Answer:
2\sqrt2
Step-by-step explanation:
a=5-2√6 ...(1)
[tex]\frac{1}{a}=\frac{1}{5-2 \sqrt{6} } \times\frac{5+2\sqrt{6} }{5+2\sqrt{6} } =\frac{5+2\sqrt{6}}{(5-2\sqrt{6})(5+2\sqrt{6})} =\frac{5+2\sqrt{6}}{5 ^2-(2\sqrt{6})^2} =\frac{5+2\sqrt{6}}{25-24} =5+2\sqrt{6}\\a+\frac{1}{a}=5-2\sqrt{6}+5+2\sqrt{6}=10[/tex]
[tex](\sqrt{a}-\frac{1}{\sqrt{a}})^2=(\sqrt{a})^2+(\frac{1}{\sqrt{a}})^2-2 \times \sqrt{a} \times \frac{1}{\sqrt{a}}=a+\frac{1}{a}-2=10-2=8\\\sqrt{a}-\frac{1}{\sqrt{a}}=\sqrt{8}=2\sqrt{2}[/tex]
given the nth term of geometric expression is (as in the diagram)
a) state the value of k
b) the first term of progression
Step-by-step explanation:
a) k = 1
b) geometric progression formula:
Tn = ar^(n-1)
first term, a = 3/2
Consider the following proportion:
2 12
— -—
7 x
Use cross products to write the equation: 2x = 84.
What is the value of x?
[tex]\displaystyle\bf 2x=84\\\\x=84:2=42\\\\\boxed{x=42}[/tex]
HELPsjskskksksksksnxhxhxjsjsns
PLEASE HELPP ILL GIVE 20 POINTS
Answer:
C=20
Step-by-step explanation:
Select the correct answer.
A distribution center is redesigning two of its shipping boxes. The volume of these two boxes needs to be the same, and their dimensions are shown.
Write a system of equations to represent the volume of each box, y. Which statement describes the number and viability of the systems solutions?
Answer:
The system has two solutions, but only one is viable because the other results in negative side lengths.
Step-by-step explanation:
correct on edmentum or plato
¿cual es el porcentaje de ganancia de un comerciante que vende a $4600 un producto que compró a $4000?(con desarrollo)
Respuesta:
15%
Explicación paso a paso:
Dado :
Precio de compra = $ 4000
Precio de venta = $ 4600
El beneficio obtenido por la venta del artículo:
Precio de venta - precio de compra
$ (4600-4000) = $ 600
El porcentaje de beneficio obtenido:
Beneficio / precio de compra * 100%
600/4000 * 100%
600/4000 * 100%
0,15 * 100%
= 15%
solve |6x+3| = 27 .....
Answer:
Step-by-step explanation:
The absolute value of a number is defined as the positive of either a positive or a negative number. By that I mean that
| 1 | = 1 and | -1 | = 1. Right?
We use that idea here. Either:
6x + 3 = 27 OR 6x + 3 = -27 and solve both equations.
6x = 24 so x = 4 OR
6x = -30 so x = -5
Choice D is the one you want.
In a class of 22 students, 7 are female and 17 have an A in the class. There are 3 students who are male and do not have an A in the class. What is the probability that a student who has an Ais a male?
Answer:
Step-by-step explanation:
total number of students=22
number of female students=7
number of male students=22-7=15
number of male students not having A=3
Number of male students having A=15-3=12
P(male student having A)=12/22=6/11
The probability that a student who has an A is male is approximately 0.632
What is probability?We can use the formula for conditional probability:
P(Male | A) = P(Male and A) / P(A)
We are given that there are 3 male students who do not have an A, so there are 22 - 3 = 19 students who have an A. Of these 19, we do not know how many are male. However, we do know that there are 7 female students, so the number of male students who have an A is:
19 - 7 = 12
Therefore, the probability that a student who has an A is male is:
P(Male | A) = 12 / 19
We can simplify this fraction by dividing the numerator and denominator by their greatest common factor (which is 1 in this case):
P(Male | A) = 12 / 19
So the probability that a student who has an A is male is approximately 0.632.
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Choose the function that has:
Domain: x*-1
Range: y# 2
O
Ax)= x+2
x-1
O
2x+1
Ax)=
x+1
2x+ 1
(x) =
x-1
Given:
[tex]Domain\neq -1[/tex]
[tex]Range\neq 2[/tex]
To find:
The function for the given domain and range.
Solution:
A function is not defined for some values that makes the denominator equals to 0.
The denominator of functions in option A and C is [tex](x-1)[/tex].
[tex]x-1=0[/tex]
[tex]x=1[/tex]
So, the functions in option A and C are not defined for [tex]x=1[/tex] but defined for [tex]x=-1[/tex]. Therefore, the options A and C are incorrect.
In option B, the denominator is equal to [tex]x+1[/tex].
[tex]x+1=0[/tex]
[tex]x=-1[/tex]
So, the function is not defined for [tex]x=-1[/tex]. Thus, [tex]Domain\neq -1[/tex].
If degree of numerator and denominator are equal then the horizontal asymptote is [tex]y=\dfrac{a}{b}[/tex], where a is the leading coefficient of numerator and b is the leading coefficient of denominator.
In option B, the leading coefficient of numerator is 2 and the leading coefficient of denominator is 1. So, the horizontal asymptote is:
[tex]y=\dfrac{2}{1}[/tex]
[tex]y=2[/tex]
It means, the value of the function cannot be 2 at any point. So, [tex]Range\neq 2[/tex].
Hence, option B is correct.
Which one of the following groups would be unbiased when asked, “What is your favorite kind of pizza?”
Group of answer choices
health & fitness fanatics leaving the gym
guests leaving a gourmet pizza restaurant
kids at the playground
families attending a sporting event
Answer:
kids at playground
children are too young to know calorie count and the health benefits of certain foods. So they would simply choose the one they think tastes best
Someone please help me with this math problem?
Answer:
The length of the shortest side of the triangle is 10 units.
Step-by-step explanation:
Let a be the shortest side of the isosceles triangle and b be the two congruent sides.
The congruent sides b are each one unit longer than the shortest side. Hence:
[tex]b=a+1[/tex]
The perimeter of the isosceles triangle is given by:
[tex]\displaystyle P_{\Delta}=b+b+a=2b+a[/tex]
This is equivalent to the perimeter of a square whose side lengths are two units shorter than the shortest side of the triangle. Let the side length of the square be s. Hence:
[tex]s=a-2[/tex]
The perimeter of the square is:
[tex]\displaystyle P_{\text{square}}=4s=4(a-2)[/tex]
Since the two perimeters are equivalent:
[tex]2b+a=4(a-2)[/tex]
Substitute for b:
[tex]2(a+1)+a=4(a-2)[/tex]
Solve for a. Distribute:
[tex]2a+2+a=4a-8[/tex]
Simplify:
[tex]3a+2=4a-8[/tex]
Hence:
[tex]a=10[/tex]
The length of the shortest side of the triangle is 10 units.
Sum of positive roots of the equation (x2 - 12x + 35) (x2 + 10x + 24) = 504 is
Look at image for reference
Answer:
(3)11
Step-by-step explanation:
We are given that
[tex](x^2-12x+35)(x^2+10x+24)=504[/tex]
We have to find the sum of positive roots of the equation.
[tex]x^2(x^2+10x+24)-12x(x^2+10x+24)+35(x^2+10x+24)=504[/tex]
[tex]x^4+10x^3+24x^2-12x^3-120x^2-288x+35x^2+350x+840=504[/tex]
[tex]x^4-2x^3-61x^2+62x+840-504=0[/tex]
[tex]x^4-2x^3-61x^2+62x+336=0[/tex]
Factor of 336
2,3,4,6,8,7,
Let x=2
[tex]2^4-2^4-61(2^2)+62(2)+336\neq0[/tex]
x=2 is not the root of equation
x=-2
[tex](-2)^4-2(-2)^3-61(-2)^2+62(-2)+336=0[/tex]
Hence x=-2 is the root of equation.
x+2 is a factor of equation.
x=3
[tex]3^4-2(3^3)-61(3^2)+62(3)+336=0[/tex]
Therefore, x=3 is the root of equation.
[tex](x+2)(x-3)(x^2-x-56)=0[/tex]
[tex](x+2)(x-3)(x^2-8x+7x-56)=0[/tex]
[tex](x+2)(x-3)(x(x-8)+7(x-8))=0[/tex]
[tex](x+2)(x-3)(x-8)(x+7)=0[/tex]
[tex]x-8=0\implies x=8[/tex]
[tex]x+7=0\implies x=-7[/tex]
Positive roots are 3 and 8
Sum of positive roots=3+8=11
Option (3) is true.
ratio and proportion
One of the angle of pair of supplementary angle is 120 degree. find the ratio of pair of supplementary angles.
Answer:
2 : 1
Step-by-step explanation:
Supplementary angles are two angles whose measures add up to 180°
If one of the angle = 120°
The other angle = sum of supplementary angle - one of the angle
= 180° - 120°
= 60°
The other angle = 60°
ratio of pair of supplementary aangle = 120° : 60°
= 120° / 60°
= 2/1
= 2 : 1
ratio of pair of supplementary aangle = 2 : 1
Triangle D E F is reflected across D F to form triangle E G F. The lengths of sides E F and F G are congruent. To prove that ΔDEF ≅ ΔDGF by SAS, what additional information is needed? ∠DEF ≅ ∠ DGF ∠DFE ≅ ∠ DFG DE ≅ DG DG ≅ GF
Answer:
[tex]\angle DFE = \angle DFG[/tex]
Step-by-step explanation:
Given
See attachment for complete question
Required
What makes DEF and DGF congruent
We have:
[tex]EF = GF[/tex] --- this is indicated by the single line on both sides
Also:
[tex]DF = DF[/tex] --- both triangle share same side
For SAS to be true;
2 sides and 1 angle must be equal in either triangles
So far, we have:
[tex]EF = GF[/tex] ---- S
[tex]DF = DF[/tex] ---- S
The additional to complete the proof is:
[tex]\angle DFE = \angle DFG[/tex] ---- angle between the above sides
Reflection is a type of rigid transformation which requires the turning of an object, shape or figure about a reference point or line. Therefore, the needed additional information is ∠DFE ≅ ∠ DFG. Option B.
Reflection implies turning the given triangle DEF about its side DF, so as to produce an image with the same dimensions but different orientation.
The required proof by Side-Angle-Side (SAS) implies that the relations will be in respect of two of its sides and their included angle.
So that,
GF ≅ FE (given)
DF is the common side to triangles DEF and DFG.
DFG is the included side.
Thus;
∠DFE ≅ ∠ DFG (Side-Angle-Side postulate, SAS)
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please I need answer right now pleasssseee
Find the lowest common multiple of
A. 12,18,36
B. 9,27,18
please plz plz
Answer:
1.)36
2.)54
Step-by-step explanation:
sana po makatulong gehehe
find the area and perimeter of a circle
Answer:
Step-by-step explanation:
r=5 cm
area=πr²
perimeter=2πr
substitute the value of r and calculate.
Answer:
78.54 [tex]cm^{2}[/tex] Area
31.42 cm Circumference/perimeter
Step-by-step explanation:
A = [tex]\pi r^{2}[/tex]
C = 2[tex]\pi[/tex]r
A = [tex]\pi[/tex][tex]5^{2}[/tex]
A = 25[tex]\pi[/tex]
A = 78.54
C = 2[tex]\pi[/tex](5)
C = 10[tex]\pi[/tex]
C = 31.42
Can someone please be generous & help I’ve been struggling all night
Answer:
Slope-intercept
y = 3/4(x) - 7
Point slope
y -5= 3/4(x - 16)
Step-by-step explanation:
In slope-intercept
We have the general slope intercept as;
y = mx + b
where m is the slope and b is the y-intercept
in this case, m = 3/4 and b = -7
So we have;
y = 3/4(x) - 7
In point-slope
we have the general form as;
y-y1 = m(x-x1)
So what we have is as follows;
y -5= 3/4(x - 16)
Where we have (x1,y1) = (16,5)
If A =
[tex]if \: a \: = \binom{53}{24} \: and \: b = \binom{32}{10} then \: prove \: that |ab| = |a| . |b| [/tex]
and B = Prove that |AB| = |A| . |B|
Ah what is the length of XB? I really need to learn how to solve this
Answer:
5.28
Step-by-step explanation:
we use the formula
H²=B²+P²
and we will get the answer
branliest if it is helpful
Answer:
Angle BXY
using pythogoras theory which is
hyp*2= opp*2 +adj*2
hypothenus being the longest part of the angle BX=?
Step-by-step explanation:
hyp= 4.2*2+ 3.2*2
hyp*2 =17.64 + 10.24
hyp*2 = 27.88
hyp =√27.88
hyp=5.28...Ans
note *2...square
how to determine proofs
Answer:
check footprints and then check finger print the finger print pour powder on it and Trace
The temperature of a chemical solution is originally 21^\circ\text{C}21 ∘ C21, degrees, start text, C, end text. A chemist heats the solution at a constant rate, and the temperature of the solution is 75^\circ\text{C}75 ∘ C75, degrees, start text, C, end text after 121212 minutes of heating. The temperature, TTT, of the solution in ^\circ\text{C} ∘ Cdegrees, start text, C, end text is a function of xxx, the heating time in minutes. Write the function's formula. T=
Answer:
T(x) = 21 + 4.5x
Step-by-step explanation:
Given :
Original temperature = 21°C
Final temperature = 75°C
Time, x = 12 minutes
The temperature, T as a function of x, heating time in minutes :
We need to obtain the constant heating rate per minute :
Final temperature = initial temperature + (constant rate change,△t * time)
75 = 21 + 12△t
75 - 21 = 12 △t
54 = 12 △t
△t = 54 / 12
△t = 4.5°C
Hence, temperature change is 4.5°C per minute.
Hence,
T(x) = 21 + 4.5x
Answer:
T= 21+4.5x
Step-by-step explanation:
I got it right on Khan Academy
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can someone give me the answer for this? __ (5 + 4) = 2 * 5 + 2 * 4
Answer:
The answer is 2_____________________________
2 x 5 = 10
2 x 4 = 8
10 + 8 = 18
______________________________
5 + 4 = 9
_______________________________
_ 9 = 18
18 : 9 = 2
Please help me with this one I seriously suck at math
Answer:
194
Step-by-step explanation:
Rectangles :
7 x 10 = 70
6 x 10 = 60
4 x 10 = 40
Triangles
[tex]\frac{6x4}{2}[/tex] = 12 (two of them = 24)
70 + 60 + 40 + 24 = 194
In a scale model of a table, 1 centimeter represents 8 inches.
C
Scale
1 cm: 8 in
Answer the following.
?
(a) The height of the real table is 48 inches. What is the
height of the table in the scale model?
[centimeters
(b) In the scale model, the length of the table is 9
centimeters. What is the length of the real table?
inches
Answer:
(a): 6 centimeters
(b): 72 inches
Step-by-step explanation:
Rule: From centimeters to inches, multiply centimeters × 8
so from inches to centimeters, divide inches by 8
Scale:
1 cm : 8 in
? cm : 48 in
6 cm : 48 in
Scale:
? in : 9 cm
72 in : 9 cm
Jim is designing a seesaw for a children’s park. The seesaw should make an angle of 45 degrees with the ground, and the maximum height to which it should rise is 1 meter, as shown below: What is the maximum length of the seesaw? Choices: A) 1 meter B) 1.4 meters C) 2 meters D) 0.5 meters
Answer:
B) 1.4
Step-by-step explanation:
The sine of an angle is equal to the ratio of the opposite side to the hypotenuse.
sin(B)=opp/hyp
The maximum length of the seesaw is 1.4 meters
Trigonometric ratio
Trigonometric ratio is used to show the relationship between the sides and angles of a right angled triangle.
Let h represent the length of the seesaw, hence using trigonometric ratio:
sin(45) = 1 / h
h = 1.4 meters
The maximum length of the seesaw is 1.4 meters
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Find the probability of no failures in five trails of a binomial experiment in which the probability of success is 30%
which of the following statements must be true, given that ΔABC≅ΔXYZ, and the measure of ∠C is 32°
[tex]\huge\boxed{\boxed{\underline{\textsf{\textbf{Answer}}}}}[/tex]
Given,
ΔABC ≅ ΔXYZ
If these 2 triangles are congruent with each other then,
∠ A = ∠ X [tex]\boxed{\bf{Corresponding \ parts \ of \ congruent \ triangles}}[/tex]
∠ B = ∠ Y [tex]\boxed{\bf{Corresponding \ parts \ of \ congruent \ triangles}}[/tex]
∠ C = ∠ Z [tex]\boxed{\bf{Corresponding \ parts \ of \ congruent \ triangles}}[/tex]
Now,
We saw that ∠ C = ∠ Z.
⟹ So, if ∠ C = 32°, then even ∠ Z will be equal to 32°. [tex]\boxed{\sf{Equal \ angles \ have \ equal \ measurements}}[/tex]
ᶛɲƧཡэʀ ↦ C. m ∠X = 32°
ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ
꧁❣ ʀᴀɪɴʙᴏᴡˢᵃˡᵗ2²2² ࿐
Which equation represents a line that passes through (2,-) and has a slope of 3?
Oy-2 = 3(x + 2)
Oy - 3 = 2(x+)
Oy+ 1 = 3(x - 2)
Oy+ < = 2(x-3)
Help?
The equation of the line is y + 1 = 3(x - 2).
The correct option is (3).
What is an equation?Equation: A statement that two variable or integer expressions are equal. In essence, equations are questions, and the motivation for the development of mathematics has been the systematic search for the answers to these questions.
As per the given data:
The line passes through the point (2, -1)
slope of the given line is 3
By using the slope intercept form of line:
y = mx + c
where m is the slope
c is the y intercept
The line passes through the point (2, -1) so substituting the point in the equation also m = 3
y = 3x + c
-1 = 3(2) + c
c = -7
The equation of the line now can be written as:
y = 3x - 7
y + 1 = 3x - 7 + 1
y + 1 = 3(x - 2)
Hence, the equation of the line is y + 1 = 3(x - 2).
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A clothing store offers a free T- shirt when a customer spends $75 or more. Lyndon has already spent $36.95 which statement best represents all of the amounts he can spend to get a free T-shirt
The perimeter of a square is 80cm
state the length of one of its side
Answer:
20cm
Step-by-step explanation:
a square has 4 equally long sides.
when we know its perimeter, that means we know the sum of all 4 sides.
since all sides are equality long, we only need to divide the perimeter by 4 to get the length of an individual side.
80/4 = 20cm
