Answer:
Hello There!
`~~~~~~~~~~~~~~~~~~~~`
Let √x - 1/√x = a
Squaring both the sides,
x + 1/x - 2 = a^2
Putting the value,
3–2√2 + 1/(3–2√2) - 2 = a^2
a^2 = 1 - 2√2 + 1/(3–2√2)
= [(3–2√2) (1–2√2) + 1] / 3–2√2
= {3 - 8√2 + 9} / 3–2√2
= [12 - 8√2] / 3–2√2
Rationalising both the sides
= {(12 - 8√2)(3+2√2)} ÷ (9–8)
= 36 + 24√2 - 24√2 + 16(2)
= 36 - 32
=> 4
a^2 = 4
a = √4
a = 2, -2
So,
√x - 1/√x = a = 2, -2.
Hope this helped you. Brainliest would be nice!
Answer:
1 (sqrt)3
_ - i _
2 2
Step-by-step explanation:
AE=EC and BF = FC
M
EF=10
M
Answer:
92
Step-by-step explanation:
E is the midpoint of AC.
F is the midpoint of BC.
FE and AB are parallel by a theorem.
m<DBF = m<EFC = 92 by corresponding angles of parallel lines cut by a transversal.
Answer:
92°
Step-by-step explanation:
A train leaves Miami at 3:00 PM. A second train leaves the same city in the same direction at 8:00 PM. The second train travels 145 mph faster than the first. Of the second train overtakes the first at 10:00 PM, what is the speed of each of the two trains
Answer:
The first train travels at 58 mph and the second train travels at 203 mph.
Step-by-step explanation:
The first train left Miami at 3:00 PM.
The second train left Miami at 8:00 PM.
Let the speed of the first train be x.
The second train travels 145 mph faster than the first, that is 145 + x
The second train overtakes the first at 10:00 PM
This means that at 10:00 PM, they were both at the same location.
That is 7 hours after the first train left and 2 hours after the second train left.
Speed is given as:
s = d / t
where d = distance traveled and t = time taken
For the first train, after 7 hours traveling at speed x:
x = d / 7
=> d = 7x _______(1)
For the second train, after 2 hours, traveling at speed 145 + x:
145 + x= d / 2
=> d = 290 + 2x ____(2)
Equating (1) and (2):
7x = 290 + 2x
=> 7x - 2x = 290
5x = 290
=> x = 290/5 = 58 mph
Therefore, the first train travels at 58 mph and the second train travels at 203 mph (58 + 145)
The product of a number and its inverse is 1. Represent it in algebraic form.
Answer:
Step-by-step explanation:
Hello
first of all we assume that this number is different from 0 as dividing by 0 is not allowed
let's not n this number
its inverse is
[tex]\dfrac{1}{n}[/tex]
and we can write
[tex]n*\dfrac{1}{n}=1[/tex]
hope this helps
Answer:
x * 1/x = 1
Step-by-step explanation:
Let x be the number
1/x is the inverse
x * 1/x = 1
Find the distance between the points (4, 0) and (–3, 4).
Answer:
[tex]\huge\boxed{\sqrt{65}\approx8.062}[/tex]
Step-by-step explanation:
The formula of a distance between two points:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
We have two points (4, 0) and (-3, 4).
Substitute:
[tex]d=\sqrt{(-3-4)^2+(4-0)^2}=\sqrt{(-7)^2+4^2}=\sqrt{49+16}=\sqrt{65}[/tex]
Find the height, x, of the triangle. A. 30 B. 40 C. 50 D. 60
Answer:
The correct option is;
A. 30
Step-by-step explanation:
Given that the perpendicular bisector forms two other right angled triangles, we have;
For the larger right angled triangle, hypotenuse length = 100
For the smaller right angled triangle, hypotenuse length = 90
We note that;
y² = x² + 10²
z² = x² + 90²
100² = z² + y ²
Therefore we have;
100² = x² + 10² + z² = x² + 10² + x² + 90² = 2·x² + 90² + 10²
10000 = 2·x² + 8200
2·x² = 10000 - 8200 = 1800
x² = 1800/2 = 900
x = 30
Quadrilaterals ABCD and EFGH are similar. If the perimeter of the quadrilateral ABCD is equal to 4y² what is the perimeter of the quadrilateral EFGH?
Answer:
Can't be determined.
Step-by-step explanation:
From the fact that the quadrilaterals are similar:
Corresponding sides are in proportion and
Corresponding angles are congruent.
We can't create a proportion, so there's nothing else that we can determine.
Answer:
Below.
Step-by-step explanation:
Similar figures have the same size but not necessarily the same size.
The respective sides will be in the same ratio in a similar figure.
So from the information given you can't say what the measure of the perimeter of quadrilateral EFGH is. All you can say is the ratio of the perimeters is the same as the ratio of the respective sides. If the ratio is 1:2 for example then the perimeter of EFGH is 2*4y^2 = 8y^2.
Denver,Engle and Fido are all who eat differing amounts of dog food Denver gets 7/19 of the dog food Engle and Fido's share of the dog food in the ratio 6:2 Show your answer as a percentage rounded to the nearest percent of necessary
Answer:
Denver: 37%
Engle: 47%
Fido: 16%
Step-by-step explanation:
Denver eats 7/19 of the dog food.
There is 12/19 left for Engle and Fido.
The ratio of Engle to Fido is 6:2.
6x + 2x = 12/19
8x = 12/19
x = (12/19)/8
x = 0.0789
2x = 0.158
6x = 0.474
7/19 = 0.368
Denver: 37%
Engle: 47%
Fido: 16%
whivh one is for least to greatest 8/10,0.9,1/2
Answer:
1/2, 8/10, 0.9
Step-by-step explanation:
Convert to decimals.
8/10 = 0.8
0.9
1/2 = 0.5
Arrange from least to greatest.
0.5, 0.8, 0.9
1/2, 8/10, 0.9
Which is the equation for a sphere with the center (2,-9,-1) and radius √r? a. (x + 2)2 + (y - 9)2 + ( z - 1)2 = r b. (x - 2)2 + (y + 9)2 + ( z + 1)2 = r c. (x - 2)2 + (y + 9)2 + ( z + 1)2 = √r d. (x + 2)2 + (y - 9)2 + ( z - 1)2 = r2
Answer: b. [tex](x-2)^2+(y+9)^2+(z+1)^2=r[/tex]
Step-by-step explanation:
The general equation of a sphere is : [tex](x - a)^2 + (y - b)^2+ (z - c)^2 = R^2[/tex], where (a, b, c) represents the center of the sphere, R represents the radius, and x, y, and z are the coordinates of the points on the surface of the sphere.
Given, Center of the sphere = (2,-9,-1)
Radius = √r
Then, the equation of the sphere would be
[tex](x - 2)^2 + (y - (-9))^2+ (z - (-1))^2 = (\sqrt{r})^2\\\\\Rightarrow\ (x-2)^2+(y+9)^2+(z+1)^2=r[/tex]
Hence, the correct option is b. [tex](x-2)^2+(y+9)^2+(z+1)^2=r[/tex] .
Question 2 (Multiple Choice Worth 1 points)
(05.05 LC)
What shape best describes the cross section cut parallel to the base of a right rectangular prism?
O Rectangle
O Parallelogram
O Square
Trapezoid
Answer:
B. parallelogram
Step-by-step explanation:
A rectangular prism has a rectangle as its base .
Sasha recorded the height and weight of all of the girls in her physical education course.
Weight Height
99 61
104 61
110 62
133 64
130 65
142 68
146 66
153 67
184 69
185 70
What is the correlation coefficient for the data
Answer:
0.9156
Step-by-step explanation:
In the picture attached, the data is plotted (I made it using MS Excel, you can use similar programmes or a calculator).
The line that best correlates the data has the following equation:
y = 0.1037x + 50.922
and its correlation coefficient is:
R² = 0.9156
Answer:
Correlation coefficient, r = 0.957
Step-by-step explanation:
Let y represent the weight
Let x represent the height
y x x² y² xy
99 61 3721 9801 6039
104 61 3721 10816 6344
110 62 3844 12100 6820
133 64 4096 17689 8512
130 65 4225 16900 8550
142 68 4629 20169 9656
146 66 4356 21316 9636
153 67 4489 23409 10251
184 69 4761 33856 12696
185 70 4900 34225 12950
[tex]\sum y = 1386[/tex], [tex]\sum x = 653[/tex], [tex]\sum x^2 = 42737[/tex], [tex]\sum y^2 = 200276[/tex], [tex]\sum xy = 91454[/tex]
Correlation coefficient formula,
[tex]r = \frac{n \sum xy - \sum x \sum y}{\sqrt{(n \sum x^2 - (\sum x)^2) (n \sum y^2 - (\sum y)^2)} } \\r = \frac{10* 91454 - 653*1386}{\sqrt{(10* 42737 - (653)^2) (10* 200276 - (1386)^2)} }[/tex]
Correlation coefficient, r = 0.957
A baker is making cookies. She uses 3 cups of flour for every 8 oz of chocolate chips
How many cups of flour are needed with 192 oz of chocolate chips?
Answer: 72cups
Step-by-step explanation:
there are 8oz in a cup, so 8oz x 3cups = 24oz
[tex]\\ \frac{24}{8} \ = \frac{x}{192} \\(24) (192) = 8x\\(3) (192) = x\\576=x\\[/tex]
[tex]\frac{576}{8} = 72cups[/tex]
The baker will need 72 cups of flour for 192oz of chocolate chips.
A polynomial has x-intercepts of 3, 0, and –1, and passes through the point (1, –8). Which of the following functions could represent this graph? 1. x3 – 2x2 – 3x 2. x2 – 2x – 3 3. 2x2 – 4x – 6 4. 2x3 – 4x2 – 6x
Answer:
option 4
Step-by-step explanation:
Given the x- intercepts say x = a, x = b, x - c then the corresponding factors are
(x - a), (x - b), (x - c) and the polynomial is the product of the factors
Here the x- intercepts are x = 3, x = 0, x = - 1, thus the factors are
(x - 3), (x - 0), (x - (- 1) , that is
(x - 3), x and (x + 1) , then
y = ax(x - 3)(x + 1) ← where a is a multiplier
To find a substitute (1, - 8) into the equation
- 8 = a(1 - 3)(1 + 1) = - 4a ( divide both sides by - 4 )
a = 2, thus
y = 2x(x - 3)(x + 1) ← expand factors using FOIL
= 2x(x² - 2x - 3) ← distribute by 2x
= 2x³ - 4x² - 6x
Answer:
D) 2x3 – 4x2 – 6x
Step-by-step explanation:
The Mali Empire of West Africa was known far and wide for the great wealth of its rulers. The empire fell in the year 161016101610. Let xxx represent any year. Write an inequality in terms of xxx and 161016101610 that is true only for values of xxx that represent years after the year the Mali Empire fell.
Answer:
x > 1610
Step-by-step explanation:
;)
Answer:
x > 1610
Step-by-step explanation:
help quick plz i will make u a brainllest
Answer:
The answer is option B.
Step-by-step explanation:
Let < D be x
Since the triangle isosceles < E is also the same as < D
Let < E also be x
Angles in a triangle add up to 180°
x + x + 102 = 180
2x = 180 - 102
2x = 78
Divide both sides by 2
x = 39°
Therefore m < D is 39°
Hope this helps you
The water usage at a car wash is modeled by the equation W(x) = 4x3 + 6x2 − 11x + 7, where W is the amount of water in cubic feet and x is the number of hours the car wash is open. The owners of the car wash want to cut back their water usage during a drought and decide to close the car wash early two days a week. The amount of decrease in water used is modeled by D(x) = x3 + 2x2 + 15, where D is the amount of water in cubic feet and x is time in hours.
Write a function, C(x), to model the water used by the car wash on a shorter day
Answer:
The second option.
Step-by-step explanation:
We are trying to find what is W(x) - D(x).
(4x^3 + 6x^2 - 11x + 7) - (x^3 + 2x^2 + 15)
= 4x^3 - x^3 + 6x^2 - 2x^2 - 11x + 7 - 15
= 3x^3 + 4x^2 - 11x - 8
This corresponds to the second option.
Hope this helps!
A function, C(x), to model the water used by the car wash on a shorter day will be 3x³ + 4x² - 11x - 8
What is an equation?
An equation is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
Given that:-
The water usage at a car wash is modelled by the equation W(x) = 4x³ + 6x² − 11x + 7, where W is the amount of water in cubic feet and x is the number of hours the car wash is open. The amount of decrease in water used is modelled by D(x) = x³+ 2x² + 15, where D is the amount of water in cubic feet and x is time in hours.Now the amount of water is cut from the total water usage so to find out the new model c(x) we need to subtract the decrease in water from the total water usage.
We are trying to find what
C(x) = W(x) - D(x)
C(x) = ( 4x³ + 6x² − 11x + 7, ) - ( x³ + 2x² + 15 )
C(x) = 4x³ - x² + 6x² - 2x³ - 11x + 7 - 15
C(x) = 3x³ + 4x² - 11x - 8
Therefore A function, C(x), to model the water used by the car wash on a shorter day will be 3x³ + 4x² - 11x - 8
To know more about equations follow
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John has 28 cards. He gives his friend Timmy 10 cards and gave the rest to his brother. Then he gained 10 cards and
lost 3. How many cards deos he have now?
Answer:
7 cards
Step-by-step explanation:
Well if John started off with 28 and gave away 10,
28-10=18
Gave tthe last 18 to his brother
18-18 = 0
Gained 10
0+10=10
Lost 3
10-3=7
Hence, John has 7 cards left.
The number -32 belongs to which sets of numbers?
A) Integers,rational
B) Whole, Integers,rational
C) Integers,Irrational
D) Whole,Integers
The number -32 belongs to set : A) integers, rational
Rational numbers are terminating or repeating real numbers. Whereas, irrational numbers are the complement of rational number with real number being the universal set. These numbers are non terminating non repeating real number.
Integers are a subset of rational number. These are numbers not in fraction or decimal, or say with a denominator 1.
Whole numbers are subsets of integers which are positive, or say integers greater than equal to 1.
Given number : -32.
Since, the number is terminating, it is rational.
Further, it is not a fraction or decimal, hence integer.
But since the number is negative, not a whole number.
Therefore A) Integers, rational is correct option.
Learn more about rational number here
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which numbers below belong to the solution set of the inequality? Check all that apply. x -9 < 32 A) 41 B) 24 C) 53 D) 40 E) 36 F) 45
Answer:
[tex]a)41[/tex]
Step-by-step explanation:
[tex]x - 9 < 32[/tex]
[tex]by \: collecting \: like \: terms[/tex]
[tex]x < 32 + 9[/tex]
[tex]x < 41[/tex]
Answer:
B) 24
D) 40
E) 36
Step-by-step explanation:
x - 9 < 32
Add 9 on both parts.
x - 9 + 9 < 32 + 9
x < 41
x is lesser than 41.
24, 40, and 36 are lesser than 41 from the list.
ASAP!! Please help me. I will not accept nonsense answers, but will mark as BRAINLIEST if you answer is correctly with solutions.
Answer:
f(x)=2(x-3)^2
Step-by-step explanation:
vertex form: a(x-h)^2+k
so find the vertex (h,k) and use it to turn it into vertex form
simplify 2(a-3)/(a-4)(a-5)+(a-1)/(3-a)(a-4)+(a-2)/(5-a)(a-3)
Answer:
[tex]\dfrac{5}{x^3-12x^2+47x-60}[/tex]
Step-by-step explanation:
Though it is not what you have written, we think you want to simplify ...
[tex]\dfrac{2(a-3)}{(a-4)(a-5)}+\dfrac{(a-1)}{(3-a)(a-4)}+\dfrac{(a-2)}{(5-a)(a-3)}\\\\=\dfrac{2(a-3)^2}{(a-3)(a-4)(a-5)}+\dfrac{-(a-1)(a-5)}{(a-3)(a-4)(a-5)}+\dfrac{-(a-2)(a-4)}{(a-3)(a-4)(a-5)}\\\\=\dfrac{2(a^2-6a+9)-(a^2-6a+5)-(a^2-6a+8)}{x^3-12x^2+47x-60}\\\\=\boxed{\dfrac{5}{x^3-12x^2+47x-60}}[/tex]
_____
When writing a fraction in plain text, parentheses are needed around the entire denominator. The order of operations tells you that a/bc = (a/b)c, not a/(bc).
It takes 20 minutes to make 4 model airplanes. How many model airplanes can be made in 2 hours?
Answer: 24 model airplanes can be made in 2 hours.
Step-by-step explanation:
Answer:I believe its 24 because each plane takes 5 minutes so that's 12 in an hour so multiply by 2 and you get 24
Step-by-step explanation:
Draw a picture of the standard normal curve and shade the area that corresponds to the requested probabilities. Then use the standard normal table to find the following probabilities. Enter the probabilities as decimals. Enter the final answer only.
1.P(z>1.38)=
2.P(1.233.P(z<−0.42)=
3.P(z<−0.42)=
4. P(−2.645.P(z<3.04)=
5. P(z<3.04)
6.P(07.P(z>−2.43)=
7.P(z>−2.43)=
Answer:
(1) P (z > 1.38) = 0.08379
(2) P (z < - 0.42) = 0.33724
(3) P (z < 3.04) = 0.99882
(4) P (z > -2.43) = 0.00755
Step-by-step explanation:
(1)
Compute the value of P (z > 1.38) as follows:
[tex]P(z>1.38)=1-P(z<1.38)\\=1-0.91621\\=0.08379[/tex]
(2)
Compute the value of P (z < -0.42) as follows:
[tex]P(z<-0.42)=1-P(z<0.42)\\=1-0.66276\\=0.33724[/tex]
(3)
Compute the value of P (z < 3.04) as follows:
[tex]P(z<3.04)=0.99882[/tex]
(4)
Compute the value of P (z > -2.43) as follows:
[tex]P(z>-2.43)=1-P(z<2.43)\\=1-0.99245\\=0.00755[/tex]
Pleas Help 9th grade work
Consider the reflectional symmetry of the shape.
How many lines of symmetry does the shape have?
2
3
4
5
Answer:
4.
Step-by-step explanation:
One line of symmetry is horizontal ( through the centre of the horizontal part of the cross).
Another is a vertical line through the centre of the vertical part.
Then there are 2 diagonal lines of reflectional symmetry.
Which of the b values are solutions to the following equation? b^2 = 2.56
Answer:
b = - 1.6 or b = 1.6
Step-by-step explanation:
[tex]b^2=2.56\quad\iff\quad b=\pm\sqrt{2.56}\\\\\pm\sqrt{2.56}=\pm\sqrt{256:100}=\pm(\sqrt{256}:\sqrt{100}\,)=\pm(16:10)=\pm1,6[/tex]
Answer:all of the above
Step-by-step explanation:on khan
What is the area of the triangle below?
3
16
O A. 24 sq. units
O B. 19 sq. units
O C. 48 sq. units
O D. 16 sq. units
Answer:
answer is 24
area of triangle=1/2 base*height
1/2*16*3=24
Answer:
24 sq. units
Step-by-step explanation:
Area of a triangle = Base x height ÷ 2
Base = 16
Height = 3
Therefore 16 x 3= 48 ÷2 = 24
I really hope this helps:)
I need help on this problem please
Answer:
x = -2
Step-by-step explanation:
Step 1: Substitute h(x) for -9
-9 = 4x - 1
Step 2: Solve for x
-8 = 4x
x = -2
Answer:
x = -2.
Step-by-step explanation:
h(x) = 4x - 1, h(x) = -9.
-9 = 4x - 1
4x - 1 = -9
4x = -8
x = -2
Check your work!
4 * (-2) - 1
= -8 - 1
= -9
Since it works out, x = -2.
Hope this helps!
Which figure shows a line of reflectional symmetry for the letter T? A letter T is folded at the horizontal line. A letter T is folded diagonally. A letter T is folded vertically through the middle. A letter T is folded diagonally through its center.
Answer:
A letter T is folded vertically through the middle.
Step-by-step explanation:
Reflectional symmetry refers to the symmetry of line that divides the given shape into two equal halves. The halves represent the mirror reflection of each other. The line of symmetry is drawn to show the reflection and it acts as a mirror. For the letter 'T', the reflectional symmetry will be drawn vertically in the middle of the letter. The line divides the letter into two equal halves with mirror images.
The figure that will depict a line of reflectional symmetry of letter T would be: A letter T folded vertically through the middle.
What is a Line of Reflectional Symmetry?A line of reflectional symmetry can be described as an imaginary line that divides a figure into two halves in such a way that each of the halves are a mirror image of the other.
When a line divides letter T vertically, two mirror images are created.
Thus, the figure that will depict a line of reflectional symmetry of letter T would be: A letter T folded vertically through the middle.
Learn more about line of reflectional symmetry on:
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List the sides of ∆XYZ in order from shortest to longest if m∠X = 51, m∠Y = 59, and m∠Z = 70
Step-by-step explanation:
Angles and sides go hand-in-hand. Although I don't see the actual triangle that's used, and that can affect my answer, the side opposite of the shortest angle will be the shortest, the side opposite of the middle angle will be the middle, and the side opposite the largest angle will be the largest. For example, if the shortest angle (m∠X = 51) is the top vertex, the base side will be the shortest.
What is the approximate value of x? Round to the nearest tenth. A right triangle is shown. Side x is opposite to angle 50 degrees. The hypotenuse has a length of 6 centimeters. Side y is opposite to angle 40 degrees. 3.1 cm 3.9 cm 4.6 cm 5.4 cm
Answer:
4.6cm
Step-by-step explanation:
A diagram showing the analysis from the question has been attached to this response. Kindly download it and view.
From the diagram,
=> We have three angles given
(i) the right angle, 90°
(ii) the angle opposite to side x, 50°
(iii) the angle opposite to side y, 40°
=> We also have one side given,
(i) the hypotenuse, of length 6cm
We can therefore apply the sine rule as follows;
[tex]\frac{sin 90^0}{6} = \frac{sin 50^0}{x} = \frac{sin 40^0}{y}[/tex] ---------------(i)
Now to get the value of x, we'll equation the first and second terms of equation (i) as follows;
[tex]\frac{sin 90^0}{6} = \frac{sin 50^0}{x}[/tex] [cross multiply]
[tex]xsin90^0 = 6 sin 50^0[/tex]
[tex]x * 1 = 6 * 0.7660[/tex]
[tex]x =4.596[/tex] cm = 4.6cm [to the nearest tenth]
Therefore, the value of x is 4.6cm to the nearest tenth
Answer:
4.6 cm
Step-by-step explanation:
just took on edge