Answer:
1) x=1; x= 0 is an extraneous solution
Step-by-step explanation:
5 = 4x + 1
5 = 4 x 1 + 1
5 = 5
x = 1
______________________
x x^2
0 x 0^2
0 x 0 = 0
x = 0
:)
Which lines are perpendicular to the line y – 1 = one-third(x 2)? check all that apply. y 2 = –3(x – 4) y − 5 = 3(x 11) y = -3x – five-thirds y = one-thirdx – 2 3x y = 7
Answer:
a and c
Step-by-step explanation:
y - 1 = 1/3(x - 2)
y = 1/3x - 4/3
Only the slope matters in this problem. If the original equation has a slope of 1/3, you need to use the reciprocal and negate it. So the perpendicular slope would be -3.
a. y 2 = –3(x – 4)
b. y − 5 = 3(x 11)
c. y = -3x – five-thirds
d. y = one-thirdx – 2 3x y = 7
So a and c are perpendicular to y - 1 = 1/3(x - 2)
I need help with this question. thanks.
Answer:
x<40
Step-by-step explanation:
x+10<50
x+10-10<50-10
x<40
very confused with this
Answer:
y=3x+3
Step-by-step explanation:
So generally you'll have a linear equation in the form of slope-intercept which looks like: y=mx+b, where m is the slope, and b is the y-intercept. the y-intercept, is the value of y, when x=0, which is going to be the constant b, because mx will be 0, because m * 0 = 0. m is the slope because as x increases by 1, the y-value increases by m, which in definition is the slope, how much a function increases as x increases by 1. So if you look at the table when x goes from -1 to 0, the y value goes from 0 to 3 or an increase in 3, and the same happens when x goes from 0 to 1. So the slope is 3, and the y-intercept as mentioned before is the value of y when x=0, which in this case is 3, which can be determined by looking at the table (look at y when x=0, it's 3). So this gives you the formula y=3x+3
A man has 1 coins in his pocket, all of which are dimes and quarters. Aif the total value of his change is $2.75, how many dimes and how many quarters they are
Using a system of equations, it is found that there are 5 dimes and 9 quarters in his pocket.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, the variables are given as follows:
Variable x: number of dimes in his pocket.Variable y: number of quarters in his pocket.He has a total of 14 coins, hence:
x + y = 14 -> y = 14 - x.
They are worth $2.75, hence, considering the value of each coin(dimes $0.1 and quarters $0.25), we have that:
0.1x + 0.25y = 2.75
Since y = 14 - x:
0.1x + 0.25(14 - x) = 2.75
x = (0.25*14 - 2.75)/0.15.
x = 5.
y = 14 - x = 14 - 5 = 9.
There are 5 dimes and 9 quarters in his pocket.
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Three numbers in the interval $\left[0,1\right]$ are chosen independently and at random. What is the probability that the chosen numbers are the side lengths of a triangle with positive area
Let [tex]a,b,c[/tex] be the randomly selected lengths. Without loss of generality, suppose [tex]a
[tex]P(A + B \ge C) = P(A + B - C \ge 0)[/tex]
where [tex]A,B,C[/tex] are independent random variables with the same uniform distribution on [0, 1].
By their mutual independence, we have
[tex]P(A=a,B=b,C=c) = P(A=a) \times P(B=b) \times P(C=c)[/tex]
so that the joint density function is
[tex]P(A=a,B=b,C=c) = \begin{cases}1 & \text{if }(a,b,c)\in[0,1]^3 \\ 0 & \text{otherwise}\end{cases}[/tex]
where [tex][0,1]^3=[0,1]\times[0,1]\times[0,1][/tex] is the cube with vertices at (0, 0, 0) and (1, 1, 1).
Consider the plane
[tex]a + b - c = 0[/tex]
with [tex](a,b,c)\in\Bbb R^3[/tex]. This plane passes through (0, 0, 0), (1, 0, 1), and (0, 1, 1), and thus splits up the cube into one tetrahedral region above the plane and the rest of the cube under it. (see attached plot)
The point (0, 0, 1) (the vertex of the cube above the plane) does not belong the region [tex]a+b-c\ge0[/tex], since [tex]0+0-1=-1<0[/tex]. So the probability we want is the volume of the bottom "half" of the cube. We could integrate the joint density over this set, but integrating over the complement is simpler since it's a tetrahedron.
Then we have
[tex]\displaystyle P(A+B-C\ge0) = 1 - P(A+B-C < 0) \\\\ ~~~~~~~~ = 1 - \int_0^1\int_0^{1-a}\int_{a+b}^1 P(A=a,B=b,C=c) \, dc\,db\,da \\\\ ~~~~~~~~ = 1 - \int_0^1 \int_0^{1-a} (1 - a - b) \, db \, da \\\\ ~~~~~~~~ = 1 - \int_0^1 \frac{(1-a)^2}2\,da \\\\ ~~~~~~~~ = 1 - \frac16 = \boxed{\frac56}[/tex]
Based on the data, which table shows a proportional relationship?
Based on the data, table that shows a proportional relationship is the first table.
What is proportional?Data is said to be proportional if it increases or decreases at a constant rate.
What table has proportional data?The first table has proportional data because the height increases by 5 centimeters everyweek, which shows a constant rate.
Note: This question is incomplete; below I attach the missing section:
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In the diagram below, all angles are given in
degrees (°).
Find the value of x.
60
x +90
X
3x
Not drawn accurately
Answer:
30°
Step-by-step explanation:
x + 90 = 2 × 60 ( angle at center = 2 × angle at circumference.)
x +90 = 120
x = 120-90
x = 30°
the area of a quadrilateral whose vertices is ABCD taken in order are (1,2) (-5,6) (7,-4) and (-2,t) be 0 ,find the value of t
PLEASE ME HELP ASAP THANK YOUUU
Answer:
<3 and <4
Step-by-step explanation:
From the diagram above,
Exterior angles are angles formed outside the triangle.
The angles are: <3 and <4
A coin is flipped, and a number cube is rolled. What is the probability of getting tails on the coin and an even number on the number cube?
A= 1/12
B= 1/8
C=1/4
D= 1/2
The probability of getting a tail on the coin and an even number on the number cube is 1/4.
option C is the correct answer.
What is probability?It is the chance of an event to occur from a total number of outcomes.
The formula for probability is given as:
Probability = Number of required events / Total number of outcomes.
We have,
The sample space for flipping a coin and rolling a cube dice.
S = (H, T) x (1, 2, 3, 4, 5, 6)
S = { (H, 1), (H, 2), (H, 3), (H, 4), (H, 5), (H, 6), (T, 1), (T, 2), (T, 3), (T, 4), (T, 5),
(T, 6) }
n(S) = 12
The number of outcomes of getting a tail and a number even number on the number cube.
= { (T, 2), (T, 4), (T, 6) }
= 3
The probability of getting tails on the coin and an even number on the number cube.
= 3/ 12
= 1/4
Thus,
The probability of getting a tail and an even number is 1/4.
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The sum of the measures of the angles of a triangle is 180°. The middle-sized angle measures 3° more than 2 times the smallest angle. The middle-sized angle measures 109° less than the largest angle. Find the measure of each angle.
Answer:
13° , 29° , 138°
Step-by-step explanation:
let x be the smallest angle , then
2x + 3 is the middle angle and
2x + 3 + 109 is the largest angle
summing the 3 angles and equating to 180
x + 2x + 3 + 2x + 3 + 109 = 180 , that is
5x + 115 = 180 ( subtract 115 from 180 )
5x = 65 ( divide both sides by 5
x = 13
2x + 3 = 2(13) + 3 = 26 + 3 = 29
2x + 3 + 109 = 29 + 109 = 138
the 3 angles are 13° , 29° , 138°
How would you set this problem up to find x?
Answer:
33x - 13 = 13x + 7
Step-by-step explanation:
If "G" is the midpoint of line FH, then both segments (lines FG and GH) must be the same length. Therefore, to find "x", you can set both segments equal to each other. After doing this, you can simplify and isolate to find "x".
FG = 33x - 13
GH = 13x + 7
FG = GH
33x - 13 = 13x + 7
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Assuming that your equation should}\\\huge\textbf{look like that: }[/tex]
[tex]\mathbf{33x - 13 = 13x + 7}[/tex]
[tex]\huge\textbf{If so:}[/tex]
[tex]\mathbf{33x - 13 = 13x + 7}[/tex]
[tex]\huge\textbf{SUBTRACT 13x to BOTH SIDES}[/tex]
[tex]\mathbf{33x - 13 - 13x = 13x + 7 - 13x}[/tex]
[tex]\huge\textbf{SIMPLIFY IT!}[/tex]
[tex]\mathbf{20x - 13 = 7}[/tex]
[tex]\huge\textbf{ADD 13 to BOTH SIDES}[/tex]
[tex]\mathbf{20x - 13 + 12 = 7 + 13}[/tex]
[tex]\huge\textbf{SIMPLIFY IT!}[/tex]
[tex]\mathbf{20x = 20}[/tex]
[tex]\huge\textbf{DIVIDE 20 to BOTH SIDES}[/tex]
[tex]\mathbf{\dfrac{20x}{20} = \dfrac{20}{20}}[/tex]
[tex]\huge\textbf{SIMPLIFY IT!}[/tex]
[tex]\mathbf{x = \dfrac{20}{{20}}}[/tex]
[tex]\mathbf{x = 1}[/tex]
[tex]\huge\text{Answer: \boxed{\mathsf{33x - 13 = 13x + 7}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
A simple random sample of size n=40 is obtained from a population with a mean of 20 and a standard deviation of 5. Is the sampling distribution normally distributed? Why?
If the sample size is n=40 ,mean of 20 and a standard deviation then the sampling distribution is normally distributed.
Given sample size is 40, sample mean is 20, sample standard deviation is 5.
We have to find whether the distribution is normally distributed or not.
Normal distribution is an arrangement of a data set in which most values cluster in the middle of the range and the rest taper off simultaneously towards either extreme. It may be one tailed or two tailed also.
Yes the given distribution whose sample size is 40, sample mean of 20 and sample standard deviation of 5 is normally distributed as the sample size is greater than 30.
Signs of normal distribution are:
Symmetric bell shapemean and median are equal both located at the center of the distribution68% approximately equals 68% falls within 1 standard deviation of the mean.Hence the sampling distribution is normally distributed.
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Which is the best estimate of StartRoot 47 EndRoot to the nearest tenth?
6.8
6.9
7.0
7.1
The closest value will be 6.9 since the value is close to 49
Square root of prime numbersThe square root of a number can both be negative or positive. According to the question, we are to determine the square root of 47
The square root of 47 must be between the square root of 36 and square root of 64
√36 = 6
√64 = 8
This shows that the answer must be between 6 and 8. Hence the closest value will be 6.9 since the value is close to 49
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Answer: 6.9
Step-by-step explanation: just did the test
0.127450980392 as fraction
[tex]\frac{1820728291}{14285714286}[/tex]
In the following exercises, simplify each expression.
779. Convert 83,000,000 scientific notation.
Answer:
The answer would be 8.3*10^7.
Step-by-step explanation:
This is because the beginning factor in scientific notation (in this case it is 8.3) must be no less than one, and no more than ten. Once we figured that out, we simply count the number of decimal points from 3 to the final 0. Try it yourself. You will discover that the resulting answer is 7 decimal movements. Now, since we are using scientific notation, we will want to multiply by ten to the power of the number of decimal movements (in this case it is 7.) And that's all! The answer is 8.3*10^7. I hope this helped (:
g Trigonometric substitution may useful when integrating the _____________ root of a sum or difference of two squares.
Trigonometric substitution may useful when integrating the integrals root of a sum or difference of two squares.
In arithmetic, trigonometric substitution is the substitution of trigonometric features for other expressions. In calculus, trigonometric substitution is a way of comparing integrals.
Moreover, one can also use trigonometric identities to simplify sure integrals containing radical expressions.
You can use trig substitution even when you do not have square roots. particularly, if you have an integrand that looks like an expression in the square roots proven inside the above table, then you can use trig substitution.
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Please help me with this question.....
[tex]\angle PYZ=116^{\circ}[/tex] (angles on a line add to 180 degrees)
[tex]\angle ZYQ=58^{\circ}[/tex] (angle bisector)
[tex]\angle XYQ=122^{\circ}[/tex] (angle addition postulate)
[tex]\angle QYP=58^{\circ}[/tex] (angle bisector)
Reflex [tex]\angle QYP=302^{\circ}[/tex] (an angle and its reflex angle add to 360 degrees)
Help 20 points please
Every week Marcela deposits $45 in a bank account that she opened with an initial
deposit of $250, so that after n weeks her balance (in dollars) is 250 + 45n. Her
brother Ronnie withdraws $30 each week from his own bank account, which he
opened with an initial deposit of $145, so that after n weeks his balance is 145-
30n. Express the ratio of Marcela's balance to Ronnie's as a rational function, and
simplify
The simplified form of the ratio of Marcela's balance to Ronnie's is [tex]\frac{50 + 9n}{29 -6n}[/tex]
Simplifying an expressionFrom the question, we are to express the ratio of Marcela's balance to Ronnie's as a rational function
From the given information,
Marcela's balance = 250 + 45n
and
Ronnie's balance = 145 - 30n
Thus,
The ratio of Marcela's balance to Ronnie's is
[tex]\frac{250 + 45n}{145 -30n}[/tex]
Simplifying
[tex]\frac{250 + 45n}{145 -30n}[/tex]
[tex]\frac{5(50 + 9n)}{5(29 -6n)}[/tex]
[tex]= \frac{50 + 9n}{29 -6n}[/tex]
Hence, the simplified form of the ratio of Marcela's balance to Ronnie's is [tex]\frac{50 + 9n}{29 -6n}[/tex]
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For the upcoming parade, Lauren needed to make her school's triangular flag into a larger, similar triangular flag. Using the information given, determine which (if any) similarity postulate she used in making her school's new flag. Pls help
The ratio of corresponding sides of the triangle are not in the same proportion, hence they are not similar.
What are similar triangles?Two triangles are said to be similar if they have the same shape and angles. Also, the ratio of their corresponding sides are to be in the same proportion.
From the image shown, if the triangles are similar, hence:
AB / DE = AC / DF = BC / EF
Hence:
5.6 / 4 = 4.9 / 3.5 ≠ 2.4 / 1.5
1.4 = 1.4 ≠ 1.6
The ratio of corresponding sides of the triangle are not in the same proportion, hence they are not similar.
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A right triangle is shown. The height and length of the hypotenuse are unknown and the length other side is 5 feet. The other angles measure 60 and 30 degrees.
From the side view, a gymnastics mat forms a right triangle with other angles measuring 60° and 30°. The gymnastics mat extends 5 feet across the floor. How high is the mat off the ground?
Five-halves ft
StartFraction 5 StartRoot 3 EndRoot Over 3 EndFraction ft
5 StartRoot 3 EndRoot
10
The height of the mat off the ground is 5 / √3 feet
How to find side of right angle triangle?The right angle triangle has an adjacent side of 5 feet.
The hypotenuse and height of the right triangle is unknown.
Therefore,
tan 30 = opposite/adjacent
tan 30 = h / 5
h = 5 tan 30
h = 5 × 0.57735026919
h = 2.88675134595
h = 2.89 feet
Therefore, it can be written in surd form as follows:
height = 5 × 1 / √3
height = 5 / √3
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Answer:
its B my good sir
Step-by-step explanation:
which one these grids is shaded red and blue
The grid that is shaded red and blue in ratio 1 : 2 is grid (c)
How to determine the grid?The complete question is in the image
The ratio is given as:
Red : Blue = 1 : 2
There are 12 squares in each grid.
This means that:
Red : Blue = 12 * 1/(1 + 2) : 12 * 2/(1 + 2)
Evaluate
Red : Blue = 4 : 8
The grid that has 4 red and 8 blue is (c)
Hence, the grid that is shaded red and blue in ratio 1 : 2 is grid (c)
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how would the expression x^3-64 be written using difference of cubes
The expression x³ - 64 can be rewritten using difference of cubes is; (x - 4)(x² + 4x + 16)
How to write an expression as difference of cubes?Difference of cubes can be rewritten in the form of;
a³ – b³ = (a – b)(a² + ab + b²)
So in this question, we are given;
x³ - 64 = x³ - (4)³
where a = x and b = 4
This gives us;
(x - 4)(x² + 4x + 4²)
⇒ (x - 4)(x² + 4x + 16)
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Find the lateral area of a cylinder that has a diameter of 18 mm and a height of 15 mm.
Answer:
848.23 mm²
Step-by-step explanation:
LA = πdh
LA = 3.14159 × 18 mm × 15 mm
LA = 848.23 mm²
Triangle A B C is shown. Side A C has a length of 27. Side C B has a length of 54.
Based on the diagram, which expresses all possible lengths of segment AB?
AB = 25
27 < AB < 81
AB = 85
AB< 27 or AB > 81
Answer:
27 < AB < 81
Step-by-step explanation:
By the triangle inequality theorem,
If CB is the longest, AB + 27 > 54, meaning AB > 27.
If AB is the longest, 27 + 54 < AB, meaning 81 < AB.
Thus, 27 < AB < 81
help meeeeeeeeeeeeeeeeee
Answer:
Step-by-step explanation:
Helpppp find the missing angles for 5 and 6
Answer:
5. 68 degrees :)
6. 55 degrees :)
Step-by-step explanation:
5.
A flat line is 180 degrees so we subtract to find x :)
Lets do that now :)
180 - 112 = 68
x = 68 degrees
6.
X will be the same as 55 degrees.
All lines are tipped the same what so that is why it is 55 degrees :)
Have an amazing day!!
Please rate and mark brainliest!!
The question is attached in the picture below. Pls help ASAP
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Your temporary equation: }[/tex]
[tex]\mathsf{5x + x = \ ?}[/tex]
[tex]\huge\textbf{We know: }[/tex]
[tex]\large\textbf{That ONE angle equals 90}^\circ\large\textbf{ and the whole entire angle is}\\\large\textbf{360}^\circ.[/tex]
[tex]\huge\textbf{Knowing that much information, we can}\\\\\huge\textbf{make the equation much easier to solve.}\\\\\\\huge\textbf{We will simplify the angle sides and it}\\\\\huge\textbf{should give you the answer behind the}\\\\\huge\textbf{the equal sign.}[/tex]
[tex]\mathbf{360^\circ - 90^\circ = \boxed{\mathbf{the\ mystery\ number\ behind\ the\ equal\ sign}}}[/tex]
[tex]\huge\textbf{Simplify it!}[/tex]
[tex]\mathbf{the\ mystery\ number\ behind\ the\ equal\ sign = \boxed{\bf 270}}}}[/tex]
[tex]\huge\textbf{New equation:}[/tex]
[tex]\mathbf{5x + x = 270^\circ}[/tex]
[tex]\huge\textbf{COMBINE the LIKE TERMS:}[/tex]
[tex]\mathbf{(5x + x) = 270^\circ}[/tex]
[tex]\mathbf{5x + x = 270^\circ}[/tex]
[tex]\huge\textbf{Remember a variable by itself is}\\\\\huge\textbf{understood as an invisible 1.}[/tex]
[tex]\huge\textbf{Anyway, back to answering the equation}[/tex]
[tex]\mathbf{5x + x}[/tex]
[tex]\mathbf{= 5x + 1x}[/tex]
[tex]\mathbf{= 6x}[/tex]
[tex]\huge\textbf{New equation:}[/tex]
[tex]\mathbf{6x = 270^\circ}[/tex]
[tex]\huge\textbf{DIVIDE 6 to BOTH SIDES:}[/tex]
[tex]\mathbf{\dfrac{6x}{6}=\dfrac{270}{6}}[/tex]
[tex]\huge\textbf{SIMPLIFY IT!}[/tex]
[tex]\mathbf{x = \dfrac{270}{6}}[/tex]
[tex]\mathbf{x = 45}[/tex]
[tex]\huge\textbf{Answer:}[/tex]
[tex]\huge\boxed{\mathsf{x = 45}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]Use the quadratic formula to determine the exact solutions to the equation.
6x2+4x−3=0
ye answer's here