[tex](2+3)^{-1}\equiv5^{-1}\pmod7[/tex] is the number L such that
[tex]5L\equiv1\pmod7[/tex]
Consider the first 7 multiples of 5:
5, 10, 15, 20, 25, 30, 35
Taken mod 7, these are equivalent to
5, 3, 1, 6, 4, 2, 0
This tells us that 3 is the inverse of 5 mod 7, so L = 3.
Similarly, compute the inverses modulo 7 of 2 and 3:
[tex]2a\equiv1\pmod7\implies a\equiv4\pmod7[/tex]
since 2*4 = 8, whose residue is 1 mod 7;
[tex]3b\equiv1\pmod7\implies b\equiv5\pmod7[/tex]
which we got for free by finding the inverse of 5 earlier. So
[tex]2^{-1}+3^{-1}\equiv4+5\equiv9\equiv2\pmod7[/tex]
and so R = 2.
Then L - R = 1.
HELP ME PLEASE!!!!! Write and solve an equation based on the relationship between the angles in the diagram below to find the value of a.
Answer:
a = 104
Step-by-step explanation:
The sum of angles around a point is 360°.
a° +126° +a° +26° = 360°
2a +152 = 360 . . . . collect terms, divide by °
2a = 208 . . . . . . . . subtract 152
a = 104 . . . . . . . . . . divide by 2
Please answer it now in two minutes
Answer:
∠ I ≈ 60.3°
Step-by-step explanation:
Using the tangent ratio in the right triangle
tan I = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{HG}{GI}[/tex] = [tex]\frac{7}{4}[/tex] , thus
∠ I = [tex]tan^{-1}[/tex] ([tex]\frac{7}{4}[/tex] ) ≈ 60.3° ( to the nearest tenth )
the answer is 10 by root 65 so the answer is 10
find tan(a) in the triangle
Answer:
tan (a) = 24/7Step-by-step explanation:
tan∅ = opposite / adjacent
From the question
AC is the adjacent
BC is the opposite
So we have
tan (a) = BC / AC
tan (a) = 24/7
Hope this helps you
Solve by completing the square: x^2+4x-5
Answer:
(x + 2)^2-9
How to find answer:
Use the formula (b/2)^2 in order to complete the square.
Hope this helps :)
Name an inscribed angle
Answer:
BHF
Step-by-step explanation:
Definition of inscribed
Select the correct answer. Which equation represents a line that is perpendicular to line FG?
Answer:
Hey there!
Equation of Line FG: [tex]y=\frac{1}{2} x+3.5[/tex], because the slope (rise over run) is 2 and we see that the y intercept is 3.5.
Equation to a Line Perpendicular to FG: [tex]y=-2x-3\\[/tex], because the equations of perpendicular lines have the same (but could also be different y-intercepts), and opposite reciprocal slopes.
Let me know if this helps :)
Answer:
C)
Step-by-step explanation:
f(-5,1) & G(9,8)
Slope of FG = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
= [tex]\frac{8-1}{9-[-5]}=\frac{7}{9+5}\\\\[/tex]
[tex]\frac{7}{14}\\\\=\frac{1}{2}[/tex]
Slope of line perpendicular to FG = -1/m = -1/(1/2) = -2
Equation of line in slope intercept form : y = mx + b
m = - 2
So, option c will be the equation of the line perpendicular to FG
Which equation is y = 3(x – 2)2 – (x – 5)2 rewritten in vertex form? Y = 3 (x minus seven-halves) squared minus StartFraction 27 Over 4 EndFraction y = 2 (x minus 1) squared minus 11 y = 2 (x minus one-half) squared minus StartFraction 53 Over 4 EndFraction y = 2 (x minus one-half) squared minus StartFraction 27 Over 2 EndFraction
Answer: y = 2 (x minus one-half) squared minus StartFraction 27 Over 2 EndFraction
or
[tex]y=2((x-\dfrac{1}{2})^2)-\dfrac{27}{2}[/tex]
Step-by-step explanation:
Vertex form of equation : [tex]f (x) = a(x - h)^2 + k,[/tex]where (h, k) is the vertex of the parabola.
[tex]y=3(x-2)^2-(x-5)^2\\\\=3(x^2+4-4x)-(x^2+25-10x)\\\\=3x^2+12-12x-x^2-25+10x\\\\=2x^2-2x-13\\\\=2(x^2-x-\dfrac{13}{2})\\\\=2(x^2-x+\dfrac{1}{4}-\dfrac{1}{4}-\dfrac{13}{2})\\\\=2((x-\dfrac{1}{2})^2-\dfrac{1+26}{4})\\\\=2((x-\dfrac{1}{2})^2-\dfrac{27}{4})=2((x-\dfrac{1}{2})^2)-\dfrac{27}{2}[/tex]
Hence, the vertex form of the equation is [tex]y=2((x-\dfrac{1}{2})^2)-\dfrac{27}{2}[/tex]
Answer:
i got y=2(x-1/2)^2- 27/2 so the last one is right
Step-by-step explanation:
:)
Which choice shows the coordinates of B' if the trapezoid is reflected across the x-axis? On a coordinate plane, trapezoid A B C D has points (2, 2), (7, 2), (5, 1), (3, 1). (–7, 2) (2, –7) (7, –2) (–2, 7)
Answer:
(7, -2)
Step-by-step explanation:
The trapezoid A B C D has points (2, 2), (7, 2), (5, 1), (3, 1).
Transformation of a point is the change in location from an original position to a new position. If a shape is transformed, all its points are also transformed. A transformation can either be a rotation, translation, reflection or dilation.
If a point O(x,y) is reflected across the y axis, the new coordinate of the point is at O'(x, -y), i.e. the x coordinate does not change, but the y coordinate is negated.
Since in trapezoid ABCD, the coordinate of point B is (7, 2). The trapezoid is reflected across the x-axis, therefore the new coordinate of B' is at (7, -2)
Answer:c
Step-by-step explanation:
I took the test
factor the trinomial.
x2+11x+24
Answer:
(x + 3)(x + 8)
Step-by-step explanation:
We're looking for two numbers that have a sum of 11 and product of 24; these numbers are 3 and 8 so the factored form is (x + 3)(x + 8).
Answer:
(x + 8)(x + 3)
Step-by-step explanation:
Hey there!
Well in the polynomial,
x^2+11x+24
we need to find out what*what = 24
8*3 = 24
8x + 3x = 11x
x*x = x^2
Factored (x + 8)(x + 3)
Hope this helps :)
I need help on this one question ASAP
Answer:
choose the last option .
you could check my answer using desmos graph (search on Google)
simplify √16n/m^3 1. 4√mn/n^2 2.4√mn/m 3.√mn/4m 4. 4√mn/m^2
Answer: [tex]4.\ \ \ \dfrac{4\sqrt{mn}}{m^2}[/tex] .
Step-by-step explanation:
The given expression: [tex]\sqrt{\dfrac{16n}{m^3}}[/tex]
'
since [tex]16=4^2[/tex]
[tex]m^3=m^{2+1}= m^2\times m[/tex] [[tex]a^{n+m}=a^n\times a^m[/tex]]
Now, the given expression becomes,
[tex]\sqrt{\dfrac{4^2n}{m^2\timesn}}=\dfrac{4\sqrt{n}}{m\sqrt{m}}[/tex]
Since there is root in denominator , so we need to rationalize
[tex]\dfrac{4\sqrt{n}}{m\sqrt{m}}\times\dfrac{\sqrt{m}}{\sqrt{m}}=\dfrac{4\sqrt{mn}}{m\times\sqrt{m}\times\sqrt{m} }\\\\=\dfrac{4\sqrt{mn}}{m\times m}\\\\=\dfrac{4\sqrt{mn}}{m^2}[/tex]
Hence, the correct option is [tex]4.\ \ \ \dfrac{4\sqrt{mn}}{m^2}[/tex] .
Determine what type of model best fits the given situation:
A model rocket fired straight up from the ground, where h is the height of the rocket and t is the time in seconds.
Answer:
Ok, i will suppose the situation that:
The rocket has a constant speed S (So the acceleration of the rocket is equal in magnitude, but opposite in direction, to the gravitational acceleration)
Here we can remember that:
Velocity = distance/time.
Then if the distance is the height of the rocket, we can write this as:
H = velocity*time
h = S*t
This is a linear model that represents the height of the rocket as a function of time.
Case 2:
The rocket is fired with an initial velocity v0, but no acceleration:
In this case the only acceleration acting on the rocket is the gravitatonal acceleration pulling the rocket down, so the acceleration is:
a = -g
To get the velocity as a function of time, we should integrate:
a = -g*t + v0
To get the height as a function of time, we integrate again:
h(t) = (-g/2)*t^2 + v0*t + p0
Where p0 is the initial position of te rocket, but the rocket starts at the ground, so p0 = 0m.
The height as a function of time is:
h(t) = (-g/2)*t^2 + v0*t
This is a quadratic equation.
Yesterday, a factory used (2)/(3) of a tub of peanut butter. They use 16 of a tub of peanut butter for each batch of peanut butter cookies. How many batches of peanut butter cookies did the factory make yesterday? help!
Answer:
4 batches
Step-by-step explanation:
1/3=2/6, 2/3=4/6
Are the terms CSC, SEC, and COT equivalent to the terms Sin^-1, Cos^-1, and Tan^-1? Are the three pairs of terms the same thing just written differently, or are they entirely different?
Answer:
Step-by-step explanation:
It depends on how it is written. By definition
[tex]\csc(x) = (\sin(x))^{-1} = \frac{1}{\sin(x)}[/tex]
[tex]\sec(x) = (\cos(x))^{-1} = \frac{1}{\cos(x)}[/tex]
[tex]\cot(x) = (\tan(x))^{-1} = \frac{1}{\tan(x)}[/tex]
however the functions
[tex]\sin^{-1}(x), \cos^{-1}(x), \tan^{-1}(x)[/tex] are the inverse functions of sine, cosine and tangent respectively. So, they are not equivalent functions
Complete the inequality with >, <,>,<,is greater than, comma, is less than, comma or ==equals. 2^52 5 2, start superscript, 5, end superscript 5^25 2 5, squared
Answer:
[tex]2^5 > 5^2[/tex]
Step-by-step explanation:
Given the expression [tex]2^5 \ 5^2[/tex], we are to complete the inequality by inserting the correct inequality signs in between the values.
Before we do that, we must know the value of each indicinal expressions.
[tex]2^5 = 2*2*2*2*2\\\\2^5 = 4*4*2\\\\2^5 = 16*2\\\\2^5 = 32[/tex]
Also,
[tex]5^{2} = 5*5\\\\5^2 = 25[/tex]
From the values gotten, we can clearly see that 32 is greater than 25. This means that 2⁵ is greater than 5². Hence the inequality sign that will complete the expression is a greater than sign (>).
The inequality will be [tex]2^5 > 5^2[/tex]
Answer:
its this
over here...
HELP please!!!
Jeanie wants a $100 000 mortgage. She arranged payments for the next 15 years. The bank charges 4.8%/a interest, compounded monthly.
a) how much is each monthly payment
b) how much interest is jeanie paying?
Answer:
in one month : 13676.57/12=1139.71
the interest on 100000 is: 205148.48-100000=105148.48
Step-by-step explanation:
A=P(1+r)^t (p is the mortgage, t is the time and r is the rate)
p=100000,t=15*12 month,r=4.8%( or 0.048)
A=100000(1+0.048/12)^(12*15)
A=205148.48 (the number rounded to the nearest hundredth)
205128.48 is the amount she has to pay it after 15 years
in one year : 205128.48/15=13676.57 ( rounded to nearest hundredth)
in one month : 13676.57/12=1139.71
the interest on 100000 is: 205148.48-100000=105148.48
The sales tax on clothing in Nebraska is 5.5%. Calculate how much tax you need to pay on a shirt if it costs $18.20 before tax. Round your answer to the nearest cent. ( pls answer asap and thanks ) will give BRANLIEST
Answer:
$1.00
Step-by-step explanation:
The tax rate in Nebraska = 5.5%
Cost of the shirt before tax = $18.20
Therefore:
Tax to be paid = 5.5% of $18.20
[tex]=0.055 \times \$18.20\\=\$1.00 $(correct to the nearest cent)[/tex]
The amount you need to pay as tax is $1.00.
A ________ is a summary description of a fixed characteristic or measure of the target population. It denotes the true value that would be obtained if a census rather than a sample was undertaken.
Answer:
standard deviation
Step-by-step explanation:
A standard deviation summary description of a fixed characteristic or measure of the target population. It denotes the true value that would be obtained if a census rather than a sample was undertaken.
3-(x-3)=25 solve the equation
Answer:
x= -19
Step-by-step explanation:
3-(x-3)=25
Distributive property to cancel out the paranthesis
3-x+3=25
Add the number
6-x=25
Subtract 6 on both sides
-x=19
Divide by -1 on both sides so the x to eliminate the negative sign
x=-19
17. Mary bought 10 quarts of juice at the
grocery. How many gallons of juice did
she buy?
A 1.4 gal
C 3.5 gal
B 2.5 gal
D 4.5 gal
Pls help
Answer:
B 2.5 Gal
Step-by-step explanation:
Answer:
I think the correct answer may be B.
Step-by-step explanation:
Ajar contains 45 red candies and 60 black candies. Suppose a candy is selected
at random. What are the odds against selecting a red candy?
Answer:
its 55
Step-by-step explanation:
45-100=55( trust me its right.)
Answer:
9/21
Step-by-step explanation:
total there are 105 candies, 60+45
45 are red so 45/105
simplified 9/21
Angle G is a circumscribed angle of circle E. Circle E is shown. Line segments F E and D E are radii. A line is drawn to connect points F and D. Tangents F G and D G intersect at point G outside of the circle. Angles E B D and F D E have measures of x degrees. What is the measure of angle G, in terms of x? x° + x° x° + 90° 180° – x° 180° – 2x°
Answer:
X+X
Step-by-step explanation:
did it on edg
Answer:
x° + x°
Step-by-step explanation:
Edge 2020
Show how you can determine that the inscribed figure inside a quadrilateral is a parallelogram. Support your argument with diagrams.
Answer:
See diagram
Step-by-step explanation:
A quadrilateral becomes a parallelogram when the diagonals bisects each other at a point E and hence proves the quadrilateral is a parallelogram. It shows both pairs of opposite sides being parallel to each other.
Following the theorem that states that, if two sides of a quadrilateral are opposite and congruent, then it is a parallelogram. Ditto for the theorem that states that, that when diagonals cuts each other at a point in a quadrilateral, then its a parallelogram.
In a bag containing cards numbered 1 to 10,one of which is drawn at random.Find the probability that it is a 5
Answer:
1/10
Step-by-step explanation:
there are 10 cards, numbered 1 through 10, there is one "5" card. so that's 1 card out of 10 cards, therefore a 1/10the chance or a 10% chance you'll get a 5 (or any specific number)
Angela shared a cab with her friends. When they arrived at their destination, they evenly divided the $63fare among the x of them. Angela also paid a $8tip. How much did Angela pay in total? Write your answer as an expression
1.if tip included in fare, total amount paid by Angela =(55$/x) +8$
if tip is not included in fare than total amount paid by angela = (63$/x)+8$
Explanation :-
According to qus
Total friends included Angela = x
Total fare paid by them =63$
If tip included in total fare, than total fare without tip=63-8
= 55$
Sothat,
amont paid by individual =total fare /total friends. 55$/x
If tip not include in total fare than total amount paid by individual =63$/x
Katya has $20.00 to spend at her college bookstore, where all students receive a 20% discount . katya wants to purchase a copy of a book that normally sells for $22.50 plus 10% sales tax. how much dose the book sell for dose katya have enough money bc bc?
Answer:
here you go :)
Step-by-step explanation:
You would take 20% of $22.50 (22.5 multiplied by .2). You would get $4.50 off of the book with the discount. So you would subtract 4.5 from 22.5 and get $18. Then you would take 10% of $18 for the sales tax. (18 multiplied by .1). You would get $1.80 towards sales tax. you would then add $1.80 to $18 and get $19.80.
A wholesaler requires a minimum of four items in each order from its retail customers the manager of one retail store is considering ordering a certain number of sofas X and a certain number of pillows that come in pairs why which graph represents the overall equation represent by the scenario appointment not apply to the scenario
Answer: Option D
Step-by-step explanation:
Answer:
✔ D.
Step-by-step explanation:
E2021
Which is the heaviest of these weight : 1/2 kg , 0.6kg, 125g, 475g
Answer:
0.475 kg
Step-by-step explanation:
1/2 kg = 0.5 kg
125g = 0.125kg
475g = 0.475kg
grams are lighter than kg and 0.5kg,0.125g, and 0.6kg are all lighter than 0.475kg
hope this helps!
Answer:
0.6 kg
Step-by-step explanation:
The easy way to find out the answer is to bring all into same unit:
1/2 kg= 1/2*1000 g= 500 g0.6 kg = 0.6*1000 g= 600 g125 g475 gComparing all four we see the greatest number is 600, so the answer is :
600 g or 0.6 kg is the heaviest weightInstructions: Find the Measure of the indicated angle to the
nearest degree.
Answer:
tan(x) is 23/28 x= the unknown angle
then multiply each side by the inverse of tan giving you x=tan^-1(23/28) which I got as 39°
Any help with this please???? Running out of time!
Answer:
Sin A = 21/29Step-by-step explanation:
[tex]Using\: A \: as\: a\: refernce\: angle ;\\Hypotenuse = 29\\Opposite =21\\Adjacent = 20\\\\Using \: SOHCAHTOA\\Sin A = \frac{Opposite}{Hypotenuse} \\\\Sin A = \frac{21}{29}[/tex]