Rational numbers are numbers that can be written in the form of a/b where a and b are integers.
What are Rational and Irrational numbers?Rational numbers are numbers that can be written in the form of a/b where a and b are integers.
Example: 1/2, 3.5 (which is writable as 7/5), 2(which is writable as 4/2), etc.
Irrational numbers are those real numbers that are not rational numbers.
For example √2, π, √13, etc.
It is an important thing to Know that all natural numbers are integers, and all integers are rational numbers. That means natural numbers are not irrational.
The given statement that any fraction is made up of two natural numbers is a rational number is true.
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Need help (pic included)
Answer:
r = 5
Step-by-step explanation:
The zeroes ( where the function intersects the x - axis) are equi-distant from the vertex line of symmetry
vertex 2,4 to get to -1 , 0 you have to go three units in the negative x direction ..... the other zero is on the OTHER side of the vertex 3 units which would be 5,0 so r = 5
Here is a graph to look at:
Solve |2x + 2| = 10
Answer:
x = - 6 , x = 4
Step-by-step explanation:
the absolute value function always gives a positive value but the expression inside can be positive or negative , that is
2x + 2 = 10 or - (2x + 2) = 10
solving both
2x + 2 = 10 ( subtract 2 from both sides )
2x = 8 ( divide both sides by 2 )
x = 4
or
- (2x + 2) = 10
- 2x - 2 = 10 ( add 2 to both sides )
- 2x = 12 ( divide both sides by - 2 )
x = - 6
Quadratic Equation Question
Answer: 0.68 or 13.92
Step-by-step explanation:
If the height is 47 meters, then the height, h, is equal to 47.
[tex]47=73t-5t^2\\\\5t^2 - 73t+47=0[/tex]
Using the quadratic formula,
[tex]t=\frac{-(-73) \pm \sqrt{(-73)^{2}-4(5)(47)}}{2(5)}\\\\\\t=\frac{73 \pm \sqrt{4389}}{10}\\\\\\ t=\frac{73+\sqrt{4389}}{10}, \frac{73-\sqrt{4389}}{10}\\\\\boxed{t \approx 0.68, 13.92}[/tex]
Yesterday, the snow was 2 feet deep in front of Archie’s house. Today, the snow depth dropped to 1.6 feet because the day is so warm. What is the percent change in the depth of the snow?
The percent change in the depth of snow from yesterday to today is
Answer:
20%
Step-by-step explanation:
Half of 2 = 1
Half of 1.6 = 0.8
1 - 0.8 = 0.2
0.2 × 100 = 20%
Norman plants a garden each
year. This year, his garden
produced 40% fewer tomatoes
than it did last year. If Norman’s
garden produced 30 tomatoes
this year, how many tomatoes
did his garden produce last year?
Answer:
50
Step-by-step explanation:
if last year 100% of the tomatoes were produced and this year 40% less were produced then that would mean 60% of tomatoes were produced this year.
if 60% = 30 then
100% = ?
100x30÷60
On a coordinate plane, a parabola opens up. It goes through (negative 8, negative 2), has a vertex at (negative 5, negative 6.5), goes through (negative 2, negative 2), and has a y-intercept at (0, 6).
Over which interval is the graph of f(x) = one-halfx2 + 5x + 6 increasing?
The graph is increasing for x > -5
logarithmic differentiation for
[tex]y = x {}^{2} [/tex]
someone help me
Answer:
[tex]\boxed {\frac{dy}{dx}= 2x}[/tex]
Step-by-step explanation:
Solving :
⇒ log y = log (x²)
⇒ log y = 2 log x
⇒ [tex]\mathsf {\frac{1}{y} \frac{dy}{dx} = \frac{1}{x} \times 2}[/tex]
⇒ [tex]\mathsf {\frac{dy}{dx}= 2x}[/tex]
Answer:
y’ = 2x
Step-by-step explanation:
Let y = f (x), take the natural logarithm of both sides ln (y) = ln (f (x))
ln (y) = ln (x²)
Differentiate the expression using the chain rule, keeping in mind that y is a function of x.
Differentiate the left hand side ln (y) using the chain rule.
y’/y = 2 In (x)
Differentiate the right hand side.
Differentiate 2 ln (x)
y’/y = d/dx = [ 2 In (x) ]
Since 2 is constant with respect to xx, the derivative of 2 ln (x) with respect to x is 2 d/dx [ln (x)]
y’/y = 2 d/dx [In (x)]
The derivative of ln (x) with respect to x is 1/x.
y’/y = 2 1/x
Combine 2 and 1/x
y’/y = 2/x
Isolate y' and substitute the original function for y in the right hand side.
y’ = [tex]\frac{2}{x}[/tex] x²
Factor x out of x².
y’ = [tex]\frac{2}{x}[/tex] (x * x)
Cancel the common factor.
y’ = [tex]\frac{2}{x}[/tex] (x * x) (The x that is under 2 and the other x that I have underlined are the ones that cancel out)
Rewrite the expression.
y’ = 2x
So therefore, the answer would be 2x.
The coordinate grid shows points A through K. Which points are solutions to the
system of inequalities listed below? (2 points)
2x + y < 10
2x - 4y > 8
EFGHJ
EFG
ACDM
AEF
Answer:
E is the solution of the inequality Coordinates of points A = (-5,4)B = (4,7)C= (-2,7)D= (-7,1)E= (4, -2)F = (1 , -6)G= (-3, -10)H= (-4 , -4)I= (9, 3)J= (7 , -4)K= (2 ,3)putting the values of coordinates in equation to check for the solution.
For A
2x + y < 10
2(-5) + 4 < 10.
-10 - 4 < 10
-14 < 10 ( true)
2x - 4y > 8
2(-5) - 4(4) > 8
-10 - 16 > 8
-26 > 8
false..
it is not the solution of the equation.
similarly we can find for other coordinates.
E is the solution
Determine the equation of the line with slope -2 that passes through the point M(-1, -3).
Answer:
Given:
Let, the slope of the line passing through the point ( m) = -2
The line passing through the point M(-1,-3)= (x1 , y1)
The equation of the line passing through the point M(-1,-3) is
y-y1 = m (x-x1)
or, y-(-3) = -2 (x-(-1))
or, y+3 = -2 (x+1)
or, y+3 = -2x-2
or, 2x+y = -2-3
Hence, 2x+y =-5 is the required equation.
(a) is the correct answer .
i need help asappppp
Answer:
a = 11, b = 7
Step-by-step explanation:
See picture
Math word problems please help
Drag the tiles to the correct boxes. Not all tiles will be used.
Which equation could represent each graphed polynomial function?
y = 14 - 5x² + 4
y = x³ + 27
y = x(x + 3)(x - 2)
y = (x + 1)(x − 3)(x² + 1)
y = x⁴- 5x² + 4 represents the first graph.
y = x(x + 3)(x - 2) represents the second graph.
How to Interpret the graph of a Polynomial?
1) The first polynomial is;
y = x⁴- 5x² + 4
Simplifying this gives us;
y = x⁴- 4x² - x² + 4
y = x²(x² - 4) - 1(x²- 4)
y = (x² - 1)(x² - 4)
y = (x - 1)(x + 1)(x - 2)(x + 2)
Thus, the zeros of this polynomial are; x = -2, -1, 1, 2
From the given graphs attached, first graph has the zeros (x-intercepts) as x = -2, -1, 1, 2.
So graph (1) represents the polynomial y = x⁴- 5x² + 4
2). The second graph shows the x-intercepts at x = -3, 0, 2
Since, y = x(x + 3)(x - 2) is the polynomial with x-intercepts at x = -3, 0, 2
Therefore, y = x(x + 3)(x - 2) represents the second graph.
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Which of the following is a true statement about the rhombus shown? A) m angle STP=90^ B) overline ST cong overline PT C) m angle SPQ=90^ D) overline SQ cong overline PR
Answer:
A
Step-by-step explanation:
.......STP=90°........
Which choices are in the solution set of the inequality below? Check all that
apply.
18x> 45
A. 3
B. 2
c.
-13
D. 5
E. 2.5
F. 9
Answer: its -0
Step-by-step explanation:
Use the Factor Theorem to determine whether x + 1 is a factor of P(x) = 2x³+4x²–2x−8.
Specifically, evaluate P at the proper value, and then determine whether x + 1 is a factor.
Answer: [tex]2x^2+2x-4-\frac{4}{x+1}[/tex]
Not a factor because there is a remainder.
Step-by-step explanation:
Let's use synthetic division to solve this..
-1 ║ 2 | 4 | -2 | -8
║ | -2| -2 | 4
║ 2 | 2| -4 | -4
[tex]2x^2+2x-4-\frac{4}{x+1}[/tex]
PS: if anyone knows a better way to do a synthetic division chart please let me know.
A negative number raised to an odd power is_____ negative.
always
never
sometimes
negative number taken to an odd power gives a negative result (because, after cancelling, there will be one minus sign left over).
the answer is always. negative numbers raised to odd powers remain negative. negative numbers raised to even powers become positive.
i rlly need help with this :(
The air force reports that the distribution of heights of male pilots is approximately normal, with a mean of 72.6 inches and a standard deviation of 2.7 inches.
Part A: A male pilot whose height is 74.2 inches is at what percentile? Mathematically explain your reasoning and justify your work. (5 points)
Part B: Air force fighter jets can accommodate heights of soldiers between 70 inches and 78 inches without compromising safety. Anyone with a height outside that interval cannot fly the fighter jets. Describe what this interval looks like if displayed visually. What percent of male pilots are unable to fly according to this standard? Show your work and mathematically justify your reasoning. (5 points)
Using the normal distribution, it is found that:
a) The pilot is at the 72th percentile.
b) 19.13% of pilots are unable to fly.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The mean and the standard deviation are given, respectively, by:
[tex]\mu = 72.6, \sigma = 2.7[/tex].
Item a:
The percentile is the p-value of Z when X = 74.2, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{74.2 - 72.6}{2.7}[/tex]
Z = 0.59
Z = 0.59 has a p-value of 0.7224.
72th percentile.
Item b:
The proportion that is able to fly is the p-value of Z when X = 78 subtracted by the p-value of Z when X = 70, hence:
X = 78:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{78 - 72.6}{2.7}[/tex]
Z = 2
Z = 2 has a p-value of 0.9772.
X = 70:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{70 - 72.6}{2.7}[/tex]
Z = -0.96
Z = -0.96 has a p-value of 0.1685.
0.9772 - 0.1685 = 0.8087 = 80.87%.
Hence the percentage that is unable to fly is:
100 - 80.87 = 19.13%.
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What is the solution to the linear equation?
8-10-28+7=8+d-10-36
0 d=-5
O d=1
0 d=5
Mark this and retur
Save and Exit
Next
Submit
Answer:
d = 15
Step-by-step explanation:
8 - 10 - 28 + 7 is equal to -23
8 + d - 10 - 36 is equal to -38 + d
if -23 = -38 +d
15 = d
The solution of the equation is d = 15
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The given equation is 8-10-28+7=8+d-10-36
In the equation d is the variable
We have to solve for d
8-10-28+7=8+d-10-36
-23 = -38+d
Add 38 on both sides
-23+38=d
15=d
Hence, the solution of the equation is d = 15
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The table shows results of an experiment that was replicated.
Which best describes the data?
They are precise and reproducible.
They are precise but not reproducible.
They are accurate and reproducible.
They are accurate but not reproducible.
The option that best describes the experiment is accurate and reproducible.
What option describes the data?All the values from the experiment are close in value to the accepted value. This indicates that the experiment is accurate. Two experiments yield the same values. This indicates that the experiment is reproducible.
Here is the table used in answering the question:
Accepted Value: 130
Experiment 1 129
Experiment 2 131
Experiment 3 129
Experiment 4 132
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Answer:
(A)They are precise and reproducible
Step-by-step explanation:
3x squared + 6 x cube - 9x squared y when factorused
[tex]3x ^{2} \: + \: {6x}^{3} \: - \: 9 {x}^{2} y[/tex]
Factor the expression with the common factor that is "3x²".[tex] \boxed{ \bold{3 {x}^{2} \: \times \: (1 \: + \: 2x \: - \: 3y)}}[/tex]
MissSpanishAnswer:
[tex]\boxed{3x²(1 + 2x - 3y)}[/tex]
Step-by-step explanation:
3x squared + 6 x cube - 9x squared y
To factor
Solution:
A process when algebraic expression is expressed as a product of two or more expressions is factorisation.
ATP,
Square = a²
Cube = a³
3x² + 6x³ - 9x²yWe can see that 3x^2 is common in this expression.
So rewrite as:
[tex]3x²(1 + 2x - 3y)[/tex]Done!
HELP! WILL GIVE BRAINLIEST AND 50 POINTS!
A study showed that low-intensity vibration therapy reduces pain levels in patients with fibromyalgia. During each session in the study, vibration pads were placed on the pain site indicated by the patient. Pain reduction was measured through self-reporting after each session.
Another study is being designed to examine whether low-intensity vibration therapy also reduces pain in patients suffering from ruptured disks in the lumbar region of the back. Three hundred male patients are subjects in the new study.
Part A: What is an appropriate design for the new study? Include treatments used, method of treatment assignment, and variables that should be measured. (4 points)
Part B: If the study consisted of 150 male and 150 female patients instead of 300 male patients, would you change the study design? If so, how would you modify your design ? If not, why not? (4 points)
Part C: Could your design be double-blind? Explain. (2 points)
Answer:
Part A: The appropriate design would be: 300 male patients chosen should be suffering from ruptured disks in the lumbar region of the back, with similar magnitude of pain (or segregating these 300 as per magnitude of pain)
Part B: If the study consisted of 150 male and 150 female patients instead of 300 malepatients, I would change the study design, because the pain level could endure for femalecould vary compare to male.
Part C:Yes, I could design a double-blind, because it is a very good ways to show theeffect of the therapy because neither the participants nor the researchers knows whichgroups of participants is assigned to which treatment, and who are the groups of participant receiving it.
Please help!!!!!!!!!!!
Let's take this problem step by step:
To find the ordered pair of the system:
⇒ must set both equations equal to each other
⇒ and solve for 'x'
Let's solve:
[tex]x^2-2x+3=-2x+19\\x^2-2x+2x+3-19=0\\x^2-16=0\\(x+4)(x-4)=0[/tex]
Let's find the x-values:
[tex](x-4)=0\\x=4\\\\(x+4)=0\\x=-4[/tex]
Let's find f(x)'s value for each 'x':
[tex]x=4\\f(4)=-2(4)+19=-8+19=11\\\\x=-4\\f(-4)=-2(-4)+19=8+19=27[/tex]
Answer: (4, 11), (-4,27)
Hope that helps!
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Step 4: Make a prediction with your data.
a) Using your equation from step 2d, ( y=0.14x+0.75 ) estimate the GPA of a student who studies for 15 hours a
week. Justify your answer.
Answer:
estimated gpa: 2.85
Step-by-step explanation:
Evaluate y=0.14x+0.75 at x = 15 (hours):
y = 0.14(15 hours) + 0.75
= 2.1 + 0.75
y = 2.85 = estimated gpa corresponding to 15 houirs of study
let a,b, and c be real numbers where a ≠ b≠c≠0. which of the following functions could represent the graph below?
The function will be f(x) = x²(x - a)²(x - b)(x - c). Then the correct option is A.
What is a function?A statement, principle, or policy that creates the link between two variables is known as a function. Functions are found all across mathematics and are required for the creation of complex relationships.
The graph is given below.
The factor of the function will be
(x - 0), (x - a), (x - b), and (x - c)
Then the function will be
Then the function can be written as
f(x) = x²(x - a)²(x - b)(x - c)
Then the correct option is A.
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Answer:
The answer on Edge is Choice A
Step-by-step explanation:
What is the slope of the graph?
Oslope = -1/3
O slope = -3
O slope = 3
O slope = 1/3
Find the distance between -6.77777 and 3.55555.
O 10.3
O 10.33332
O 10.3333332
13.33332
Answer:
10.33332
Step-by-step explanation:
-6.77777 is 6.77777 units away from 0. So there's 6.77777+3.55555 which is 3.55555 units away from 0.
Add those two numbers together and it's 10.33332
Answer:
10.33332
Step-by-step explanation:
distance between -6.77777 and 3.55555 is 10.33332
EEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE I NEED HELP
Answer:
B.
Step-by-step explanation:
It is the only one that is not a fraction or a decimal that terminates or repeats.
What is the value of cos theta in the diagram below
O 3/5
O3/4
O 4/5
O4/3
The value of cos θ is 3/5.
What is Trigonometry?Trigonometric ratios can be used to determine the ratios of any two sides out of a total of three sides of a right-angled triangle in terms of the respective angles.
Here, given point on circle is (0.6, 0.8) or (3/5 , 4/5)
x - axis (base) = 3/5
y - axis (Perpendicular) = 4/5
Radius (Hypotenuse) = 1
Now, we know
cos θ = Base / Hypotenuse
cos θ = 3/5
Thus, the value of cos θ is 3/5.
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Use trigonometry to find the height of the triangle. Then use the height to find the area. Round to the nearest hundredth
Answers:
height = 4.46 units
area = 26.73 square units
Both values are approximate
===========================================================
Explanation:
h = height of the triangle
Focus on the smaller triangle on the left.
Use the cosine ratio to find h
cos(angle) = adjacent/hypotenuse
cos(27) = h/5
h = 5*cos(27)
h = 4.4550326 approximately
Your calculator needs to be in degree mode.
We can now find the area of the overall largest triangle.
area = 0.5*base*height
area = 0.5*12*4.4550326
area = 26.7301956
area = 26.73
Answer with a step-by-step explanation:
1) First, let us find the height of the triangle.
For that let us use cos theta to find the triangle's height.
Let us use the below formula to find it.
cos Θ = Adjacent ÷ hypotenuseLet the height (adjacent ) be h.
Let us find it now.
cos Θ = Adjacent ÷ hypotenuse
cos 27° = h ÷ 5
0.8910 = h ÷ 5
0.8910 × 5 = h
4.455 = h
Therefore the height of the triangle is 4.455 units.
2) And now let us find the area of the triangle.
The formula to find the area of a triangle is:
Area = [tex]\frac{1}{2}[/tex] × base × heightLet us find it now.
A = [tex]\frac{1}{2}[/tex] × base × height
A = [tex]\frac{1}{2}[/tex] × 12 × 4.455
A = [tex]\frac{1}{2}[/tex] × 53.46
A = 26.73 units²
Can someone help me please???
Answer:
c is the answer. I hope that helps
