Answer:
[tex]\large \boxed{\sf \ \ \dfrac{5-\sqrt{3}}{2} \ \ }[/tex]
Step-by-step explanation:
Hello,
[tex]\dfrac{1+2\sqrt{3}}{1+\sqrt{3}}=\dfrac{(1+2\sqrt{3})(1-\sqrt{3})}{(1+\sqrt{3})(1-\sqrt{3})}\\\\ \text{... to eliminate the root in the denominator ...} \\\\=\dfrac{1-\sqrt{3}+2\sqrt{3}-2*3}{(1-3)}\\\\=-\dfrac{1+\sqrt{3}-6}{2}\\\\=-\dfrac{\sqrt{3}-5}{2}\\\\=\dfrac{5-\sqrt{3}}{2}\\[/tex]
Do not hesitate if you have any question
A scientist counts 35 bacteria present in a culture and finds that the number of bacteria triples each hour. The function y = 35 ∙ 3x models the number of bacteria after x hours. Estimate when there will be about 550 bacteria in the culture.
Answer:
After 5 hoursStep-by-step explanation:
If a scientist counts 35 bacteria present in a culture and finds that the number of bacteria triples each hour and the function y = 35 ∙ 3x models the number of bacteria after x hours, in order to estimate when there will be about 550 bacteria in the culture we will substitute y = 550 into the modeled equation and calculate the value of x as shown;
If y = 35*3x
when y = 550
550 = 35*3x
Dividing both sides by 35;
550/35 = 35*3x/35
3x = 550/35
x = 550/3*35
x = 550/105
x = 5.24
This means that there will be 550 bacteria in the culture after approximately 5 hours
PLEASE HELP!!!
In a survey, 250 adults and children were asked whether they know how to
swim. The survey data are shown in the relative frequency table.
Answer:
82% Add .34+.48.
Step-by-step explanation:
The question is asking how many people CAN swim. This is why the answer is 82. But if the question asks how many people CANT swim the answer will be 18. This is why some people might get confused.
The roots of 100x2 – 20x + 1 = 0 is:
Answer:
x = 0.1Step-by-step explanation:
[tex]100x^2-20x+1=0\\\\(10x)^2-2\cdot10x\cdot1+1^2=0\\\\(10x-1)^2=0\\\\10x-1=0\\\\10x=1\\\\x=0.1[/tex]
What equation of the circle would center (-3.2 , -2.1 ) and radius 4.3 ? ( fast please I will give u brainlest)
Answer:
Look at the attached picture
Step-by-step explanation:
It is given that the center of the circle is (-3.2,2.1) and radius is 4.3.
Answer:
( x+3.2) ^2 + ( y+2.1) ^2 = 4.3^2
Step-by-step explanation:
We can write the equation of a circle as
( x-h) ^2 + ( y-k) ^2 = r^2
where ( h,k) is the center and r is the radius
( x- -3.2) ^2 + ( y--2.1) ^2 = 4.3^2
( x+3.2) ^2 + ( y+2.1) ^2 = 4.3^2
9. Read the following word problem, then create a linear equation to model the problem. Provide work to show how your linear equation models the problem, such as a brief description, a picture, or a table. Finally, use the linear equation you created to solve the problem.
$2400 is divided between two accounts. One account pays 2% interest, while the other account pays 3.5% interest. At the end of one interest period, the interest earned is $81. How much was invested in each account?
Answer:
$200 at 2%.
$2200 at 3.5%.
Step-by-step explanation:
Let the two amounts be x and y.
x earns 2% interest, and y earns 3.5% interest.
Since the total is $2400, then
x + y = 2400
Now we can solve for y and express the second amount in terms of x.
y = 2400 - y
The two amounts are x and 2400 - x.
In one interest period, the amount of interest earned is the amount of money in the account multiplied by the interest.
2% = 0.02; 3.5% = 0.035
The x amount earns 0.02x interest.
The y amount earns 0.035y interest.
The total interest earned is the sum of the interest amounts of the two accounts.
0.02x + 0.035y
We now replace y with 2400 - x, and we set the sum of the interest amounts equal to the total interest earned, $81.
0.02x + 0.035(2400 - x) = 81
The equation above is the linear equation.
Now we solve it. Distribute on the left side.
0.02x + 84 - 0.035x = 81
Combine like terms on the left side.
-0.015x + 84 = 81
Subtract 84 from both sides.
-0.015x = -3
Divide both side by -0.015.
x = 200
$200 was deposited in the account earning 2%.
y = 2400 - x
y = 2400 - 200
y = 2200
$2200 was deposited in the account earning 3.5%.
!!geometry! Find the value of x if m∠P=18°
Answer:
x = 72
Step-by-step explanation:
If P is 18 degrees and Q is 90 degrees you just add them up and subtract it by 180.
Drag each tile to the correct box.
Three geometric sequences are given below.
Sequence A: 160, 40, 10, 2.5,
Sequence B: -21, 63, -189, 567, ...
Sequence C: 8, 12, 18, 27,
Order the sequences from least common ratio to greatest common ratio.
Sequence A
Sequence C
Sequence B
Answer:
Sequence B, Sequence A, Sequence C
Step-by-step explanation:
Data obtained from the question include the following:
Sequence A: 160, 40, 10, 2.5,
Sequence B: -21, 63, -189, 567, ...
Sequence C: 8, 12, 18, 27
Next, we shall determine the common ratio of each sequence. This is illustrated below:
Common ratio (r) is simply obtained by dividing the 2nd term (T2) by the 1st term (T1) or by dividing the 3rd term (T3) by the 2nd term (T2). Mathematically, it is expressed as:
r = T2/T1 = T3/T2
For sequence A:
160, 40, 10, 2.5
2nd term (T2) = 40
Ist term (T1) = 160
Common ratio (r) =..?
r = T2/T1
r = 40/160
r = 1/4
r = 0.25
Therefore, the common ratio is 0.25.
For sequence B:
-21, 63, -189, 567
2nd term (T2) = 63
Ist term (T1) = -21
Common ratio (r) =..?
r = T2/T1
r = 63/-21
r = - 3
Therefore, the common ratio is - 3.
For Sequence C:
8, 12, 18, 27
2nd term (T2) = 12
Ist term (T1) = 8
Common ratio (r) =..?
r = T2/T1
r = 12/8
r = 3/2
r = 1.5
Therefore, the common ratio is 1.5.
Summary:
Sequence >>>>> Common ratio
A >>>>>>>>>>>>> 0.25
B >>>>>>>>>>>>> - 3
C >>>>>>>>>>>>> 1.5
From the above illustration,
Ordering the sequence from least to greatest common ratio, we have:
Sequence B, Sequence A, Sequence C.
1. Between finishing their dinner and going to bed, Zac and Lucy had 4 hours.
These pie charts show how they spent their time.
Video games
12°
Reading
Watching TV
Watching TV
Video games
135º 160°
102° / 60°
186°
30°/45°
Homework
Homework/ Reading
It’s exercise 10 please
Answer:
Ok, I can see only a) to c)
a) Lucy spent the most time reading.
b) 20 minutes.
c) 22 minutes.
Step-by-step explanation:
Reason for b):
First convert hours to minutes.
1 hour = 60 minutes
4 hours = ?
4 × 60 = 240 minutes.
Homework is 30°
Total in the pie chart is 360° so:
30/360 × 240 mins = 20 mins
Answer is Zac spent 20 minutes to do his homework.
Reason for c):
Watching TV:
Zac: 135°
Lucy: 102°
Zac:
135/360 × 240 minutes = 90 minutes
Lucy:
102/360 × 240 minutes = 68 minutes
To find how many minutes Zac spent watching TV than Lucy:
90 minutes - 68 minutes = 22 minutes.
Do you understand, Kiara 12004?
Please help, thanks :) (Question is attached below)
Answer:
Solution : Graph 4
Step-by-step explanation:
Let's break down this function,
{ y = 5 if x ≤ - 2, y = 0 if x = 3, y = - 1 if x > 3 }
As you can see, graph 4 is the only one that represents this.
• When y = 5, x ≤ - 2. This is represented by a ray with a colored hole, indicating that x = - 2. At the same time this ray extends infinitely in the negative direction, indicating that x < - 2.
• When y = 0, x = 3. This is represented as the point ( 3, 0 ).
• And when y = - 1, x > 3. At y = - 1 another respective ray, that has a non - filled hole, indicates that x ≠ 3. The ray extends infinitely in the positive direction, meeting the criteria that x > 3.
Given that
7
x
−
2
y
=
35
Find
y
when
x
=
−
9
Answer:
y = - 49
Step-by-step explanation:
Given
7x - 2y = 35 ← substitute x = - 9 into the equation
7(- 9) - 2y = 35, that is
- 63 - 2y = 35 ( add 63 to both sides )
- 2y = 98 ( divide both sides by - 2 )
y = - 49
Answer:
[tex]\boxed{y = -49}[/tex]
Step-by-step explanation:
=> [tex]7x-2y = 25[/tex]
Given that x = -9
=> [tex]7(-9)-2y = 35[/tex]
=> [tex]-63 -2y = 35[/tex]
Adding 63 to both sides
=> [tex]-2y = 35+63[/tex]
=> [tex]-2y = 98[/tex]
Dividing both sides by -2
=> [tex]y = 98/-2[/tex]
=> [tex]y = -49[/tex]
what is the inverse of the fuction f(x)=19/x
Answer:
[tex]f^-^{1} (x)=\frac{19}{x}[/tex]
Step-by-step explanation:
To find the inverse of this function, switch the variables like this:
[tex]\frac{19}{x}\\\\x=\frac{19}{y} \\[/tex]
Then, solve for y, like this:
[tex]y= \frac{19}{x} \\[/tex]
Replace y with [tex]f^-^{1} (x)[/tex].
[tex]f^-^{1} (x)=\frac{19}{x}\\[/tex]
State if the gives angles are coterminal.
Answer:
Below
Step-by-step explanation:
Coterminal angles are angles with same terminal angles
Mathematically speaking these angles should have the same coordinates in a trigonomitrical circle
●●●●●●●●●●●●●●●●●●●●●●●●
Angles like 0° and 360° are coterminal since to we made a spin from 0° to 360°
For two angles A and B to be coterminal they should verify this relation :
A = B + k*360° with k an integer
So A-B = k*360°
●●●●●●●●●●●●●●●●●●●●●●●●
7) :
35° and 395°
395° -35° = 360°
360° is a multiple of 360° so these angles are coterminal
8) :
140° and 860°
860° - 140° = 720°
720° is a multiple of 360°
720 = 360° × 2
9) :
350° and -710°
350 -(-710) = 350+ 710 = 1060°
1060° isn't a multiple of 360°
So these angles aren't coterminal
10) :
130° and -230°
130 -(-230) = 130+230 = 360°
So these angles are coterminal
11) :
30° and -690°
30 -(-690) = 30+ 690 = 720°
720 is a multiple of 360 so these angles are coterminal
12) :
210° and 10°
210-10 = 200
200 isn't a multiple of 360 so these angles aren't coterminal
Give the excluded values for 6/t+5 + 2/t-5 = 3t-1/t^2-25. Do not solve
A)25
B)-5,5
C)5,25
D)-5,5,25
Please help i don’t understand
Answer:
B -5, and 5
Step-by-step explanation:
you can't have zero on the bottom
what is 1 add 1 please help!!!!!!!!!!!!!!!PS first person to get it correct gets brainiest
Answer: 2
Step-by-step explanation:
Answer:
2...........
Step-by-step explanation:
1 + 1 = 2............
A television set costs $350 cash. When bought on hire purchse, a deposit of $35 is required, followed by 12 monthly payments of $30. How much is saved by paying cash?
Answer:
$45
Step-by-step explanation:
find the hire purchase price: 12 months x $30 = $360 + $35 deposit = $395
difference: 395 - 350 = $45
Please help I am not sure how to solve this problem.
Answer:
Measure of arc TSU = 201°
Step-by-step explanation:
For the inscribed circle of triangle XYZ, we have;
∠XZY = 21°
Segment TZ and segment UZ are tangent to circle R
Therefore, ∠ZUR = ∠ZTR = 90° (angle formed by a tangent)
Length UR = Length TR = Radius of circle R
∴ ΔZTR ≅ ΔZUR Side Angle Side (SAS) rule of Congruency
∴ ∠RZT ≅ ∠RZU, (Congruent Parts of Congruent Triangles are Congruent, CPCTC)
∠XZY = ∠RZT + ∠RZU (Angle summation)
21° = ∠RZT + ∠RZU = 2×∠RZU (Transitive property)
∠RZU = 21°/2 = 10.5° = ∠RZT
∴ ∠URZ = 180- 90 - 10.5 = 79.5° = ∠TRZ (CPCTC)
arc TU = ∠URT = ∠URZ + ∠TRZ = 79.5 + 79.5 = 159° (angle addition)
∴ Measure of arc TSU = 360° - 159° = 201° (Sum of angles at the center of the circle R)
Measure of arc TSU = 201°.
Two angles are supplementary (meaning they add up to 180 ° ). The ratio of the relationship of the measure of Angle A to the measure of Angle B is 3:4. What are the measure of both angles?
Answer:
Angle A= 77.14°
Angle B= 102.86°
Step-by-step explanation:
Supplementary angles are angles that add up to 180°, as stated in the question.
This means that Angle A + Angle B= 180°
The measure of Angle A to Angle B is 3:4
3:4 --------> 3+4 = 7 total parts
Hence, angle A will be 3/7 of the total angle (180°)
angle B will be 4/7 of the total angle (180°)
That is, angle A = 3/7 × 180° = 77.1428°
angle B= 4/7 × 180° = 102.857°
Approximately, angle A = 77.14° while angle B= 102.86°
The arm and blade of a windshield wiper have a total length of 30 inches. The blade is 24 inches long and the wiper sweeps out an angle of 125 degrees.
Answer:
942.5 in²
Step-by-step explanation:
The formula for the area (A) of a sector of a circle is
A = ½r²θ
where θ is the angle in radians.
1. Convert the angle to radians
θ = 125°
[tex]\theta = 125^{\circ} \times \dfrac{\pi \text{ rad }}{180^{\circ}} =\frac{25}{36} \pi\text{ rad}[/tex]
2. Area swept out by wiper arm
A = ½r²θ = ½ × (30 in)² × θ = ½ × 900 in²× θ = 450 θ in²
3. Area missed by wiper
A = ½r²θ = ½ × (6 in)² × θ = ½ × 36 in²× θ = 18 θ in ²
4. Area covered by wiper
A = 450 θ in² - 18 θ in² = 432 θ in²
5. Insert the value of θ
A = 432 × 25/36 π in² = 300π in² ≈ 942.5 in²
The area swept out by the wiper blade is 942.5 in².
Mikel gave a $1.32 tip for an order that cost $8.80. Determine whether or not each tip below is proportional to Mikel's tip. $2.22 tip for a $14.80 order $1.86 tip for a $10.50 order $0.78 tip for a $5.20 order
Answer:
1. Proportional
2. Not proportional
3. Proportional
Step-by-step explanation:
Mike's proportion
Michael gave $1.32 tip for an order that cost $8.80
$1.32÷$8.80=0.15
Given
1. $2.22 for $14.80
$2.22÷$14.80 =0.15
It is proportional to Mike's tip
2. $1.86 for $10.50
$1.86÷$10.50=0.1771
It I not proportional to Mike's tip
3. $0.78 for $5.20
$0.78÷$5.20=0.15
It is proportional to Mike's tip
Therefore,
1. Proportional
2. Not proportional
3. Proportional
Answer:
The first one is proportional
The second one is not proportional
The third one is proportional
Step-by-step explanation:
I just got it right on Khan
PLEASE HELP ME with this question! I really need help...
Answer:
One of the other perpendicular bisectors must pass through point B
Step-by-step explanation:
Let's look at the choices:
— incenter equidistant from B and C.
The incenter is on the perpendicular bisector of BC. Every point on that line is equidistant from B and C. This statement is True.
__
— angles B and C are congruent.
As we said above, A (on the perpendicular bisector of BC) is equidistant from B and C. That makes the triangle isosceles. The congruent angles are B and C, opposite congruent sides AC and AB. This statement is True.
__
— the perpendicular bisector of BC passes through the incenter.
The incenter is the point of concurrence of the angle bisectors. Since the perpendicular bisector of BC goes through the a.pex of triangle ABC at A, it is the angle bisector there. Hence the incenter lies on that line. The statement is True.
__
— B lies on one of the other perpendicular bisectors.
This will be true if the triangle is equilateral. Nothing in the problem statement indicates this is the case. The statement is False.
What’s the y- intercept and x-intercept of y = 3/4x + 3
Answer:
see below
Step-by-step explanation:
y = 3/4x + 3
To find the y intercept, let x =0 and solve for y
y = 0+3
The y intercept is 3
To find the x intercept, let y =0 and solve for y
0 = 3/4x+3
-3 = 3/4x
-3 *4/3 = 3/4x*4/3
-4 =x
The x intercept is -4
━━━━━━━☆☆━━━━━━━
▹ Answer
y-intercept = 3
x-intercept = -4
▹ Step-by-Step Explanation
y = mx + b
y = 3/4x + 3
0 = 3/4x + 3
-3 = 3/4x
-3 * 4/3 = 3/4x * 4/3
x = -4
Hope this helps!
CloutAnswers ❁
Brainliest is greatly appreciated!
━━━━━━━☆☆━━━━━━━
Simplify the expression: (− 2/3 pq^4)^2·(−27p^5q)
Answer:
-12p^7q^9
Step-by-step explanation:
(-2/3Pq^4)^2×(-27P^5q)
= ((-2)^2)/3^2 × P^2 q^4-2 × (-27qp^5)
= ((-2)^2)/3^2 × 27p^7q9
= (((-2)^2 x 27p^7q9)/3^2
= -((4×27p^7q^9)/9)
= -(108p^7q^9)/9
= -12p^7q^9
Please answer it now in two minutes
Answer:
59.0
Step-by-step explanation:
Given a right angled triangle, ∆XYZ, to know which trigonometric ratio formula to apply in finding the measure of angle X, note the following:
Opposite side to angle X = 6
Hypotenuse = 7
Therefore, we would apply the following trigonometric ratio formula to solve for m<X:
[tex] sin X = \frac{6}{7} [/tex]
[tex] sin X = 0.8571 [/tex]
[tex] X = sin^{-1}(0.8571) [/tex]
[tex] X = 58.99 [/tex]
[tex] m < X = 59.0 [/tex] (rounded to nearest tenth)
The slope of a line is -4, and the y-intercept is -3. What is the equation of the line written in slope-intercept form?
Oy= 4x - 3
y=-4x + 3
Oy=-4x - 3
Answer:
y=-4x-3
Step-by-step explanation:
y=mx+b
y=b=-3 ( y intercept is when x=0, then y=b=-3)
y=-4x-3
Solve this problem. Reduce to lowest terms.
John worked in his garden for 4 3/4hours on Saturday and 2 1/2 hours on Sunday. How
many hours did he work in all?
0 6 hours
O 7 hours
4 hours
5 hours
32 is an example of A. an algebraic equation B. a numerical expression C. a numerical equation D. an algebraic expression Reset
ayuda plis nosé donde estoy q Brainli es este
ayuda
Answer:
hmm I'm not sure but i think it's B. a numerical expression
Sowwy if this didn't help :c
At the beginning of the school year, Jamie had $500 in her savings account. She wants to have at least $200 left in the account at the end of the school year. Each week, she withdraws $30 for spending money. To determine how many weeks she can spend $30, Jamie wrote and solved this inequality. 500 − 30x ≥ 200 −500 −500 −30x ≥ −300 x ≥ 10 Review Jamie's work. What was her error? Jamie should have used the less than or equal to sign when writing the inequality. Jamie should have reversed the inequality when using the division property of inequality. Jamie should have added 500 to both sides. Jamie should have started by dividing by –30.
Answer:
Jamie should have reversed the inequality when using the division property of inequality.
Step-by-step explanation:
Jamie wrote
500 − 30x ≥ 200
Subtract 500 from both sides
500-500-30x ≥ 200-500
-30x ≥ -300
Divide both sides by -30
x ≥ 10
Instead of reversing the inequality when using the division property of inequality
500 − 30x ≥ 200
Subtract 500 from both sides
500-500-30x ≥ 200-500
-30x ≥ -300
Divide both sides by -30
x <or= 10
the answer is B i hope this helps
^_^
what is the mean devuation of the following numbers
Answer:
hi pls do enter the no.s
what is the value of the exponent expression below?
Answer:
6Option C is the correct option.
Step-by-step explanation:
[tex] {36}^{ \frac{1}{2} } [/tex]
Write the number in exponential form with a base of 6
[tex] =( {6}^{2}) \: ^{ \frac{1}{2} } [/tex]
Simplify the expression by multiplying the exponents
[tex] = 6[/tex]
Hope this helps..
Best regards!!
Problem solving: Janine is 7 years younger than Lucy and 4 years older than
Samantha. The average of their ages is 16. How old is:
a. Janine?
b. Samantha?
c. Lucy?
Answer:
Janine=12.6(repeating) Samantha=15.6(repeating) Lucy=19.6(repeating)
Step-by-step explanation:
Lets concentrate on one person, Janine.
Janine = Lucy - 7
Janine = Samantha - 3
If the averae of the 3 people's ages is 16, then we should multiple that by three to get 48, the number of their ages combined.
Janine + Lucy + Samantha = 48
The differences between Janine to Lucy and Janine to Samantha combined is 10, so we can subtract that from 48 to get 38, which is 3 times Janines age.
38/3=12.6(repeating)
That is Janine's age. We can use that to find both Lucy's and Samantha's ages respectively by using their equations. Lucy's is 19.6(repeating) and Samantha's is 15.6(repeating). I hope you can give me brainliest, and that this helped!