Rút gọn biểu thức sau
(2/2-√5 - 2/2+√5):√20
Answers
\(▪▪▪▪▪▪▪▪▪▪▪▪▪ {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪\)
let's solve for value of (2/2-√5 - 2/2+√5) :
\( \dfrac{2}{2 - \sqrt{5} } - \dfrac{2}{2 + \sqrt{5} } \)\( \dfrac{2(2 + \sqrt{5} ) - 2(2 - \sqrt{5} )}{ {2}^{2} - 5} \)\( \dfrac{4 + 2 \sqrt{5} - 4 + 2 \sqrt{5} }{4 - 5}\)\( \dfrac{4 \sqrt{5} }{ - 1} \)\( - 4 \sqrt{5} \)now, let's simply the ratio :
\( - 4 \sqrt{5} : \sqrt{20} \)\( \dfrac{ - 4 \sqrt{5} }{ \sqrt{20} } \)\( \dfrac{ - 4}{ \sqrt{4} } \)\( - \sqrt{4} \)Therfore , the required ratio is :
\( - \sqrt{4} :1\)Related Questions
what is the vaulue of |6| - | -6| - (-6)
Answers
Answer:
I think it is just 6
Step-by-step explanation:
I hope it helped!
What is the equation of the line in slope-intercept form?
Enter your answer in the boxes y= blank x + blank
Answers
Answer:
-3 + 4
Step-by-step explanation:
Answer:
y= 3/5x + 3. You go up 3 to where the other point is, then go over 5 to reach it. The y-intercept is 3 because that 3 is on the Y axis
Step-by-step explanation:
PLEASE HELP!!
A) 78
B) 145
C) 113
D) 102
Answers
Answer:
D
Step-by-step explanation:
the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.
∠ BCD is an exterior angle of the triangle , then
∠ BCD = 35° + 67° = 102°
Solve the equation for t A=s(t+r)x
Answers
Answer:
t = (A/sx) - r
Step-by-step explanation:
Solve for t like this:
\(A = s(t+r)x\\A = sx(t+r)\\\\\frac{A}{sx} = t+r\\\frac{A}{sx} - r = t\\t= \frac{A}{sx} - r\)
What is the solution for the system of linear equations shown in the graph?
answers are in the second image
Answers
Step-by-step explanation: The solution to this system of equations will be where the two lines on the graph intersect with each other.
Notice that both of them intersect to the left of the y-axis which means our x - coordinate must be negative.
They also intersect above the x-axis so our y-coordinate must be positive.
So the only option with a negative x-coordinate
and a positive y-coordinate is (-1/4, 3/4).
Assume the random variable x is normally distributed with mean μ=86 and standard deviation σ=4. Find the indicated probability. P(73
Answers
P(73 < X < 83) = [probability value] (calculated using z-scores and the standard normal distribution)
The probability P(73 < X < 83) for a normally distributed random variable with a mean μ = 86 and standard deviation σ = 4, we can standardize the values using the z-score formula.
First, calculate the z-score for the lower value (73):
z1 = (73 - 86) / 4
Next, we calculate the z-score for the upper value (83):
z2 = (83 - 86) / 4
Using the standard normal distribution table or a calculator, we can find the probabilities associated with these z-scores. Then, we calculate the difference between the two probabilities to find the desired probability: P(73 < X < 83) = P(z1 < Z < z2).
The final probability value can be determined by subtracting the cumulative probability associated with the lower z-score from the cumulative probability associated with the higher z-score.
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an angle measures 2.8 radians and the initial ray of the angle points in the 3-o'clock direction. a circle with a radius 2.6 cm long is centered at the angle's vertex. the terminal point is how many radii to the right of the circle's center? radii the terminal point is how many cm to the right of the circle's center? cm
Answers
Therefore, the terminal point is 0.26 radii to the right of the circle's center and 0.67 cm to the right of the circle's center.
The angle in question has an initial ray pointing in the 3-o'clock direction and measures 2.8 radians. It is centered at the vertex of a circle with a radius of 2.6 cm. To calculate the number of radii and the number of cm the terminal point is to the right of the circle's center, we need to use the formula for arc length. Arc length is equal to the circumference of the circle multiplied by the central angle's measurement, divided by 2π.
So, the arc length of this angle is equal to 2.6 cm times 2.8 radians divided by 2π, or\(2.6 x 2.8 / 6.28 = 0.67 cm.\) The terminal point is 0.67 cm to the right of the circle's center, which is equal to \(0.67/2.6 = 0.26 radii.\)
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if a slice of bread with 1 gram of fat, 10 grams of carbohydrate, and 2 grams of protein contains 57 calories, calculate the percent of calories provided by fat. if a slice of bread with 1 gram of fat, 10 grams of carbohydrate, and 2 grams of protein contains 57 calories, calculate the percent of calories provided by fat. 57% 9% 16% 30%
Answers
The correct answer is not provided among the given options. The percentage of calories provided by fat in the slice of bread is approximately 15.8% ≈ 16%
The caloric content of macronutrients differs: fat provides 9 calories per gram, while carbohydrates and protein provide 4 calories per gram each. To calculate the calories from fat, we multiply the grams of fat by the caloric value of fat:
Calories from fat = 1 gram of fat × 9 calories/gram = 9 calories
Next, we calculate the total calories in the slice of bread by summing up the caloric contributions from each macronutrient:
Total calories = (1 gram of fat × 9 calories/gram) + (10 grams of carbohydrates × 4 calories/gram) + (2 grams of protein × 4 calories/gram) = 9 + 40 + 8 = 57 calories
Finally, we can calculate the percentage of calories provided by fat by dividing the calories from fat by the total calories and multiplying by 100:
Percentage of calories from fat = (9 calories / 57 calories) × 100 ≈ 15.8%
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evaluate the limit, if it exists. (if an answer does not exist, enter dne.) lim t→4 t2 − t − 12 t − 4
Answers
The limit of the given function as t approaches 4 is 7.
To evaluate the limit, we substitute the value of 4 into the function. By direct substitution, we get (4*2 - 4 - 12) / (4 - 4). Simplifying this expression, we have (16 - 4 - 12) / 0, which equals 0 / 0. This is an indeterminate form, which means we need to apply further algebraic manipulation to determine the limit.
To find the limit, we can factor the numerator as (t - 4)(t + 3). This allows us to cancel out the common factor of (t - 4) in the numerator and denominator. After canceling out (t - 4), the expression becomes (t + 3). Now we can evaluate the limit by substituting the value of t as it approaches 4 into the simplified expression.
Taking the limit as t approaches 4 of (t + 3), we get (4 + 3), which equals 7. Therefore, the limit of the given function as t approaches 4 is 7.
In summary, by factoring the numerator and canceling out the common factor of (t - 4), we simplified the expression to (t + 3). Substituting the value of t as it approaches 4 into the simplified expression gives us the limit of 7.
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can someone please help me find angle ADB
Answers
The measure of the angle ADB, obtained from the relationship between the base angles of an isosceles triangle and the angle formed at the center and on the circumference of circle is; ∠ADB = 55°
What is an isosceles triangle?An isosceles triangle is a triangle that has congruent base angles.
The angle at the m∠A = 180°- (30° + 70°) = 80°
The two tangent and secant theorem indicates that the half the difference between the arcs CD and AB is; 30°, therefore;
30 = (1/2) × (AB - CD)
The congruence relationship between the segment BC and AB indicates that the base angle of the isosceles triangle ABC and the angle ACB
Therefore, the angle ACB = 55°
The angle at the center a of a circle is twice the angle formed at the circumference of a circle.
Arc AB = 2 × angle ACB = 2 × 55° = 110°
Arc CD = 110 - 2 × 30 = 50°
∠DBC = 50°/2 = 25°
∠DBA = 70° - 25° = 45°
Angle ADB = 180 - 80 - 45 = 55
Angle ADB = 55°
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Please answer my question now in two minutes
Answers
Answer:
given,triangle EFG is congruent to triangle HIJ,THEIR corresponding sides are equal,
so, 10x=x+45
10x_x=45
or,9x=45
therefore , x=5
again,
3y = y+14
or, 3y_y=14
or, y=14/2
therefore the value of y is 7.
so the value of x is 5 and y is 7.
hope its helpful to uh...
CAN SOMEONE HELP ME PLS ASAP
Answers
B
Explanation:
10x1=10
(not sure haven’t done this in a very long time)
C 17. At high school A, the mean score of 50 students on a science test is 75.
At high school B, the mean score of 40 students on the same test is 80.
What is the mean score of the 90 students?
Answers
Answer:
Mean score of 90 students = 77.2
Step-by-step explanation:
Mean score of 50 students from school A = 75
Mean score of 40 students from school B = 80
We need to find mean score of the 90 students?
First we will find sum of scores of students from school A
We know that: \(Average=\frac{Sum\:of\:Terms}{Number\:of\:terms}\)
We have Average = 75, Number of terms = 50, We need to find Sum of terms (scores)
\(Average=\frac{Sum\:of\:Terms}{Number\:of\:terms}\\75=\frac{Sum\:of\:Terms}{50}\\Sum\:of\:Terms= 75\times 50\\Sum\:of\:Terms=3750\)
So, Sum of scores for School A = 3750
Now, we will find sum of scores of students from school B
We know that: \(Average=\frac{Sum\:of\:Terms}{Number\:of\:terms}\)
We have Average = 80, Number of terms = 40, We need to find Sum of terms (scores)
\(Average=\frac{Sum\:of\:Terms}{Number\:of\:terms}\\80=\frac{Sum\:of\:Terms}{40}\\Sum\:of\:Terms= 80\times 40\\Sum\:of\:Terms=3200\)
So, Sum of scores for School B = 3200
Now, We will find mean score of the 90 students?
Mean score of 90 students will be:
\(Average=\frac{Sum\:of\:Terms}{Number\:of\:terms}\\Average=\frac{3750+3200}{90}\\Average=\frac{6950}{90}\\Average = 77.2\)
So, mean score of 90 students = 77.2
QUESTION 9 of 10: You enter a bid. Your cost on the product you make is $112 per unit. If you bid at $138 per unit, what percent is the price
you bid over your cost? (Round to the nearest percent)
a) 19%
b) 23%
C) 81%
Submit
Answers
From the information given, the percentage increase in the price bid over the cost will be 23%.
Cost on the product = $112.
Amount bid = $138
Therefore, the Percentage increase will be:
= (138 - 112) / 112 × 100
= 26/112 × 100
= 23%
Therefore, from the calculation above, it can be seen that the percentage increase in the price bid over the cost will be 23%.
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A cab company charges $ 2 per cab ride, plus an additional $ 1 per mile driven. How long is a cab ride that costs $ 45 ?
Answers
45-2=43 or 1(45) -2
The cross-section of the prism below is an equilateral triangle.
a) What is the area of the shaded face?
b) How many rectangular faces does the prism have?
c) What is the total area of these rectangular faces?
7 cm Scroll down
8 cm
Answers
a.) The area of the shaded face would be =54cm²
b.) The number of rectangular faces that the prism has =3
c.) The total area of the rectangular faces would be=162cm².
How to calculate the area of the shaded face in the diagram above?To calculate the area of the shaded face, the formula that should be used = length×width.
where;
Length = 9cm
width = 6cm
Area = 9×6 = 54cm²
The total number of rectangular faces = 3
The total area of these rectangular face would be area of one rectangular face multiplied by 3.
That is;
54×3 = 162cm²
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Sunil asks Sandra for 15 cookies. Saki then asks Sandra for 12 cookies. If Sandra originally had sixty cookies, What fraction of the initial amount of cookies does she have?
Answer
1/1
of the initial amount of cookies
Answers
Answer: 11/20
Step-by-step explanation: you take the original 60 cookies and take away the 12 and the 15 to get 33. The original whole number was 60/60. Now it would be 33/60, but in simplest form it is 11/20.
Sandra has 9/20 of the original cookies left.
How many different anagrams (including nonsensical words) can be made from the letters in the word statistics, using all the letters?
Answers
50,400 different anagrams can be made from the letters in the word statistics.
Given word : STATISTICS
Anagrams are words formed by jumbling the positions of the letters given in the word.
For such problems we do factorial of number of words and divide by the repeated letters factorials.
Total number of letters = 10
They can be permutated among themselves in 10! ways.
Some letters are repeated in word STATISTICS
Since, there are 3 S's and 3 T's and 2 I's
So, Number of anagrams = \(\frac{10!}{3!.3!.2!}\)
= \(\frac{10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3!}{3! \times 3 \times 2 \times 1 \times 2 \times 1}\)
= \(\frac{10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4}{3 \times 2 \times 2}\)
= 10 × 9 × 8 × 7 × 2 × 5
= 50,400
50,400 different anagrams can be made from the letters in the word statistics.
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ginger wants to join a gym she goes to the local gym and is told that there is a one time fee of 100$ to join and then a monthly fee of 30$ write an agebraic expression to represent the total cost of joining the gym using "m" as a variable
Answers
The expression to represent the total cost of joining the gym using m as a variable is 100 + 30m.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Local gym:
one time fee = $100
Monthly fee = $30
The total cost for m months.
= 100 + 30m
Thus,
The total cost for m months is 100 + 30m.
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Please I need help ASAP ;-;
Image is above
What is the area of the shaded region?
_____ Square units
Answers
Answer:
164
Step-by-step explanation:
Because 12 times 16 minus 18
Half the value of 3x-9 is x+37. What is the value of x?
Answers
Answer:
x = 83
Step-by-step explanation:
You know that half of 3x-9 is x+37. That means 2(x+37) = 3x-9. Solve the left side of the equation. You will get 2x+74. Now the whole equation is 2x+74=3x-9. Well, move the like terms to each of their sides. You will now have 74+9 = 3x-2x. Simplify and you will get 83 = x.
Hope this helps! Please mark me as brainliest!
Answer:
x=83
Step-by-step explanation:
Since we know that half of 3x-9 is x+37, that's the same as saying the double of x+37 or 2(x+37) is equal to 3x-9. So, we can write this equation: 3x-9=2(x+37). Now, all we have to do is use simple algebra to solve the problem:
Steps Justification
3x-9=2(x+37) Original Equation
3x-9=2x+74 Distributive Property of Equality
x-9=74 Subtraction Property of Equality (Subtract 2x from both sides)
x=83 Addition Property of Equality (Add 9 to both sides)
Hope this helps!! :)
Solve -9 < 4x + 3 ≤ 19.
Answers
\(-9<4x+3 \leq 19 \\ \\ -12<4x \leq 16 \\ \\ \boxed{-3<x \leq 4}\)
I NEED HELP PLEASE FAST
50 points
Answers
The values of x in each equation are;
1) 128
2) 1500
How do you form an equation?Forming an equation involves expressing a mathematical relationship or statement using mathematical symbols and symbols of equality. The goal is to represent a real-life situation, a mathematical problem, or a hypothesis in a clear and concise way that can be easily analyzed and solved.
We have that;
1) let the number be x
85/100 * x = 108.8
x = 108.8 * 100/85
= 128
2) Let the number of the kettle corn be x;
6/10 * 2500 = x
x = 1500
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Help please i will give brainliest
Answers
Answer:
48
Step-by-step explanation:
To find how many 1/3 cm length cubes fill the prism, we first need to find the volume, which is equal to
length * width * height = 1 cm * (2 + 2/3) cm * (2/3) cm
= 1 cm * (6/3 + 2/3) cm * (2/3) cm
= 1 cm * (8/3) cm * (2/3) cm
= (8/3) cm ² * (2/3) cm
= (16/9) cm³
Therefore, the volume is 16/9 cm³.
Next, one cube with side lengths of 1/3 has a volume of ((1/3) cm)³ = (1/27)³
We thus need to find how many of 1/27 goes into 16/9
If we multiply 16/9 by 1=3/3 (as 9*3=27), we can equalize the bases, making 16/9 = 48/27
All that's left is to figure out how many times 1/27 goes into 48/27, which is equal to (48/27)/(1/27) = 48
Solve for xxx.
Your answer must be simplified.
15 < -5 x
Answers
Answer:
x < - 3
Step-by-step explanation:
Given
15 < - 5x
Divide both sides by - 5, reversing the symbol as a result of dividing by a negative quantity
- 3 > x , that is
x < - 3
The simplified expression is x < -3.
What is an inequality?An inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. It is the condition of being unequal. It is used most often to compare two numbers on the number line by their size.
For the given situation,
The expression is 15 < -5x
⇒ \(15 < -5 x\)
Divide both sides by -5,
⇒ \(\frac{15}{-5} < \frac{-5}{-5} x\)
When we divide an inequality with negative number, we need to change the sign,
⇒ \(-3 > x\)
⇒ \(x < -3\)
Hence we can conclude that the simplified expression is x < -3.
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I REALLY NEED HELP QUICK PLEASE!!!
Answers
Answer:
If the correction of 6 * 6X is accurate then I hope this is the answer.
Step-by-step explanation:
6(6x)+3x=3+3x+5
1. First multiply 6 by 6
36x+3x=3+3x+5
2. Then add 36X and 3X
39x=3+3x+5
3. After that add 3 and 5
39x=3x+8
4. Subtract 3x from both sides of the equation.
39x−3x=8
5. Subtract 3x from 39x
36x=8
6. Divide
36X. 8
______. = ______
36. 36
7. 36X and 36 cancel out because they
are common factors
8. The common factor between 8 and 36 is 4.
S you are left with. 2
X= _____
9
_
9. If you would like the decimal, than it is, X = 0.2
A twelve pack of Orange Crush is priced at $3.00. What is the unit rate or the price per soda?
Answers
Divide price by quantity:
3.00 / 12 = $0.25 per can.
2.1n - 5.31 = 18
Pls help please show work
Answers
Answer:
n= approx. 6.04
Step-by-step explanation:
18-5.31=12.69
12.69/ 2.1= about 6.04
Enter the letter for the function graphed
below.
and
a) y = √x-5
b) y =√x-5
c)y=5-√√x
d) y = √x + 5
e) y = √√x + 5
Fr
Answers
Answer:
Step-by-step explanation:
Edexcel_transistion_from_GCSE_to_A-level_files(1).pdf
Kim's hourly wage is $14. She works 37 hours per week. What is her monthly income?
Answers
Answer:
2072
Step-by-step explanation:
Multiply 14 x 37
518 x 4
2072
Answer: $2,072 a month
Step-by-step explanation:
multiply 14 by 37 to see her weekly rate which is $518 a week. then multiply 518 by 4 (because there are about 4 weeks in a month). then you get the answer of $2,072