse) relates these two measurements
we can plug in our known values into sin:
sin = opposite / hypotenuse
sin (38) = 16 / x
(note: sin 38 = 0.61566147532, which we can round to 0.61566)
0.61566 = 16 / x
· x ·x {multiply both sides by x to get rid of fraction}
0.61566(x) = 16
÷ 0.61566 ÷0.61566 {divide both sides by 0.61566 to isolate 1x}
x = 25.9883702043
{round to nearest hundredth}
x = 25.99
so, the measure of x is 25.99 {rounded to the nearest hundredth}
hope this helps!! have a lovely day :)
Answer:
cosx=adjacent/hypotenuse
triangle angle =180-(90+38)
=52°
cos(52°)=16/x
x=16/cos52
x≈23.373
Give the equation of a line that goes through the point ( 4 , 9 ) and is parallel to the line − 3 x + 7 y = 21 .
Answer:
[tex]\sf y=\dfrac{3}{7}x+\dfrac{51}{7}[/tex]
Step-by-step explanation:
Given equation: -3x + 7y = 21
Slope-Intercept Form: y = mx + b -
where:
m is the slopeb is the y-intercept (when x = 0)Note: parallel lines have the same slope.
1. Rewrite the given equation in slope-intercept form:
[tex]\sf -3x + 7y = 21\ \textsf{[add 3x to both sides]}\\\\-3x + 3x + 7y = 21 + 3x\\\\7y = 3x + 21\ \textsf{[divide both sides by 7]}\\\\\dfrac{7y}{7}=\dfrac{3x+21}{7}\\\\\implies y=\dfrac{3}{7}x+3[/tex]
Here, this equation has a slope of ³⁄₇ and a y-intercept of 3.
2. Find the equation of the parallel line:
substitute the point (4, 9) into the equation to find the value of b
[tex]\sf y=\dfrac{3}{7}x+b\\\\9=\dfrac{3}{7}(4)+b\\\\9=\dfrac{12}{7}+b\\\\\dfrac{63}{7}-\dfrac{12}{7}=\dfrac{12}{7}-\dfrac{12}{7}+b\\\\\dfrac{51}{7}=b[/tex]
[tex]\sf \textsf{Equation:}\ y=\dfrac{3}{7}x+\dfrac{51}{7}[/tex]
3. Check your work:
[tex]\sf y=\dfrac{3}{7}x+\dfrac{51}{7}\\\\9=\dfrac{3}{7}(4)+\dfrac{51}{7}\\\\9=\dfrac{12}{7}+\dfrac{51}{7}\\\\9=\dfrac{63}{7}\\\\9=9\ \checkmark[/tex]
[tex]\sf \textsf{Therefore, the equation of the parallel line is:}\ y=\dfrac{3}{7}x+\dfrac{51}{7}[/tex]
Another example:
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Answer:
[tex]\sf y=\dfrac{3}{7} x+\dfrac{51}{7}[/tex]
Step-by-step explanation:
First, write the given equation in slope-intercept form. That is, you can make y the subject in the given equation.
Slope intercept form
y = mx + c
Here,
m = slope
c = y-intercept
Let us write the given equation in slope-intercept form.
− 3x + 7y = 21
Add 3x to both sides.
7y = 3x + 21
Divide both sides by 7.
[tex]\sf y=\dfrac{3}{7}x +\dfrac{21}{7} \\\\y=\dfrac{3}{7}x +3[/tex]
We know that the slopes of parallel lines are equal. Therefore, the slope(m) of the new line is 3/7.
The new line is going through ( 4, 9 ). Using that, let us find the value of c (y-intercept), by substituting the values of m, y, and x.
( 4, 9 ) → ( x , y )
m → 3/7
Let us find the value of c
[tex]\sf y = mx+c\\\\9 =\dfrac{3}{7}*4+c\\\\ 9=\dfrac{12}{7}+c\\\\ 9-\dfrac{12}{7}=c\\\\\dfrac{63-12}{7} =c\\\\\dfrac{51}{7} =c[/tex]
And now let us write the equation of the new line.
[tex]\sf y =mx+c\\\\\sf y=\dfrac{3}{7} x+\dfrac{51}{7}[/tex]
If T: (x, y) → (x + 6, y + 4), then T-1: (x,y) → _____.
( x/6, y/4 )
( x - 4, y - 6)
(-6 x, -4 y)
( x - 6, y - 4)
T is a linear transformation from R²→R² with basis {(1,0),(0,1)}
T: (x,y)→(x+6,y+4)
A function from one vector space to another that preserves the underlying (linear) structure of each vector space is called a linear transformation.
Then the vector (1,0) goes to (1+6,4)=(7,4)=7(1,0)+4(0,1)
and the vector (0,1) goes to (6,1+4)=(6,5)=6(1,0)+5(0,1)
So, the matrix of the transformation is
[tex]\left[\begin{array}{ccc}7&6\\4&5\end{array}\right][/tex]
The inverse of the matrix is
[tex]\left[\begin{array}{ccc}\frac{5}{11}&\frac{-6}{11}\\ \\\frac{-4}{11}&\frac{7}{11}\end{array}\right][/tex]
So, the Inverse Transformation is given by
[tex]T^{-1}(x,y)=\left[\begin{array}{ccc}\frac{5}{11}&\frac{-6}{11}\\ \\\frac{-4}{11}&\frac{7}{11}\end{array}\right]\left[\begin{array}{ccc}x\\y\end{array}\right] =(\frac{5x-6y}{11}, \frac{-4x+7y}{11})[/tex]
So, no option is correct. And the answer is
[tex]T^{-1}(x,y)=(\frac{5x-6y}{11}, \frac{-4x+7y}{11})[/tex]
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The sum of two numbers is 48. If one number is three more than twice the second number, which of the following is the
smaller number?
O 24
O 15
O 30
O 33
Answer:
15 (second option listed)
y = 15
x = 30
Step-by-step explanation:
setting up this statement algebraically:
[where x = one of our numbers, y = other number]
x + y = 48
x = (2y + 3)
x = 2y + 3
plug x [now in terms of y] into the original equation
(2y + 3) + y = 48
3y + 3 = 48
- 3 - 3
3 y = 45
÷3 ÷3
y = 15
from this value, we can plug it back into the y-value of the original equation to find our x-value
x + y = 48
x + 15 = 48
- 15 - 15
x = 33
{to check: 33 is 2y + 3}
we know that y = 15 (smaller number) and that x = 33 (larger number)
so, the solution to the question of which is the smaller number is 15
A pair of equations is shown below.
Answer: (2,5)
Step-by-step explanation: Step 1: Identify key concepts for Part A
y=7x-9
Slope: 7
y int. : -9
y=3x-1
Slope: 3
y int. : -1
Since you know this information, you can plot the points and graph it.
Part B
To solve a system of equations, you need to identify the point whereby the two graphs intersect, and since you're solving it graphically, just find the point of intersection. You should get an answer of: (2,5)
(x=2) and (y=5)
What is the probabily of the 90th percentile given mean of 262 and a standard deviation of 45
The probability of the 90th percentile given a mean of 262 and a standard deviation of 45 is 319.672
Here,
The formula for the percentile probability is
[tex]P=\mu+z\sigma[/tex]
P=262 + 1.2816(45)
P = 319.672
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Use the drawing tool(s) to form the correct answer on the provided graph.
Graph the solution to the following linear inequality in the coordinate plane.
5x - y > -3
27
Drawing Tools
Select
Line
Dashed Line
Shaded Region
Click on a tool to begin drawing.
10
8
6
The solution to the inequality 5x - y > -3 is shown in the graph.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
An inequality shows the non equal comparison of two or more variables and numbers.
The solution to the inequality 5x - y > -3 is shown in the graph.
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What are “like terms”? Why can we only add like terms?
13.)What is the closure property? What does it have to do with adding, subtracting, and multiplying polynomials?
Answer:
Like terms are mathematical terms that contain the same variables. We combine like terms, because it simplifies algebraic expressions.
Closure property is the term for when you add or multiply two whole numbers together, and the result is always just a whole number. It is related to adding, subtracting, and multiplying polynomials, because when something is closed, the output will result in being the same type of object as the inputs.
Step-by-step explanation:
Like terms: When combining like terms, we add their coefficients. For instance, if we have 3y and 4y, we get 7y. That is because we added (3+4) to get 7, and plugged in the variable "y".
Closure property: Adding, subtracting, or multiplying two polynomials will output a polynomial.
A gas mixture has a total pressure of 0.56 atm and consists of He and Ne. If the partial pressure of the He in the mixture os 0.27 atm. What is the partial pressure of the Ne in the mixture?
The partial pressure of the Ne in the mixture is 0.29 atm if the as mixture has a total pressure of 0.56 atm and consists of He and Ne.
What is Dalton's law?Dalton's law states that the total partial pressures of all the gases in a mixture of non-reacting gases at a constant temperature equal the pressure the mixture exerts.
We have:
A gas mixture has a total pressure of 0.56 atm and consists of He and Ne. If the partial pressure of the He in the mixture os 0.27 atm.
According to Dalton's law
Total pressure = partial pressure of He + Partial pressure of Ne
0.56 = 0.27 + P(Ne)
P(Ne) = 0.29 atm
Thus, the partial pressure of the Ne in the mixture is 0.29 atm if the as mixture has a total pressure of 0.56 atm and consists of He and Ne.
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One polygon has a side of length 2 feet. A similar polygon has a corresponding side of length 4 feet. The
ratio of the perimeter of the smaller polygon to the larger is
021
01/2
014
Answer:
the largest is 014 because I did it and the teacher said it is correct
Step-by-step explanation:
teacher checked work
I dive to 17 metres for 23 minutes. after a 30 minute surface interval, i plan to dive to 16 metres. what is the maximum allowable time for the second dive
Answer:
i don't know
Step-by-step explanation:
i don' know
Jej pls help someone didnt get right b4 i give 50 points
Answer:
Mixed Number: 11 1/5
Improper Fraction: 56/5
Step-by-step explanation:
Given:
It takes 3/7 tonnes of sand to make a tonne of concrete.
Mason has 4 4/5 tonnes of sand.
To Find:
How much concrete, in tonnes, can he make?
Give your answer as a fraction in its simplest form.
Solve:
By the given , takes 3/7 tonnes of sand = tonne of concrete.
Thus, we divide the total of tonnes of sand Mason have by how many it takes to make a tonne of concrete.
Hence, we have;
[tex]4\frac{4}{5}\div \frac{3}{7}[/tex]
Convert to improper fraction;
[tex]=\frac{24}{5}\div \frac{3}{7}[/tex]
Using the fraction rule;
[tex]\frac{a}{b}\div \frac{c}{d}=\frac{a}{b}\times \frac{d}{c}[/tex]
[tex]=\frac{24}{5}\times \frac{7}{3}[/tex]
Cross-cancel common factor - 3
[tex]=\frac{8}{5}\times \frac{7}{1}[/tex]
Multiply fraction:
[tex]=\frac{56}{5}[/tex]
Convert improper to mixed number:
[tex]=11\frac{1}{5}[/tex]
Hence, the answer is [tex]\mathrm{11\frac{1}{5}\;or\;\frac{56}{5} }[/tex]
RevyBreeze
Answer:
[tex]\rm Improper \ fraction : \sf \sf \dfrac{56}{5} \ of \ concrete[/tex]
[tex]\rm Mixed \ fraction: \sf 11\dfrac{1}{5} \ of \ concrete[/tex]
Explanation:
[tex]\sf concrete = total \ tones \ of \ sand \ \div \ unit \ rate \ of \ sands \ required \ to \ make \ concrete[/tex]
Here given:
total tones of sand = 4 4/5unit rate of sand required = 3/7Concrete:
[tex]\sf \rightarrow 4\dfrac{4}{5} \div \dfrac{3}{7}[/tex]
[tex]\rightarrow \sf \dfrac{24}{5}\div \dfrac{3}{7}[/tex]
[tex]\rightarrow \sf \dfrac{24}{5}\times \dfrac{7}{3}[/tex]
[tex]\rightarrow \sf \dfrac{56}{5}[/tex]
[tex]\rightarrow \sf 11\dfrac{1}{5}[/tex]
what is the area of the trapezium?
Answer:
156 cm²
Explanation:
This figure is a trapezium.
Formula of Area of Trapezium = 1/2 × (a + b) × height
Here given:
a = 9 cmb = 30 cmh = 8 cm==============
Area of trapezium: 1/2 × (9 + 30) × 8 = 156 cm²
Answer:
area of the trapezium is 156
Step-by-step explanation:
Which table represents a linear function?
Answer:
The table on the far left is a linear function.
Step-by-step explanation:
The table on the far left is the function
[tex]y = \frac{1}{2} x[/tex]
Lucy is knitting a blanket and needs to buy some more yarn. at her local craft store, 2 skeins of yarn cost $7 and 8 skeins of yarn cost $28. what is the constant of proportionality in this direct variation?
Answer:
4
Step-by-step explanation:
Proportionality between skein values
8:2=4:1
Proportionality between cost values
28:7=4:1
The variation(both the skein values and cost values) has the constant of 4 ie the 1st skein value × 4= the last skein value & the 1st cost value × 4=the last cost value
A/n ____ is a part of a circle that represents an angle.
Answer:
An Arc is a part of a circle that represents an angle.
. An elevator in a building starts with five passengers and stops at seven floors. Say every passenger is equally likely to get off at each floor and all the passengers leave independently of each other. a. How many ways are there for the passengers to be assigned a floor? b. How many ways are there for the passengers to be assigned a floor but no two passengers are on the same floor?
There are 16807 number of ways the passengers to be assigned a floor and there are 2520 number of ways the passengers to be assigned a floor but no two passengers are on the same floor.
Given that an elevator starts with five passengers and stops at the seven floors of a building.
From the given information, the total number of floors n=7.
The number of passengers r = 5.
(a) Compute the number of ways that 5 passengers can be assigned to seven floors.
Here, repetition is allowed.
From the known information, if r numbers are selected from n number of observations then the total number of observations that can be drawn from n number of observations is [tex]n^r[/tex].
If 5 passengers can be assigned to seven floors is 7⁵ = 16807.
(b) Compute the number of ways that the passengers to be assigned a floor but no two passengers are on the same floor.
Here, repetition is not allowed.
If 5 passengers can be assigned to seven floors but no two passengers are on the same floor is 7x6x5x4x3 = 2520.
Hence, the number of ways that 5 passengers can be assigned to seven floors is 16807, and the number of ways that the passengers to be assigned a floor but no two passengers are on the same floor is 2520.
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Line q and m are cut by transversal lines j and k. The line and the measures of some of the angles created by the intersections of the lines are shown in the diagram below. What is the measure, in degrees, of angle 1?
Answer:
70
Step-by-step explanation:
180 minus 110 is 70
straight lines are 180 degrees
Persons taking a 30-hour review course to prepare for a standardized exam average a score of 620 on that exam. persons taking a 70-hour review course average a score of 780. based on these two data points, create a linear equation for the function that describes how score varies as a function of time. use this function to predict an average score for persons taking a 43-hour review course. round your answer to the tenths place.
Answer:
Answer for linear equation: y=4x+500 and Avg score for persons taking 43-hour review course is 672
\frac { 6 ^ { n + 2 } - 6 ^ { n } } { 6 ^ { n + 1 } + 6 ^ { n } }
Solve this ...
this is the question of laws of indices(exponent)
Work Shown:
[tex]m = \frac{6^{n+2}-6^{n}}{6^{n+1}+6^{n}}\\\\m = \frac{6^{n}*6^2-6^{n}}{6^{n}*6^1+6^{n}}\\\\m = \frac{6^{n}*36-6^{n}}{6^{n}*6+6^{n}}\\\\m = \frac{6^{n}(36-1)}{6^{n}(6+1)}\\\\m = \frac{6^{n}(35)}{6^{n}(7)}\\\\m = \frac{35}{7}\\\\m = 5\\\\[/tex]
Therefore,
[tex]\frac{6^{n+2}-6^{n}}{6^{n+1}+6^{n}}=5\\\\[/tex]
DNA molecules include the base units adenine, thymine, cytosine, and guanine
(A, T, C, and G). The sequence of base units along a strand of DNA encodes
genetic information. In how many different sequences can A, T, C, and G be
arranged along a short strand of DNA that has only 5 base units?
The number of ways different the sequences of adenine, thymine, cytosine and guanine can be arranged along a short strand of DNA with 5 base units is 120
What is permutation?
Permutation is the number of ways of arrangement for a given set.
The formula for a permutation is given as P(n, r) = n! / (n-r)!
Where n = items chosen from = 5
r is the number of items = 4
Substitute values into the formula
P(5, 4) = [tex]\frac{5!}{5-4!}[/tex]
P(5,4) = [tex]\frac{5 * 4* 3*2*1}{1}[/tex]
P(5,4) = [tex]\frac{120}{1}[/tex]
P(5,4) = 120
Therefore, the number of ways different the sequences of adenine, thymine, cytosine and guanine can be arranged along a short strand of DNA with 5 base units is 120
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Answer:
The answer is actually 120.
Step-by-step explanation:
I have the keysheet to the questions.
Please help i dont get this at all so please i will highly appreciate it .Thank youuu!!!
Answer:
I'm pretty sure it is d... .......
Kayla has 18 bottles of bubbles. She wants to give 2 bottles to each of her 6 friends. How many bottles will she have left over? Which expression solves the problem?
Expressions:
(18/2)/6
(18/2)+6
(18*2)-6
(18*2)+6
Answer: she would have 6 bottles left, (18/2)/6
Step-by-step explanation:
she has 18 bottles, when you divide it by two, she could give two bottles to 9 people. but, she only wants to give it to 6 friends. meaning that she would be left with 3 pairs of bubbles. as in, 6 bottles.
The lowest point in the United States is the Sierra Nevada in California. Its altitude is 300 feet below the sea level. Identify the absolute value of the point. (Sierra Nevada).
Answer:
300 feet
Step-by-step explanation:
The absolute value of a number is defined as that number's distance from 0 (the origin) on a number line, regardless of direction.
In this case, the origin can be represented by sea level. Since the lowest point of 300 feet is taken by reference to sea level, it can be said that the absolute value of the point is 300 feet, since this represents its vertical distance from sea level.
Hope this helps!
