Answer:
[tex]\frac{\sqrt{5}-\sqrt{2} }{3}[/tex]
Step-by-step explanation:
[tex]\frac{1}{\sqrt{5} + \sqrt{2} }[/tex]
[tex]\frac{1}{\sqrt{5} + \sqrt{2} } * \frac{\sqrt{5} - \sqrt{2} }{\sqrt{5} - \sqrt{2} }[/tex]
[tex]\frac{\sqrt{5} - \sqrt{2} }{(\sqrt5)^{2} - \sqrt{2})^2 } }[/tex]
[tex]\frac{\sqrt{5} - \sqrt{2} }{5-2}[/tex]
[tex]\frac{\sqrt{5}-\sqrt{2} }{3}[/tex]
D and E are points on sides AB and AC respectively of triangle ABC such that DE || BC. If AD = x-1, DB = x – 3, AE = x + 3 and EC = x , the value of x is:
9514 1404 393
Answer:
9
Step-by-step explanation:
The triangles are similar, so corresponding sides are proportional.
AE/AD = EC/DB
(x+3)/(x -1) = x/(x -3)
x^2 -9 = x^2 -x . . . . . . . cross multiply
x = 9 . . . . . . . . . . . add x+9-x^2 to both sides
2 consecutive postive nos are such that the sum of their squares is 113. Find the 2 numbers
Answer:
7,8
Step-by-step explanation:
n^2+(n+1)^2=113; this is the information we are provided in the question.
n^2+n^2+2n+1=113 ; just expanding the numbers
2n^2+2n-112=0 ; moving everything to the same side
n^2+n - 56= 0 ; divide everything by two
(n-7)(n+8)=0 : factor the polynomial
so answers for n are: 7 and -8. since the questions asks for positive numbers -8 cannot be correct.
so n=7
n+1 = 8
Test 645 for divisibility by 2, 3, 5, 9, and 10.
Answer:To test for divisibility, you look for answers that are whole numbers when you divide 59859 by either 2, 3, 5, 9, or 10.
To start divide it by each of them:
59859/2=29929.5
59859/3= 19953
59859/5= 11971.8
59859/9= 6651
59859/10= 5985.9
Now look at which of the choices are whole numbers
3 and 9 are the only non decimal numbers, therefore, C would be your answer.
Step-by-step explanation:
Make 'r' the subject of this formula: 3r - 5 = p
Answer:
hey I am not about what the question says but I think this is the answer:
3r=p+5
so the subject is 3r
The sum of the first eight terms in a Geometric Series is 19680 and the sum of the first four terms is 240. A) Find the first term. B) Find the common ratio. C) Justify your answers by showing steps that demonstrates your answers generate S8=19680 and S4=240.
Answer:
First Term = 6
Common Ratio = 3
Step-by-step explanation:
According to the Question,
Given, The sum of the first eight terms in a Geometric Series is 19680 and the sum of the first four terms is 240 .Thus, [tex]S_{8} = 19680[/tex] & [tex]S_{4} = 240[/tex] .
The Sum of n-term of Geometric Mean is [tex]S_{n} = \frac{a(r^{n-1)} }{r-1}[/tex] Where, r>1 , a=First term of G.P & r=common Ratio .Now, on solving [tex]\frac{S_{8} }{S_{4} }[/tex] we get,
[tex]\frac{19680}{240} = \frac{\frac{a(r^{8-1)} }{r-1}}{\frac{a(r^{4-1)} }{r-1}}[/tex]
[tex]82 = \frac{r^{8}-1 }{r^{4}-1 }[/tex]
[tex]82r^{4}-82 = r^{8}-1\\r^{8}-82r^{4}+81 = 0\\r^{8}-81r^{4}-r^{4}+81 = 0\\(r^{4}-81)( r^{4}-1) =0[/tex](r=1 is not possible so neglect [tex]( r^{4}-1) =0[/tex] )
So, r=3 Now Put this value in [tex]S_{4} = {\frac{a(r^{4-1)} }{r-1}}[/tex] We get a=6 .
(05.02)
Solve the following system of equations: (1 point)
x − 2y = 14
x + 3y = 9
Group of answer choices
(1, 12)
(−1, −12)
(12, −1)
(12, 1)
solve for x and y, round to one decimal place
Answer:
x=48
y=50
Step-by-step explanation:
mark me as BRAINLIEST
follow me
carry on learning
correct me if im wrong
Can you guys help me pleaseeeee!
Answer: A) True
Step-by-step explanation:
GF and KJ are marked with one dash indicating the are congruent. Same for FH and JL but this time it's marked with 2 dashes. Angles F and J are congruent because they are both right angles. So, we have a side congruent an angle congruent and a side congruent. We can use SAS to say they are congruent.
(Brainliest?)
Financial software can do all of the following except ____.
A.
prepare your taxes
B.
apply for loans
C.
keep track of expenses
D.
monitor your savings
Answer: Apply for loans
Step-by-step explanation:
I just took the quiz off gradpoint :) trust me its right!!!!
There is a bag with only red marbles and blue marbles. The probability of randomly choosing a red marble is 1 /9 . There are 63 marbles in total in the bag and each is equally likely to be chosen. Work out how many red marbles there must be.
Answer: 7 red marbles.
Step-by-step explanation:
Since we are given the information that there are only red marbles and blue marbles in the bag and that the probability of randomly choosing a red marble is 1 /9 while there are 63 marbles in total.
Then the number of red marbles will be:
= 1/9 × 63
= 7
There are 7 red marbles
The number if blue marbles will be:
= 63 - 7
= 56 blue marbles
You are on a ship at sea. You see a lighthouse in the distance. You know the lighthouse is 145 feet tall. You measure the angle of elevation to the top of the lighthouse at 5 degrees. How far are you from the bottom of the lighthouse? *
Answer:
1657.14 ft
Step-by-step explanation:
Tan = opposite / adjacent
tan 5 = 145 / adjacent
0.0875 = 145 / adjacent
adjacent = 145 / 0.0875
= 1657.14 ft
The measures of the angles of a triangle are shown in the figure below. Solve for x.
Answer:
x=57°
Step-by-step explanation:
the sum of the measures of the angles of a triangle add up to 180°.
it is given that there is a 33°, and a right angle which is 90°.
to find x:
x=180°-(90°+33°)
x=180°-123°
x=57°
Answer:
180° - 33° - 90° = 57°
x = 57°
Solve the absolute value inequalty ⎜3x + 5⎟≤ - 2 a No Solution b - 2 ≤ x ≤ - 7 c All real numbers d -7/3 ≤ x ≤ -3/7
Answer:
Step-by-step explanation:
First, absolute value is always POSITIVE ⇒ the given inequality has No Solution!!
Just to show you how to solve this kind of problems:
1). If (3x + 5) ≥ 0, then 3x + 5 ≤ - 2
3x ≤ - 5 - 2
3x ≤ - 7
x ≤ - [tex]\frac{7}{3}[/tex]
2). If (3x + 5) < 0, then - (3x + 5) ≤ - 2
3x + 5 ≥ 2
3x ≥ - 3
x ≥ - 1
x ∈ ∅
Simplify the following expressions without using calculator 8/(2sqrt(6) + 3) - 4/(2sqrt(6) -3)
Step-by-step explanation:
[tex] \tt \longrightarrow \dfrac{8}{2 \sqrt{6} + 3 } - \dfrac{4}{2 \sqrt{6} - 3 } \\ \\ \tt \longrightarrow \dfrac{8(2 \sqrt{6} - 3) - 4(2 \sqrt{6} + 3)}{(2 \sqrt{6} + 3)(2 \sqrt{6} - 3 ) } \\ \\ \tt \longrightarrow \dfrac{16\sqrt{6} - 24 - 8 \sqrt{6} - 12}{(2 \sqrt{6} ) {}^{2} - (3) {}^{2} } \\ \\ \tt \longrightarrow \dfrac{8\sqrt{6} - 36}{24 - 9 } \\ \\ \tt \green{\longrightarrow \dfrac{8\sqrt{6} - 36}{15 }} [/tex]
i need the base and hight
Answer:
Height = 5 and Base = 10
Step-by-step explanation:
The base of the parallelogram is twice the perpendicular height of the parallelogram. The area of the parallelogram is 50 cm².
Formula for area of parallelogram = base × height
Base = 2h
Height = h
∴ Area = 2h × h = 50
Solution:
2h × h = 50
2h² = 50
[tex]\frac{2h^{2} }{2} = \frac{50}{2}[/tex]
h² = 25
[tex]\sqrt{h^{2} } = \sqrt{25}[/tex]
h = 5
∴ height = 5 and base = 2(5) = 10
Use Venn diagrams notation to describe the shading of
A
B
Answer:
A ∩ B
Step-by-step explanation:
The shaded part is in common between the two diagrams
We can write this part in this way :
A ∩ B
I will pay for the answer.
Answer:
D
8x^2-12x+5
thanx for youer sug
Answer:
[tex]8x^2-12x+5[/tex]
Step-by-step explanation:
This is the same as saying h(g(x)). All you do is take the g(x) equation and plug that in for x in the h(x) equation.
h(x) = 4x+1 Plug in g(x) equation for x
h(g(x)) = [tex]4(2x^2-3x+1)+1[/tex] Distribute the 4 and simplify
h(g(x)) = [tex]8x^2-12x+5[/tex]
Solve 2 ≤ 2x + 4 < 10 for x.
–1 ≤ x < 3
1 < x < 3
–1 < x < 3
1 ≤ x < 3
Answer:
-1 ≤ x < 3
Step-by-step explanation:
2 ≤ 2x + 4 < 10
Subtract 4 from all sides
2-4 ≤ 2x + 4-4 < 10-4
-2 ≤ 2x < 6
Divide all sides by 2
-2/2 ≤ 2x/2 < 6/2
-1 ≤ x < 3
Simplify (12^0)(12^6). Write your answer using an exponent. Explain how you found your answer.
Step-by-step explanation:
(12^0)(12^6)
1 ×12⁶. (a⁰=1, a is a number)
=12⁶
The voltage E in an electrical circuit is modeled by E=3.8cos(110π t). What is the maximum voltage?
Answer:
Max E=3.8 Voltage
Step-by-step explanation:
[tex]maximum-value -of cos(\theta) =1, when \theta=0,360,720\\110\pi t=0, therefore t=0, 1.04, 2.08 etc[/tex]
The maximum voltage for the electric circuit is E = 3.8 when the value of the trigonometric function cos(110π t) has the maximum value = 1, from the range of cosine function.
What is the range of the trigonometric function cosine?The range of the trigonometric function of cosine, that is, cos θ, is [-1, 1], that is, -1 ≤ cos θ ≤ 1.
How do we solve the given question?We are given that the voltage E in an electrical circuit is modeled by E = 3.8cos(110π t).
We are asked to find the maximum voltage E that can be obtained from the circuit.
The voltage E = 3.8cos(110π t).
In the given formula 3.8 is constant and cos(110π t) is variable. The value of E is maximum when the trigonometric function cos(110π t) attains the maximum value.
Since its a cos function, the maximum value it can attain = 1, as the range of the trigonometric function of cosine, that is, cos θ, is [-1, 1], that is, -1 ≤ cos θ ≤ 1.
When the variable attains the maximum value = 1, the value of the voltage E = 3.8*1 = 3.8.
∴ The maximum voltage for the electric circuit is E = 3.8 when the value of the trigonometric function cos(110π t) has the maximum value = 1, from the range of cosine function.
Learn more about the ranges of trigonometric functions at
https://brainly.com/question/9565966
#SPJ2
which of the following is a geometric sequence?
Answer:
D
Step-by-step explanation:
notice how everything goes up by 3? that's a sequence.
The weight of three articles is 856 kg. If two of the articles weigh 502kg, what is 1/2 the weight of the third article?
Answer:
177 kg
Step-by-step explanation:
Find the weight of the third article by finding the difference between 502 and 856, since 856 kg is the total weight and 502 kg is the weight of the other 2 articles:
856 - 502
= 354
Now, find 1/2 of the weight, by dividing this by 2:
354/2
= 177
So, 1/2 the weight of the third article is 177 kg
Craig threw a handful of identically shaped buttons into the air then collected 14 bottoms that landed on the carpet. Is this sample of the buttons likely to be biased yes or no
Answer:
possible?? but I think that there is a typo, and that there would not be a bias
Step-by-step explanation:
can we assume that there are no typos in the question
he threw BUTTONS in the air, and look at buttons that landed with the BOTTOMS facing up ??? in that case the weight might bias the orientation of the landing... I think that you have a typo and it just says that he collected 14 BUTTONS, in that case given that they are "IDENTICAL" we most likely can assume that there would be no bias (size color, texture are all the same)
Parallelogram ABCD is adjacent to rhombus DEFG, as shown below, and FC intersects AD at H.
B
D
H
E
If m Z B=118 and m2 AHC=138, determine and state m GFH.
Answer:16,284
Step-by-step explanation:
Lauren uses a calculator to find Three-fourths divided by StartFraction 3 plus 9 over 36 EndFraction and gets a result of Nine-fourths. Which statement best describes her work?
Answer:
11/20
Step-by-step explanation:
a telephone pole is 24 feet tall
Answer:i honestly dont know just trying to get points
Step-by-step explanation:
can someone help me I don't understand
Answer:
(a) 165 m/min
(b) 107.14m/min
Step-by-step explanation:
The slope of the distance time graph gives speed.
Here, the speed of the segment A is
[tex]v_A= \frac{900-0}{4-0}=225 m/min[/tex]
The speed of segment B is
[tex]v_B= \frac{1500- 900}{14-4}= 60 m/min[/tex]
(a) The change in speed is
= 225 - 60 = 165 m/min
(b) The average speed is defined as the ratio of total distance to the total time.
So, the average speed is
[tex]= \frac{1500}{14}= 107.14 m/min[/tex]
For the function Rx) = 1/x+1 which of these could be a value of F(x) when x is
close to -1
O A. -0.01
OB. 0.01
O c. 1
O D. -10,000
Answer:
D. -10000
Step-by-step explanation:
you really need to copy or type the question better.
I can only assume what you really mean.
I guess, you want to say that F(x) = 1/(x+1)
when the value for x gets close to -1, the whole expression gets close to 1/0, which would bring numbers with larger and larger absolute values, leading to infinity.
you also did not say from what direction we are getting closer to -1.
we could come from -2 and move closer and closer to -1.
in this case (x+1) would always be smaller than 0 (negative sign).
or we could come from +1 and then 0 and move towards -1, in which case (x+1) would airways be bigger than 0 (positive sign).
anyway, when being closer and closer to -1, the absolute value of the resulting functional values will get bigger and bigger.
the only answer option with a larger absolute value is D (-10000).
so, that had to be the solution, and it also means that we are coming from -2 to -1, and the sign is negative.
How many eighths does it take to equal 1/4 model
Answer:
2 eighths.
Step-by-step explanation:
Answer:
2 eighths
Step-by-step explanation:
1/8 + 1/8 = 2/8 or 1/4
Which of the following is the correct definition of payment shock??
Answer:
payment shock refers to a dramatic increase in an individual's debts and liabilities that may cause them to default on their financial obligations. Put simply, payment shock occurs when, rather suddenly, someone is obligated to pay more in monthly debt than they can afford from their income
Answer: The new payment after the initial fixed-rate period is much higher
than the homeowner expected.
Step-by-step explanation: took the quiz.