Step-by-step explanation:
2).
Given that 1/(7+5√2)
We know that
The Rationalising factor of a+√b is a-√b
The denominator = 7+5√2
The Rationalising factor of 7+5√2 is 7-5√2
On Rationalising the denominator then
=> [1/(7+5√2)]×[ (7-5√2)/(7-5√2)]
=> [1×(7-5√2)]/(7+5√2)(7-5√2)]
=> (7-5√2)/[(7+5√2)(7-5√2)]
=> (7-5√2)/[7²-(5√2)²]
Since , (a+b)(a-b) = a²-b²
Where , a = 7 and b = 5√2
=> (7-5√2)/(49-50)
=> (7-5√2)/(-1)
=> -7+5√2
=> 5√2-7
3).
Given that (x-2)³
This is in the form of (a-b)³
Where, a = x and b = 2
We know that
(a-b)³ = a³-3a²b+3ab²-b³
=> (x-2)³ = x³-3(x²)(2)+3(x)(2)²-2³
=> (x-2)³ = x³-6x²+12x-8
The coefficient of x² is -6
8.54÷0.35= what the answer
The required solution is 24.4 to the given numerical expression 8.54 ÷ 0.35.
What is the division operation?In mathematics, divides left-hand operands into right-hand operands in the division operation.
The numerical expression is given in the question as:
8.54 ÷ 0.35
We have to determine the solution to the given expression
As per the question,
8.54 ÷ 0.35
8.54 / 0.35
(854/100) / (35/100)
Reciprocal the terms of numerator
854/100 × 100/35
854/35
Apply the division operation to get the solution
24.4
Thus, the required solution is 24.4 to the given numerical expression.
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solve for the missing angles
m∠ 2 = 97° m∠ 6 = 83°
Answer: ∠1 and ∠5∠2 and ∠6∠3 and ∠7∠4 and ∠8
Step-by-step explanation:
∠3 and ∠6∠4 and ∠5
The missing angles m∠ 3 is 97°, m∠10 is 97°,m∠9 is 83 degrees, m∠5 is 97 degrees, m∠7 is 83 degrees and m∠16 is 97 degrees.
What are Angles?An angle is formed when two straight lines or rays meet at a common endpoint.
The given angles m∠ 2 = 97° and m∠ 6 = 83°.
We have to find the other angles.
m∠ 3 is equal to m∠ 2
m∠ 3 is 97°
m∠10 is corresponding angle to m∠ 2
m∠10 is 97°
Now m∠9 + m∠10 = 180
m∠9 + 97 =180
m∠9 = 180-97
m∠9 is 83 degrees.
As m∠6 is 83 degrees.
m∠6+m∠5 = 180
83+m∠5=180
m∠5 is 97 degrees.
m∠7 is 83 degrees.
m∠16 is 97 degrees.
Hence, the missing angles m∠ 3 is 97°, m∠10 is 97°,m∠9 is 83 degrees, m∠5 is 97 degrees, m∠7 is 83 degrees and m∠16 is 97 degrees.
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which graph represents y as a function of x
Answer:
A
Step-by-step explanation:
find y. round to the nearest tenth
Answer:
x is 90 z is 60 and y is 30
Step-by-step explanation:
9) Assume that the random variable X is normally distributed, with mean = 90 and standard deviation o = 12. Compute the probability P(57 < X < 105).
A) 0.7888 B) 0.8944 C) 0.8914 D) 0.8819
Answer:
Step-by-step explanation:
The mean, \(\bar{x}\), is 90 and the standard deviation, \(\sigma\), is 12. We are looking for the probability that the variable X will fall between 57 and 105. We use the z-score table for this, AFTER we find the z scores. The formula to find the z-scores for us is:
\(P(\frac{57-\bar{x}}{\sigma}\leq z\leq \frac{105-\bar{x}}{\sigma})\) and we fill in accordingly:
\(P(\frac{57-90}{12}\leq z\leq \frac{105-90}{12})\) which simplifies to
\(P(-2.75\leq z\leq 1.25)\) and we will break them up into 2 different sets as follows:
P(-2.75 ≤ z ≤ 0) + P(0 ≤ z ≤ 1.25)
and based on the fact that z scores are given from 0 on up, we are going to convert the first one by using the logic that if z is greater than -2.75 but less than 0, by symmetry, z is greater than 0 but less than 2.75:
P(0 ≤ z ≤ 2.75) + P(0 ≤ z ≤ 1.25) and we go to the z-score table.
Locate 2.7 down along the left side and move over til you're under the .05; that gives us the z-score for 2.75 which is .4970. Do the same for 1.25 to get a z-score of .3944. Add them together to get a final z-score that covers the range of values for X:
.4970 + .3944 = 0.8914
what is the scale factor
please someone help me
Answer:
1/4Step-by-step explanation:
The scale factor is the ratio of corresponding side of the image to te original:
k = A'C'/ACk = 6/24 = 1/4The linear function graphed below represents Brenda’s monthly cell phone bill based on the number of hours she uses. What is her hourly rate?
Answer:
the answer is $12 per hour
Step-by-step explanation:
just took the quiz
Answer:
its A $12 per hour
Step-by-step explanation:
just took the test
Myra wrote a computer program that had 75 lines of code. She realized that she could make the code more efficient and removed 20% of the lines.
Shade the grid to show the percent that Myra removed.
Answer:
Now Myra has 60 lines of code, no grid picture attached.
Step-by-step explanation:
If Myra removed 20% of the lines and she started with 75 lines of code, then she is removing 1/5 of those lines of code.
75 divided by 5 is 15, and 75 - 15 = 60
Now Myra would have 60 lines of code. It's unclear what grid you are talking about though - could you attach a picture of the grid you need to shade in?
What is 11 % of 700?
Answer:
77
Step-by-step explanation:
Answer:
11
Step-by-step explanation:
Find the composite figure.
5m, 12m, 12m
A- 174 m2
B- 149 m2
C- 53 m2
D- 720 m2
Answer:
174 m²
Step-by-step explanation:
Triangle: \(\frac{1}{2} (12*5)=30\)m²
Square: 12 * 12 = 144 m²
144+30=174m²
-4 1/5 + 3 2/3 + -1 2/5 =
Answer:
-29/15 or -1 14/15
Step-by-step explanation:
Answer:
-29/15 or mixed form -1 14/15
It costs $5 for an adult and $2 for a student to visit the National Botanical Gardens. Adults can be members of the Botanical society and can visit for free. A group of 30 adults and students visited the gardens. Five were members and it cost the group $104. How many students
Answer:
30 students!!!!?????
A farmer is constructing a small fenced in area that can be describe with the ordered pairs (2,3), (2,8), (6,8), and (6,3). The units for both x and y are feet. Make a graph. The find the amount of fencing he will need.
We need to find the perimeter of the shape given by the coordinates. Let's start by drawing a Cartesian coordinate system and identifying the points. This will give us information about the geometric shape.
A Cartesian coordinate system is given in the photos below and the indicated points [(2,3), (2,8), (6,3) and (6,8)] are marked.
We can see that this shape is a rectangle. A rectangle is home to two sides of different lengths, long and short. To find the perimeter of a rectangle, we add the length of the long side and the length of the short side and multiply the result by \(2\). (Because a rectangle must have \(2\) long sides and \(2\) short sides).
The rectangle in the figure has a long side length of \(5\) feet and a short side length of \(4\) feet.
Perimeter: \(2(L+S) = 2(5+4)=18ft.\)
Stella drives 25 miles in 20 minutes. If she drove two hours in total at the same rate, how far did she go?
Alberto started out bench pressing 60 pounds. He then added 5 pounds every week. Determine whether the situation is linear or nonlinear, and proportional or nonproportional
Answer
linear
nonproportional
Step-by-step explanation:
Since for each equal change in time (1 week), there is an equal change in weight (5 lb), the situation is linear.
At time zero, the first week, the weight was not zero. It was 60 lb, so it is not proportional.
Answer:
linear
nonproportional
-3x (- -8x+52+:
+5+3)
A. 11x²8x-9
11x³8x² - 9x
B.
C. 24x³15x² - 9x
D.
24x²15x - 9
Answer:
To simplify the expression -3x(-8x+52+5+3), we can distribute the -3x to each term inside the parentheses:
-3x(-8x+52+5+3) = 24x² - 156x - 15x - 9x
Simplifying further by combining like terms, we get:
-3x(-8x+52+5+3) = 24x² - 180x - 9x
Therefore, the simplified expression is 24x² - 189x. None of the options given match this answer. Therefore, there seems to be an error in the original question.
Step-by-step explanation:
Help! I will Mark Brainliest!
For the graphed function f(x) = (4)x − 1 + 2, calculate the average rate of change from x = 1 to x = 2.
−3
3
2
−2
Answer:
Your answer is B. I had some help from my mom.
Step-by-step explanation:
the average rate of change on the interval [1, 2] is found by computing
(f(2) - f(1))/(2 - 1)
= ((4^1+2) - (4^0+2)/1
= (6-3)
= 3
Write an equation for a line that is parallel to y = -3x – 5 that goes through the point (-1, 8)
Answer:
y = -3x +5
Step-by-step explanation:
Parallel means that both slopes are the same.
This gives us y = -3x + C so far.
To find the y-intercept, we need to get x to 0.
Since we know the point (-1, 8), we can plug the number in into our equation
y = -3x + C.
8 = -3(-1) + C
8 = 3 + C
8 - 3 = C
5 = C or C = 5.
Now plug in C into our unsolved equation to get y = -3x +5.
write a positive or negative integer that represents the situation. the temperature is 31 degrees above zero.
The integer that represents the given situation is a positive 31.
The temperature being 31 degrees above zero means that it is warmer than the freezing point of water. In this context, "above zero" refers to the Celsius or Fahrenheit scale, where zero represents the freezing point of water. Therefore, a temperature of 31 degrees above zero is a positive value indicating a warm temperature.
In this case, it can be assumed that the temperature is being measured in Celsius since 31 degrees above zero on the Fahrenheit scale would correspond to a very high temperature of approximately 87 degrees Fahrenheit. Overall, the integer that represents this situation is positive 31, which signifies a warm temperature above the freezing point.
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Epositas $545,680 pesos en una cuenta que ofrece pagar 2.25.% semestral durante año y 10 meses a) ¿Cuánto recibirás en total al final del plazo?
Responder:
$ 555,911.5
Explicación paso a paso:
Dado
Principal = $ 545,680
Interés = 2,25%
Tiempo = 10 meses = 10/12 años
Debemos buscar la cantidad después de 10 meses.
Monto = Principal + Intereses
Interés = PRT / 100
Interés = 545,680 * 2,25 * 10/1200
Intereses = 12,277,800 / 1200
Interés = 10.231,5
Cantidad = 545,680 + 10,231.5
Cantidad = 555,911.5
por lo tanto, la cantidad después de 10 meses es $ 555,911.5
Veronica bought a shirt and a sweater for a total price of $65. The price of the sweater was $2 more than twice the price of
the shirt. What was the price of the shirt?
Answer: 32.5
Step-by-step explanation: you divide it.
Simplify \(\frac{sec(a)-csc(a)}{sec(a)+csc(a)}\)
The simplified version of (sec a - cosec a) / (sec a + cosec a) is cosec 2a(cosec 2a - 2) / (sec²a - cosec²a).
What is trigonometry?The study of correlations between triangles' side lengths and angles is known as trigonometry. The field was created in the Hellenistic era in the third century BC as a result of the use of geometry in astronomical research.
Given:
(sec a - cosec a) / (sec a + cosec a)
Multiply the numerator and denominator by (sec a - cosec a)
(sec a - cosec a) / (sec a + cosec a) × (sec a - cosec a)
(sec²a + cosec²a -2sec a cosec a) / (sec²a - cosec²a)
As we know,
\(sec^2a + cosec^2a = sec^2a \ cosec^2a\)
sec² a cosec² a - 2sec a cosec a / (sec²a - cosec²a)
sec a cosec a (sec a cosec a - 2) / (sec²a - cosec²a)
cosec 2a(cosec 2a - 2) / (sec²a - cosec²a)
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Help me please correct answers only
Answer:
well your answer should be "F"
Step-by-step explanation:
we have
Y<-2x+10 -----> inequality A
The solution of the inequality A is the shaded area below the dashed line
Y = -2x+10
The y-intercept of the dashed line is (0,10)
The x-intercept of the dashed line is (5,0)
Y<1/2x-2 ----> inequality B
The solution of the inequality B is the shaded area below the dashed line
Y= 1/2x-2
The y-intercept of the dashed line is (0,-2)
The x-intercept of the dashed line is (4,0)
The solution of the system of inequalities is the shaded area between the two dashed lines
Remember that
If a ordered pair is a solution of the system of inequalities, then the ordered pair must lie on the shaded area of the solution
therefore
The solution are the points
E, F and G
i hope this helps
What is the value of –7.94 + 2.13 – 4.65?
Answer:
-10.46
Step-by-step explanation:
Find the equation in slope-intercept form of a line through (2, 4) with slope 0. Oy=2 Ox=2 Oy=4 0 x = 4
SORRY I NEED HELP AGAIN
(see photo for question again)
Answer:
x=24
y=25
Step-by-step explanation:
3y =75 by alternate interior angles theorem
y =25
4x+9+75=180
4x+84=180
4x=96
x=24
Which inequality is represented by this graph?
Help please :’/
Answer:A
Step-by-step explanation:
It is a solid line and the area below is shaded so it has to be less than the slope, hope this helped!
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Answer:
Its A because you find the slope, -1/3 which is followed by x. The x intercept is 1 so you do plus one. Because the line is solid and negative, it makes it a less-than equal to sign. Hope this helps at all!
Step-by-step explanation:
use vectors to decide whether the triangle with vertices p(2, −1, −1), q(3, 2, −3), and r(7, 0, −4) is right-angled.
To determine whether the triangle with vertices P(2, -1, -1), Q(3, 2, -3), and R(7, 0, -4) is right-angled, we can use vectors.
First, we calculate the vectors formed by the sides of the triangle:
Vector PQ = Q - P = (3, 2, -3) - (2, -1, -1) = (1, 3, -2)
Vector PR = R - P = (7, 0, -4) - (2, -1, -1) = (5, 1, -3)
Next, we take the dot product of these two vectors:
PQ · PR = (1, 3, -2) · (5, 1, -3) = 1 * 5 + 3 * 1 + (-2) * (-3) = 5 + 3 + 6 = 14
If the dot product is zero, then the two vectors are perpendicular, indicating that the triangle is right-angled.
In this case, since PQ · PR = 14 ≠ 0, the triangle with vertices P, Q, and R is not right-angled.
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Chiyoko wants to fence off a section of her backyard to be an exercise space for her dogs, as shown in the diagram. Chiyoko must find the perimeter to figure out how much fencing she needs. How can Chiyoko express the perimeter in the most simplified way?
A.4(x + 4)
B. x(x + 4)
C. 5x + 4
D . 5x + 8
Answer:
D
Step-by-step explanation:
i did it
Answer:
It is D
Step-by-step explanation:
The way to find the perimeter is to add the side lengths and then simplify by combining like terms.
answer for me this simple question. and thanx