You get everything you need from factoring the last expression:
[tex]x^4-y^4=-176\sqrt7[/tex]
The left side is a difference of squares, and we get another difference of squares upon factoring. We end up with
[tex]x^4-y^4=(x^2-y^2)(x^2+y^2)=(x-y)(x+y)(x^2+y^2)[/tex]
Plug in everything you know and solve for [tex]x-y[/tex]:
[tex]-176\sqrt7=(x-y)\cdot4\cdot22\implies x-y=\boxed{-2\sqrt7}[/tex]
Answer:
-2sqrt(7)
Step-by-step explanation:
Solution:
From the third equation, $x^4 - y^4 = -176 \sqrt{7}.$
By difference of squares, we can write
\[x^4 - y^4 = (x^2 + y^2)(x^2 - y^2) = (x^2 + y^2)(x + y)(x - y).\]Then $-176 \sqrt{7} = (22)(4)(x - y),$ so $x - y = \boxed{-2 \sqrt{7}}.$
ASAP!! Please help me. I will not accept nonsense answers, but will mark as BRAINLIEST if you answer is correctly with solutions.
Answer:
The logarithmic parent function is the only one with negative numbers in the range
Step-by-step explanation:
Hello,
These functions have been very well known, I remind you their graphs below
The logarithmic parent function is the only one with negative numbers in the range
range for square root is [tex]\mathbb{R^{+}}[/tex]
range for logarithmic is [tex]\mathbb{R}[/tex]
range for exponential is [tex]\mathbb{R^{+}}[/tex]
THAT S TRUE
The square root and logarithmic parent functions have the same domain
domain for square root is [tex]\mathbb{R^{+}}[/tex]
domain for logarithmic is [tex]\mathbb{R}[/tex]
THAT S WRONG
The square root parent function domain is the most restricted
domain for square root is [tex]\mathbb{R^{+}}[/tex]
domain for exponential is [tex]\mathbb{R^{+}}[/tex]
THAT S WRONG
All three parent functions have the same domain
domain for square root is [tex]\mathbb{R^{+}}[/tex]
domain for exponential is [tex]\mathbb{R^{+}}[/tex]
domain for logarithmic is [tex]\mathbb{R}[/tex]
THAT S WRONG
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
On a coordinate plane, a line goes through (negative 4, negative 1) and (0, 1). Square a is around (negative 5, negative 2), square b is around (negative 1, 1), square c is around (1, 2), and square d is around (4, 4). The linear equation y = one-half x + 1 is represented by the graphed line. A second linear equation is represented by the data in the table. A 2-column table with 4 rows. Column 1 is labeled x with entries negative 2, 0, 2, 4. Column 2 is labeled y with entries 7, 6, 5, 4. In which square is the solution located?
Answer: D
Step-by-step explanation:
The solution of the two equations does not exist since they are parallel.
What is Slope?Slope of a line is the ratio of the change in y coordinates to the change in x coordinates of two points.
Equation of a line in slope intercept form is y = mx + b, where m is the slope and b is y intercept.
Given linear equation of a line in slope intercept form as,
y = 1/2 x + 1
Here slope = 1/2 and y intercept = 1
y intercept is the y value of a point where it touches the y axis.
A second linear equation is to be found by using the values in the table.
Taking two points (2, 7) and (0, 6).
Slope = (6 - 7) / (0 - 2) = (-1) / (-2) = 1/2
Since the point (0, 6) is given, 6 is the y coordinate when the line touches the Y axis.
y intercept = 6
Equation of the second line is,
y = 1/2 x + 6
Since the slopes of two lines are equal, they are parallel.
There is no solution for two parallel lines.
Hence there is no solution for the linear equations given.
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The physical plant at the main campus of a large state university recieves daily requests to replace florecent lightbulbs. The distribution of the number of daily requests is bell-shaped and has a mean of 61 and a standard deviation of 11. Using the empirical rule (as presented in the book), what is the approximate percentage of lightbulb replacement requests numbering between 61 and 94?
Answer:
P(61≤ X≤94) = 49.85%
Step-by-step explanation:
From the given information:
The mean of the bell shaped fluorescent light bulb μ = 61
The standard deviation σ = 11
The objective of this question is to determine the approximate percentage of light bulb replacement requests numbering between 61 and 94 i.e P(61≤ X≤94)
Using the empirical (68-95-99.7)rule ;
At 68% , the data lies between μ - σ and μ + σ
i.e
61 - 11 and 61 + 11
50 and 72
At 95%, the data lies between μ - 2σ and μ + 2σ
i.e
61 - 2(11) and 61 + 2(11)
61 - 22 and 61 +22
39 and 83
At 99.7%, the data lies between μ - 3σ and μ + 3σ
i.e
61 - 3(11) and 61 + 3(11)
61 - 33 and 61 + 33
28 and 94
the probability equivalent to 94 is when P(28≤ X≤94) =99.7%
This implies that ,
P(28≤ X≤94) + P(61≤ X≤94) = 99.7%
P(28≤ X≤94) = P(61≤ X≤94) = 99.7 %
This is so because the distribution is symmetric about the mean
P(61≤ X≤94) = 99.7 %/2
P(61≤ X≤94) = 49.85%
Theresa has two brothers, Paul and Steve, who are both the same height. Paul says he is 16 inches shorter than times 1 1/3 Theresa’s height. Steve says he is inches shorter than times Theresa’s height. If they are both right, how tall is Theresa? write an expression to show how tall steve is
Answer:
Theresa is 58.82 in tall
Step-by-step explanation:
Steve: x=1.33y-6
x=72.24
PLZ HELP Which represents a quadratic function? f(x) = 2x3 + 2x2 – 4 f(x) = –7x2 – x + 2 f(x) = –3x + 2 f(x) = 0x2 + 3x – 3
Answer:
f(x) = -7x² - x + 2
Step-by-step explanation:
Quadratic functions are set up in the form ax² + bx + c. f(x) = 0x² + 3x -3 is also set up in this format but 0x² would simplify to 0 which means the equation is actually f(x) = 3x-3 and does not fit in the quadratic function format. The other equations are also not set up in ax² + bx + c.
Polynomial is an equation written as the sum of terms of the form kx^n.
where k and n are positive integers.
A polynomial with degree 2 is called a quadratic equation.
The quadratic equation is in the form of ax² + bx + c.
The equation that represents a quadratic equation is
f(x) = -7x² - x + 2.
It is in the form of ax² + bx + c
Where a = -7, b = -1, and c = 2
Option B is the correct answer.
What is a polynomial?Polynomial is an equation written as the sum of terms of the form kx^n.
where k and n are positive integers.
We have,
A polynomial with degree 2 is called a quadratic equation.
The quadratic equation is in the form of ax² + bx + c.
Now,
f(x) = 2x³ + 2x² - 4
This is not a quadratic equation since it has a degree of 3.
f(x) = -7x² - x + 2
This is a quadratic equation since its degree is 2.
It is in the form of ax² + bx + c
Where a = -7, b = -1 and c = 2
f(x) = -3x + 2
This is not a quadratic equation.
Its degree is 1.
f(x) = 0x² + 3x - 3
f(x) = 3x - 3
This is not a quadratic equation.
Thus,
The equation that represents a quadratic equation is
f(x) = -7x² - x + 2.
It is in the form of ax² + bx + c
Where a = -7, b = -1, and c = 2
Option B is the correct answer.
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If ABCD is a rectangle, calculate x as a function of α
Answer:
Step-by-step explanation:
The length of this triangle is 10 squares
and the width is 4 squares
The diagonals divide the rectangle into four triangles
These traingles are isoceles
Each two triangles facing each others are identical
<B = 90 degree
B = alpha + Beta
Let Beta be the angle next alpha
The segment that is crossing Beta is its bisector since it perpendicular to the diagonals wich means that:
Beta = 2x
Then B = alpha + 2x
90 = alpha +2x
90-alpha = 2x
x = (90-alpha)/2
Answer:
x = 90 - 2α
Step-by-step explanation:
Solution:-
- Consider the right angled triangle " ABD ". The sum of angles of an triangle is always "180°".
< BAD > + < ADB > + < ABD > = 180°
< ABD > = 180 - 90° - α
< ABD > = 90° - α
- Then we look at the figure for the triangle "ABE". Where " E " is the midpoint and intersection point of two diagonals " AC and BD ".
- We name the foot of the perpendicular bisector as " F ": " BF " would be the perpendicular bisector. The angle < BAE > is equal to < ABD >.
< ABD > = < BAE > = 90° - α ... ( Isosceles triangle " BEA " )
Where, sides ( BE = AE ).
- Use the law of sum of angles in a triangle and consider the triangle " BFA " as follows:
< ABF> + < BFA > + < BAF > = 180°
< ABF > = 180 - (90° - α) - 90°
< ABF > = α
Where, < BAF > = < BAE >
- The angle < ABD > = < ABE > is comprised of two angles namely, < ABF > and < FBE > = x.
< ABD > = < ABE > = < ABF > + x
90° - α = α + x
x = 90 - 2α ... Answer
what happens to the resistance as the conductor is made thicker
Answer:
The resistance decreases.
Step-by-step explanation:
The resistance decreases as the conductor is made thicker.
First of all, resistance is like some sort of an obstacle right?
So if the conductor is made thicker it will be easy for the electrons to pass through.
And if the conductor is made thinner it won't be easy for the electrons to pass through. Which makes the resistance increase as there will be collision between the electrons.
Hope this helped ;) ❤❤❤
How does the graph of g(x) =
X+4
-6 compare to the graph of the parent function )-te
g(x) is shifted 4 units right and 6 units up from f(x).
O g(x) is shifted 4 units right and 6 units down from f(x).
O g(x) is shifted 4 units left and 6 units up from f(x).
O g(x) is shifted 4 units left and 6 units down from f(x).
Answer:
O g(x) is shifted 4 units left and 6 units down from f(x).
Step-by-step explanation:
O g(x) is shifted 4 units left and 6 units down from f(x).
The graph of g(x) is shifted 4 units to the left and 6 units down from f(x).
What is Translation of Functions?Translation of functions is defined as the when each point in the original graph is moved by a fixed units in the same direction.
There are horizontal translation and vertical translation of functions.
Given functions are,
g(x) = 1/(x + 4) - 6
f(x) = 1/x
Here when a function f(x) changes to f(x + k) when it is translated k units left.
Here 1/x changes to 1/(x + 4).
So g(x) is shifted 4 units left.
Similarly a function f(x) changes to f(x) - k, if it is translated k units down.
So g(x) also shifted 6 units down.
Hence the correct option is D.
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Which of the following options could represent a possible set of interior angles of a triangle? 100°, 130°, and 130° 30°, 70°, and 80° 25°, 3°, and 35° 45°, 105°, and 120°
Answer:
2) 30, 70, 80
Step-by-step explanation:
Well there has to be 3 angles that all add up to 180°.
1)
100+130+130
=360
2)
30+70+80
= 180
3)
25+3+35
=63
4)
45 + 105 + 120
=150
150+120
270
A rectangle measures 6 cm by 4 cm. Another rectangle with adjacent sides 8 cm and x cm is geometrically similar to it. Find the two possible value of x.
Answer:
5 1/3 or 5.33333333333333333333333333333333333333333333333333333
Step-by-step explanation:
to find the scale factor, you must divide the two equal sides.
[tex]\frac{6}{8}[/tex]
which equals
[tex]\frac{3}{4}[/tex] or 0.75
Now, the way to get the value of x is to divide 4 by 3/4 0r 0.75
[tex]\frac{4}{0.75}[/tex]
Which equals
5.333 repeating or 5 1/3
Hope this helps. If you have any follow-up questions, feel free to ask.
Have a great day! :)
Plz help pre calc!!!!
Solve.
6x + y = 14
-2x - y = -4
Enter your answer, in the form (x, y), in the boxes.
Answer:
[tex]\huge\boxed{(2.5,\ -1)}[/tex]
Step-by-step explanation:
[tex]\underline{+\left\{\begin{array}{ccc}6x+y=14\\-2x-y=-4\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad4x=10\qquad\text{divide both sides by 4}\\.\qquad\dfrac{4x}{4}=\dfrac{10}{4}\\.\qquad\boxed{x=2.5}\\\\\text{put it to the first equation}\\6(2.5)+y=14\\15+y=14\qquad\text{substract 15 from both sides}\\15-15+y=14-15\\\boxed{y=-1}[/tex]
Answer:
x = 5/2, y = -1
Step-by-step explanation:
6x + y = 14
-2x - y = -4
Add the two equations together to eliminate y
6x + y = 14
-2x - y = -4
-----------------------
4x = 10
Divide by 4
4x/4 = 10/4
x = 5/2
Now solve for y
-2x -y = -4
-2( 5/2) -y = -4
-5 -y = -4
Add 5 to each side
-5+5 -y =-4+5
-y = 1
Divide by -1
y = 1
Amanda is cooking a turkey for dinner. The recipe says that the turkey should cook for 1\dfrac121 2 1 1, start fraction, 1, divided by, 2, end fraction hours. She has been cooking the turkey for 252525 minutes. According to the recipe, how many more minutes does the turkey need to cook?
Answer:
The turkey needs to cook for 5 more minutesStep-by-step explanation:
According to recipe, Amanda should cook for total of 1/2 hour which is 30 minutes. If she has been cooking for 25 minutes, the remaining time needed for the turkey to cook will be the difference between the total time and the time she has already spent in cooking.
[tex]minutes\ left = 30 minutes - 25 minutes\\\\munites\ left = 5 minutes[/tex]
Hence, the turkey needs to cook for 5 more minutes
What does the denominator of the fraction \dfrac23 3 2 start fraction, 2, divided by, 3, end fraction mean?
Answer: It represents that 2 will be divided into 3 equal parts.
Step-by-step explanation:
Numerator is the top number in a fraction. It represents the total item it has to divide.Denominator is the bottom number in a fraction. it represents the number of equal parts the item is divided into.The given fraction : [tex]\dfrac{2}{3}[/tex]
here, Numerator = 2
Denominator = 3
It represents that 2 will be divided into 3 equal parts.
i Will give brainliest
Answer: B
Step-by-step explanation:
Option A simplifies to 7/15
Option B simplifies to 11/21
If 1/2 is equal to .50, then when subtracted 7/15 would be equal to 0.46666667 and 11/21 would be equal to 0.52380952... meaning that 11/21 would be closer to 1/2 (or .50).
Hope this helps!
Please answer this in two minutes
Answer:
X = 59°Step-by-step explanation:
To find Angle X we use sine
sin∅ = opposite/ hypotenuse
From the question
WY is the opposite
WX is the hypotenuse
So we have
sin X = WY/ WX
sin X = 6/7
X = sin-¹ 6/7
X = 58.99
X = 59° to the nearest tenth
Hope this helps you
Answer:
x=arcsine (6/7) = 58.98 degrees
Step-by-step explanation:
Performing a trigonometrical function. We can find the value of the angle:
1) sin x =6/7
x=arcsine (6/7)
x= 58.98º
I WILL GIVE BRAINLIEST!!! A teacher is grading the final exam. He notices that the mean test score is 61, and the standard deviation is 10. The test scores were normally distributed. if there were 450 students in the data sample, how many would have a test score between 61 and 71 *Round your answer to the nearest full value.
Answer:
The number of students that would have a test score between 61 and 71 are 154 students
Step-by-step explanation:
The given information are;
The mean test score, μ = 61
The standard deviation, σ = 10
The sample size, n = 450
The z score is given as follows;
[tex]Z=\dfrac{x-\mu }{\sigma }[/tex]
We therefore have at x = 61,
[tex]Z=\dfrac{61-61 }{10 } = 0[/tex]
P(x > 61) = P(Z > 0) = 1 - 0.5 = 0.5
For x = 71, we have;
[tex]Z=\dfrac{71-61 }{10 } = 1[/tex]
P(x < 71) = P(Z < 1) = 0.84134
The probability that the score will be between 61 and 71 is the difference between the two probabilities, which is 0.84134 - 0.5 = 0.34134
Given that the probability is equivalent to the proportion of the students that would have a test score between 61 and 71, we have;
The number of students that would have a test score between 61 and 71 = 0.34134 × 450 = 153.6 ≈ 154 to the nearest whole number.
Name the algebraic property demonstrated in the example below: (1 point) x ⋅ y ⋅ z = y ⋅ x ⋅ z
Answer:
commutative property of multiplication
Step-by-step explanation:
find the area of a sector of a circle with radius 6 centimetre if angle of sector is 60 degree
Answer:
Step-by-step explanation:
[tex]area=\frac{\pi r^2 \times\theta}{360} =\frac{\pi 6^2 \times 60}{360} =6 \pi \approx 18.85~ cm^2[/tex]
Gum
Packages of gum
Pieces of gum
1
15
2
30
3
45
4
How many pieces of gum are in 4 packages of gum?
Answer:
60 pieces
Step-by-step explanation:
The rate of pieces to packages is 15/1.
Multiply this rate by 4 to get the answer.
15 * 4 = 60
━━━━━━━☆☆━━━━━━━
▹ Answer
60 pieces of gum
▹ Step-by-Step Explanation
[tex]\left[\begin{array}{cccc}1&2&3&4\\15&30&45&60\\\end{array}\right][/tex]
The pattern is multiply the number of packs by 15 therefore, the answer will be 60 pieces of gum.
Hope this helps!
CloutAnswers ❁
Brainliest is greatly appreciated!
━━━━━━━☆☆━━━━━━━
evaluate sine squared theta for theta equals 45 degrees
64, -48, 36, -27
which formula describes the sequence?
Answer:
The formula would be
T(n) = 64 (-3/4)^n, n=0,1,2,...
or sometimes
T(n) = T(n-1)(-3/4), T(0) =64, n=0,1,2,...
Step-by-step explanation:
The common ratio is -3/4, i.e.
(-3/4) * 64 = -48
(-3/4) * 48 = 36
(-3/4) * 36 = -27
...
The formula would be
T(n) = 64 (-3/4)^n, n=0,1,2,...
or sometimes
T(n) = T(n-1)(-3/4), T(0) =64, n=0,1,2,...
Note: Would have been easier if the choices were supplied.
What is the measure of Angle D F E? Triangle D E F. The exterior angle to angle F is 142 degrees. 38 degrees 52 degrees 118 degrees 142 degrees
as the exterior angle is known
sum of that angle and f angle = 180
142 + f = 180
f = 180 - 142
f = 38
Answer:
38
Step-by-step explanation:
Add the angle and f angle (180)Now add 142 + f = 180 Now subtract 180 - 142 (= f) Finally you get your answer 38Hope this helps you :)
Write an equation of the line that passes through the point (-6, -5) with slope 6.
A. y +5= -6(x+6)
B.y+6= -6(x+5)
C. y+6=6(x+5)
D.y+5= 6(x+6)
Answer:
The answer is option D.
Step-by-step explanation:
Equation of a line is y = mx + c
where
m is the slope
c is the y intercept
Equation of a line from given a Slope and a point is
y - y1 = m(x - x1)
Where ( x1 , y1) is the point
Equation of the line using point (-6 , -5) and slope 6 is
y + 5 = 6(x - 6)Hope this helps you
This is probably pretty easy, I could solve all the other ones but I got stuck on this one.
Answer:
78
Step-by-step explanation:
Let x be the score on the next test
We are averaging 6 tests and want an average of 75
( 82+91+38+78+83+x) /6 = 75
Multiply each side by 6
( 82+91+38+78+83+x) = 75*6
( 82+91+38+78+83+x) =450
Combine like terms
x+372 = 450
Subtract 372 from each side
x+372-372 = 450-372
x =78
The graphs below are both absolute value functions. The equation of the red
graph is f(x) = [X]. Which of these is the equation of the blue graph, g(x)?
Answer:
The answer is option C.
[tex]g(x) = \frac{1}{2} |x| [/tex]
Hope this helps you
find the sum of the following ap .1) 1/15, 1/12, 1/10,....,to 11 terms
Answer:
33/20
Step-by-step explanation:
1/12 - 1/15 = 5/60 - 4/60 = 1/60
d = 1/60
a_n = a_1 + d(n - 1)
a_11 = 1/15 + (1/60)(11 - 1)
a_11 = 1/15 + 1/6
a_11 = 4/60 + 10/60
a_11 = 14/60
a_11 = 7/30
a_12 = 14/60 + 1/60
a_12 = 15/60
a_12 = 1/4
s_n = n(a_1 + a_n)/2
s_11 = 11(1/15 + 7/30)/2
s_11 = 11(2/30 + 7/30)/2
s_11 = 11(9/30)/2
s_11 = 99/60
s_11 = 33/20
A Line Segment has the points (1,-2), and (3,-2). What are the new points after its dilated by a scale factor of 3/2 or 1.5
Answer:
The new points after dilation are
(3/2, -3) and (9/2,-3)
Step-by-step explanation:
Here in this question, we want to give the new points of the line segment after it is dilated by a particular scale factor.
What is needed to be done here is to multiply the coordinates of the given line segment by the given scale factor.
Let’s call the positions on the line segment A and B.
Thus we have;
A = (1,-2) and B = (3,-2)
So by dilation, we multiply each of the specific data points by the scale factor and so we have;
A’ = (3/2, -3) and B’= (9/2,-3)
Which one of the following would most likely have a positive linear correlation coefficient?
A. temperature of a refrigerator compared to the number of items inside of it
B. amount of money spent on baby food as a child ages
C. length of a driveway compared to number of cars owned
D. distance driven in a car compared to the hours spent driving
Answer:
this question is not clear please send clear question
Which volume formula or formulas show(s) a joint variation? I =3 V = s 3 II =πr2h V = π r 2 h III =ℎ V = B h Select one: a. III only b. I only c. II and III only d. I, II, and III
Answer:
C. . II and III only
Step-by-step explanation:
Given:
I. V=s^3
II.V=πr^2h
III. V=Bh
From the above
I. V varies directly as cube of s
II. V varies jointly as square of r and h where π is the constant of proportionality.
III. V varies jointly as B and h
Therefore, the volume formula which shows a joint variation are
II.V=πr^2h and III. V=Bh
Answer is C. II and III only