Answers
The answer is:
The answer is the fourth option,
[tex]f(-3)=-\frac{1}{3}[/tex]
Why?Piecewise functions are functions that are composed by two or more expressions, the expression to use will depend of the domain or input that we need to evaluate.
We are given the piecewise function:
[tex]\left \{ {{\frac{1}{x}, if x<-2} \atop{x^{2}, ifx\geq 2}} \right.[/tex]
There, we know that:
We should use the first expression if the value to evaluate is less than -2.
So, for this case, the function will be:
[tex]f(x)=\frac{1}{x}[/tex]
We should use the second expression if the value to evaluate is greater or equal than 2.
So, for this case, the function will be:
[tex]f(x)=x^{2}[/tex]
Now, since we are given that the value to evaluate is -3, and its less than -2, we need to use the first expression, and evaluate it.
[tex]-3<-2[/tex]
So, evaluating the function we have:
[tex]f(x)=\frac{1}{x}[/tex]
[tex]f(-3)=\frac{1}{-3}[/tex]
[tex]f(-3)=-\frac{1}{3}[/tex]
Hence, we have that the answer is the fourth option,
[tex]f(-3)=-\frac{1}{3}[/tex]
Have a nice day!
Related Questions
Starting at the top of a square pyramid and make a vertical slice cutting pyramid in half what is the shape of the newly-exposed section
I really appreciate it if you can check my answer. I I think it’s a triangle.
Answers
Answer: Triangle
Step-by-step explanation: If you cut it vertically, the base is changed into a triangle.
Hope this helps!
(a + b - c )(a + b + c )
Answers
If you are looking for the expanded version, this is it. It is also possible to group either an a from (a^2 + 2b) or a b from (2ab + b^2). Hope this helps!
Answer:
[tex](a+b-c)(a+b+c)=a^2+2ab+b^2-c^2[/tex].
Step-by-step explanation:
We want to expand: [tex](a+b-c)(a+b+c)[/tex].
We use the distributive property to obtain:
[tex](a+b-c)(a+b+c)=a(a+b+c)+b(a+b+c)-c(a+b+c)[/tex].
We now expand to get:
[tex](a+b-c)(a+b+c)=a^2+ab+ac+ab+b^2+bc-ac-bc-c^2[/tex].
This finally simplifies to
[tex](a+b-c)(a+b+c)=a^2+2ab+b^2-c^2[/tex].
What is the standard deviation of the data set?
7,3,4, 2, 5, 6,9
Answers
Answer:
2.4103
Step-by-step explanation:
The first step in evaluating the sample standard deviation of a data set involves the determination of the sample mean.
The sample mean is simply the average value of the data set;
sample mean = [tex]\frac{7+3+4+2+5+6+9}{7}=5.1429[/tex]
The next step is to evaluate the sum of the squares of deviations from the mean;
sum of squares of deviation = [tex](7-5.1429)^{2}+(3-5.1429)^{2}+(4-5.1429)^{2}+(2-5.1429)^{2}+(5-5.1429)^{2}+(6-5.1429)^{2}+(9-5.1429)^{2}=34.8571[/tex]
We then divide the sum of squares of deviation by (n-1) where n is the sample size to obtain the sample variance;
variance = [tex]\frac{34.8571}{7-1}=5.8095[/tex]
The standard deviation is simply the square-root of variance;
[tex]\sqrt{5.8095}=2.4103[/tex]
find the equations of the tangents to the curve y= x(x-1)(x+2) at the points where the curve cuts the x axis
Answers
First of all, we compute the points of interest, i.e. the points where the curve cuts the x axis: since the expression is already factored, we have
[tex]x(x-1)(x+2) = 0 \iff x=0\ \lor\ x-1=0\ \lor\ x+2=0[/tex]
Which means that the roots are
[tex]x=0\ \lor\ x=1\ \lor\ x=-2[/tex]
Next, we can expand the function definition:
[tex]y = x(x-1)(x+2) = x^3 + x^2 - 2x[/tex]
In this form, it is much easier to compute the derivative:
[tex]y' = 3x^2+2x-2[/tex]
If we evaluate the derivative in the points of interest, we have
[tex]y'(-2) = 6,\quad y'(0)=-2,\quad y'(1)=3[/tex]
This means that we are looking for the equations of three lines, of which we know a point and the slope. The equation
[tex]y-y_0=m(x-x_0)[/tex]
is what we need. The three lines are:
[tex]y-0=6(x+2) \iff y = 6x+12[/tex] This is the tangent at x = -2
[tex]y-0=-2(x-0) \iff y = -2x[/tex] This is the tangent at x = 0
[tex]y-0=3(x-1) \iff y = 3x-3[/tex] This is the tangent at x = 1
Francis teaches the piano. He charges each student an enrollment fee of $100 plus $15 per hour of piano lessons. The average cost of lessons for a student per hour is $25.
If h represents the number of hours a student spends in lessons, which equation can be used to find the value of h?
Answers
Answer:
y=15x+100
Step-by-step explanation:
increases by 15, 100 is starting free
What is the volume of the pyramid 7x7x8
Answers
Answer:
The volume of the pyramid is [tex]130\frac{2}{3}\ units^{3}[/tex]
Step-by-step explanation:
we know that
The volume of the pyramid is equal to
[tex]V=\frac{1}{3}BH[/tex]
where
B is the area of the base
H is the height of the pyramid
Find the area of the base B
In this problem we have a square base
[tex]B=7^{2} =49\ units^{2}[/tex]
we have
[tex]H=8\ units[/tex]
substitute
[tex]V=\frac{1}{3}(49)(8)=\frac{392}{3}\ units^{3}[/tex]
Convert to mixed number
[tex]\frac{392}{3}=\frac{390}{3}+\frac{2}{3}=130\frac{2}{3}\ units^{3}[/tex]
you do length x width x be aight divided by 3 to get 392/3
You’re setting sales goals for next month you base your goals on previous average sales the actual sales for the same month for the last four years have been 24 units, 30 units, 23 units, and 27 units what is the average number of units you can except to sell next month?
Answers
Answer:
26 units
Step-by-step explanation:
As the sales for the same month in past four years is given, they will be used to determine the sales for next month.
We have to find the average of previous 4 years' sale for the same month
So,
n = 4
The formula for average is:
[tex]Avg = \frac{Sum of values}{number of values}[/tex]
[tex]=\frac{ 24+30+23+27}{4}[/tex]
[tex]= \frac{104}{4}[/tex]
[tex]= 26[/tex]
26 is the average number of units that can be expected to be sold the next month ..
based on the previous average sales, one can expect to sell an average of 26 units next month.
To calculate the average number of units one can expect to sell next month based on past sales, we need to find the mean of the provided sales data. The actual sales data for the last four years are 24 units, 30 units, 23 units, and 27 units. To find the average (mean), we add up these amounts and then divide by the number of data points.
The sum of the units sold is 24 + 30 + 23 + 27 = 104 units. Since there are four years of data, we divide 104 units by 4 to get the average.
Average units sold = 104 units / 4 = 26 units.
Therefore, based on the previous average sales, one can expect to sell an average of 26 units next month.
Quadrilateral ABCD is inscribed in a circle with m<A = (x2)°, m<B = (7x - 10)°,
and
m<C = (3x)°.
What is m<D?
Answers
Answer:
106°
Step-by-step explanation:
A quadrilateral inside a circle is a cyclic quadrilateral.
It means that the angles opposite are supplementary (add up to 180).
If we draw the quadrilateral ABCD, the angles A and C are supplementary and the angles B and D are supplementary.
Since we know A and C, we can write:
A + C = 180
x^2 + 3x = 180
x^2 +3x - 180 = 0
(x+15)(x-12) = 0
x= -15, or x = 12
Now, if we put x = -15, some angles become negative, so we disregard it and take x = 12.
Now finding B:
B = 7x - 10
B = 7(12) - 10
B = 74
We also know that B + D = 180, so:
B + D = 180
74 + D = 180
D = 180 - 74 = 106
There is a mound of g pounds of gravel in a quarry. Throughout the day, 400 pounds of gravel are added to the mound. Two orders of 900 pounds are sold and the gravel is removed from the mound. At the end of the day, the mound has 1,500 pounds of gravel. Write the equation that best describes the situation.
Answers
Answer:
The equation that best describes the situation is:
[tex]g +400 -1800 = 1,500[/tex]
Step-by-step explanation:
The initial amount of gravel is g.
[tex]g[/tex]
Then we know that 400 pounds are added
[tex]g +400[/tex]
Two orders of 900 pounds are sold and the gravel is removed from the mound. This is:
[tex]g +400 -2 * 900[/tex]
[tex]g +400 -1800[/tex]
At the end of the day, the mound has 1,500 pounds of serious. This is:
[tex]g +400 -1800 = 1,500[/tex]
The equation that best describes the situation is:
[tex]g +400 -1800 = 1,500[/tex]
And
[tex]g= 1500 +1800 - 400\\\\g=2900[/tex]
The equation that best describes the given situation is[tex]\rm g + 400 - (2\times 900) = 1500[/tex] and this can be determined by forming the linear equation with the help of given data.
Given :
Throughout the day, 400 pounds of gravel are added to the mound.Two orders of 900 pounds are sold and the gravel is removed from the mound.At the end of the day, the mound has 1,500 pounds of gravel.Let the initial amount of gravel be 'g'. Then after the addition of 400 pounds of gravel, the total gravel becomes:
= g + 400
Given that two orders of 900 pounds are sold and the gravel is removed from the mound so, the total gravel now becomes:
[tex]\rm = g + 400 - (2\times 900)[/tex]
= g + 400 - 1800
= g - 1400
At the end of the day, the mound has 1,500 pounds of gravel, that is:
g - 1400 = 1500
g = 1500 + 1400
g = 2900
Therefore, the equation that best describe the given situation is:
g + 400 - 1800 = 1500
For more information, refer to the link given below:
https://brainly.com/question/19770987
Please help and thank you
Answers
Answer:
A
Step-by-step explanation:
Define each of the terms.
f(x) is the total level of radioactivity.
x is the total number of weeks.
[tex]\frac{1}{2}[/tex] is the weekly decay factor.
30 is the initial level of radioactivity.
What is the amplitude, period, and phase shift of f(x) = −4 sin(2x + π) − 5?
Amplitude = −4; period = 2π; phase shift: x = -pie/2
Amplitude = −4; period = π; phase shift: x = pie/2
Amplitude = 4; period = π; phase shift: x = -pie/2
Amplitude = 4; period = 2π; phase shift: x = pie/2
Answers
Answer:
Amplitude = -4; period = π; phase shift: x = π/2
Step-by-step explanation:
* Lets revise the trigonometry translation
- If the equation is y = A sin (B(x + C)) + D
* A is the amplitude
- The amplitude is the height from highest to lowest points and
divide the answer by 2
* The period is 2π/B
- The period is the distance from one peak to the next peak
* C is the horizontal shift (phase shift)
- The horizontal shift is how far the function is shifted to left
(C is positive) or to right (C is negative) from the original position.
* D is the vertical shift
- The vertical shift is how far the function is shifted vertically up
(D is positive) or down (D is negative) from the original position.
* Now lets solve the problem
∵ f(x) = A sin (B(x + C)) + D
∵ f(x) = -4 sin (2x + π) - 5 ⇒ take 2 from the bract (2x + π) common factor
∴ f(x) = -4 sin 2(x + π/2) - 5
∴ A = 4 , B = 2 , C = π/2 , D = -5
∵ A is the amplitude
∴ The amplitude is -4
∵ The period is 2π/B
∴ The period = 2π/2 = π
∵ C is the horizontal shift (phase shift)
∴ The phase shift π/2 (to the left)
* Amplitude = -4; period = π; phase shift: x = π/2
The amplitude of the function f(x) = −4 sin(2x + π) − 5 is 4, its period is π, and it has a phase shift of x = -π/2.
Explanation:The amplitude of a trigonometric function like f(x) = −4 sin(2x + π) − 5 is the coefficient in front of the sine function which determines the maximum and minimum value of the function's graph. In this case, the amplitude is the absolute value of -4, which is 4.
The period of the function is found by taking 2π divided by the coefficient of x inside the sine function, which is 2 in this case, yielding a period of π.
The phase shift of the function is determined by solving the equation 2x + π = 0 for x, which gives us a phase shift of x = -π/2. Therefore, the correct description is amplitude of 4, a period of π, and a phase shift of x = -π/2.
Plz help me with this
Answers
Answer: D) at least 6mm
Step-by-step explanation:
95% confidence is 2 standard deviations.
5mm + 2(0.5) = 5 + 1 = 6
The oysters must be at least 6 mm
which equation can you use to solve for x
Answers
As for a specific equation, I could not say. However, I can tell you how to find x!
The first thing to remember is that a straight line has a 180 degree angle.
You see on the bottom side that we have a 146 degree angle. Now look at the top side. Look closely, and you will see that the two sides are actually identical!
Don't see it? Look at the line on top between x and 56, and imagine it is not there. You see that we actually have the same 146 degree angle, just flipped right side up!
However, this angle does not say 146, but makes an extra line between them with x and 56. This means that x + 56 equals 146!
So we can find x by subtracting 56, from 146, which is... 90!
Karoline has 16 marbles oneeight of them are blue how many of coroliens marbles are blue
Answers
Answer:
2
Step-by-step explanation:
Total Marbles = 16
Fractional amount blue marbles = 1/8
Number of blue marbles = fractional amount * Total marbles
Number of blue marbles = 1/8 * 16
Number of blue marbles = 2
Answer: 2
Step-by-step explanation:
16 divided by 1/8 = 2
M(4, 2) is the midpoint of RS. The coordinates of S are (6, 1). What are the coordinates of R?
Answers
Answer:
(2, 3)
Step-by-step explanation:
There is an easy way to solve this.
Set it up like this, where one end point is on top of the midpoint.
To get from 6 to 4, you subtract 2. So subtract 2 from 4 (that's where the x coordinate comes from). To get from 1 to 2, you add 1. So add 1 to 2 (that's where the y coordinate comes from)
If this sounds confusing, please comment and I'll help ASAP.
Can 2.5, the square root of 18 and 5 form a right triangle?
Answers
Answer:
Step-by-step explanation:
if 2.5, sqrt(18), and 5 make up the sides of a right triangle, then they must satisfy A^2+B^2=C^2, where C is the longer side (hypotenuse).
In this case, 5 is the greater of the 3, so let's see if it satisfies our equation:
2.5^2+sqrt(18)^2=5^2
-> 6.25+18 = 24.25 =/= 25
-> Therefore the answer is a resounding no.
The numbers 2.5, the square root of 18, and 5 cannot form a right triangle. This is determined via the Pythagorean Theorem, which these numbers do not satisfy when squared and added together.
Explanation:In the context of mathematics, specifically geometry, a set of numbers can form a right triangle if they adhere to the Pythagorean Theorem. This theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be expressed as a² + b² = c².
Here, let's test the three numbers you've given: 2.5, √18, and 5. First, square each of the values: 2.5² = 6.25, (√18)² = 18, and 5² = 25.
If we consider 2.5 and √18 as sides a and b, and 5 as side c (the hypotenuse), the Pythagorean theorem would look like this: 6.25 + 18 = 24.25 ≠ 25. Thus, these numbers cannot form a right triangle because they do not satisfy the Pythagorean Theorem.
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Given the line 2x - 3y - 5 = 0, find the slope of a line that is perpendicular to this line.
wlw.
ооо
win
wiw
Answers
Answer:
The slope of a line that is perpendicular to the given line is [tex]-\frac{3}{2}[/tex]
Step-by-step explanation:
The equation of the line in Slope-Intercept form is:
[tex]y=mx+b[/tex]
Where "m" is the slope of the line and "b" is the y-intercept.
Solve for "y" from the equation of the line [tex]2x - 3y - 5 = 0[/tex]:
[tex]2x - 3y - 5 = 0\\\\-3y=-2x+5\\\\y=\frac{-2}{-3}x+\frac{5}{-3}\\\\y=\frac{2}{3}x-\frac{5}{3}[/tex]
You can observe that the slope of this line is:
[tex]m=\frac{2}{3}[/tex]
By definition, the slopes of perpendicular lines are negative reciprocal, then, the slope of a line that is perpendicular to the give line, is
[tex]m=-\frac{3}{2}[/tex]
Given the following diagram, find the missing measure.
Answers
Answer:
∠4 = a + b
Step-by-step explanation:
Given ∠2 = a and ∠3 = b
The sum of the 3 angles in a triangle = 180°
Subtract the sum of the 2 given angles from 180 for ∠1
∠1 = 180 - (a + b) = 180 - a - b
Now
∠1 and ∠4 form a straight angle and are supplementary, hence
∠4 = 180 - (180 - a - b) = 180 - 180 + a + b = a + b
Which choice is equivalent to the expression below? -25
Answers
Answer:
Option A.
Step-by-step explanation:
The given expression is
[tex]-25[/tex]
According to the reflexive property of equality, all values are equal to itself.
a = a
where, a be any real number.
Using the reflexive property we can say that
[tex]-25=-25[/tex]
It means -25 is equal or equivalent to -25.
Therefore, the correct option is A.
Note: If the given expression is [tex]\sqrt{-25}[/tex], then
[tex]\sqrt{-25}=\sqrt{25}\sqrt{-1}[/tex] [tex][\because \sqrt{ab}=\sqrt{a}\sqrt {b}][/tex]
[tex]\sqrt{-25}=5i[/tex] [tex][\because \sqrt{-1}=i][/tex]
Then the correct option is B.
Answer:5i
Step-by-step explanation:
A college-entrance exam is designed so that scores are normally distributed with a mean of 500 and a standard deviation of 100. Using the eight-part symmetry of the area under a normal curve, what is the probability that a randomly chosen exam score is above 800?
The probability is__?
Answers
Answer:
The probability is 0.0015
Step-by-step explanation:
We know that the average [tex]\mu[/tex] is:
[tex]\mu=500[/tex]
The standard deviation [tex]\sigma[/tex] is:
[tex]\sigma=100[/tex]
The Z-score is:
[tex]Z=\frac{x-\mu}{\sigma}[/tex]
We seek to find
[tex]P(x>800)[/tex]
The Z-score is:
[tex]Z=\frac{x-\mu}{\sigma}[/tex]
[tex]Z=\frac{800-500}{100}[/tex]
[tex]Z=3[/tex]
The score of Z = 3 means that 800 is 3 standard deviations from the mean. Then by the rule of the 8 parts of the normal curve, the area that satisfies the conficion of 3 deviations from the mean has percentage of 0.15%
So
[tex]P(x>800)=0.0015[/tex]
Express 0.6239 as a fraction.
Answers
The value of 0.6239 as a fraction or proportion is
A fraction is a mathematical expression that represents a part or a division of a whole. It is used to represent numbers that are not whole numbers or integers. A fraction consists of two components:
1. Numerator: The numerator is the number on the top of the fraction. It represents the quantity or part of the whole being considered.
2. Denominator: The denominator is the number at the bottom of the fraction. It represents the total number of equal parts into which the whole is divided.
Multiply and divide 0.6239 by 10000,
0.6239 = [tex]\frac{0.6239}{10000} \times[/tex] 10000
= [tex]\frac{6239}{10000}[/tex].
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which linear function has the same y -intercept as the one that is represented by the graph ?
Answers
Answer:
The answer is C: y = 2x + 3
Step-by-step explanation:
I took the test
Linear function is, y = 2 x + 3.
What does the y-intercept of this relationship represent?The slope and y-intercept values indicate characteristics of the relationship between the two variables x and y. The slope indicates the rate of change in y per unit change in x. The y-intercept indicates the y-value when the x-value is 0.Which is a y-intercept of the graphed function?The y -intercept of a graph is the point where the graph crosses the y -axis. (Because a function must pass the vertical line test , a function can have at most one y -intercept . ) The y -intercept is often referred to with just the y -value.How do you find the y-intercept of a graph?On a graph, the y-intercept can be found by finding the value of y when x=0. This is the point at which the graph crosses through the y-axis.According to the question:
From the points we can see the y-intercept of the line is 3 as it passes through point (0, 3).
y = 2 x - 4
y-intercept is -4 ≠ 3, incorrect.
y = 2 x - 3
y- intercept is -3 ≠ 3, incorrect.
y = 2 x + 3
y- intercept is 3 = 3, correct.
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Apply the distributive property to factor out the greatest common factor.
30+42=
Answers
Answer:
[tex]30+42=6(5+7)[/tex]
Step-by-step explanation:
Let [tex]a,b,c\in \mathbb R[/tex], according to the distributive property:
[tex]a(b+c)=ab+ac[/tex]
The prime factorization of 30 is
[tex]30=2\cdot 3\cdot 5[/tex]
The prime factorization of 42 is
[tex]42=2\cdot 3\cdot 7[/tex]
The Greatest common factor is [tex]2\times 3=6[/tex]
[tex]\implies 30+42=6\times5+6\times7[/tex]
[tex]\implies 30+42=6(5+7)[/tex]
Answer:
Step-by-step explanation:
6(5+7
A principal of $3300 is invested at 8.5% interest, compounded anually. How much will the investment be worth after 11 years? Round your answer to the nearest dollar. Please help..
Answers
Answer:
[tex]\boxed{\$8378}[/tex]
Step-by-step explanation:
The formula for compound interest is:
A = P(1 + r)ⁿ
Data:
P = 3300
APR = 8.5 %
t = 11 yr
Calculations:
n = 11 × 12 = 132
r = 0.085/12 = 0.007 083
A = 3300(1 + 0.007 083)¹³²
= 3300 × 1.007 083¹³²
= 3300 × 2.5539
= 8378
[tex]\text{The investment will be worth }\boxed{\mathbf{\$8378}}[/tex]
Really need help with this!!!
Answers
Answer:
Principal Amount= $500
Formula for compound interest:
[tex]A = p (1 + \frac{r}{n} )^{nt}[/tex]
Formula for simple interest:
A = p(1 + r(t) )
what is x in -2-3x=19
Answers
Answer:
x=-7
Step-by-step explanation:
Since you are solving for x, you need to work backwards. Add 2 to both sides: -2 and 2 cancel out, and 19 plus 2 is 21. Isolate the x by dividing both sides by -3. -3 cancels out, and 21 divided by -3 is -7.
Answer:
-7
Step-by-step explanation
−2−3x=19
−2+−3x=19
−3x−2=19
Step 2: Add 2 to both sides.
−3x−2+2=19+2
−3x=21
Step 3: Divide both sides by -3.
−3x
−3
=
21
−3
x=−7
The formula gives the height of an object in free fall at time t and acceleration g.
[tex]h = \frac{1}{2}gt^{2} [/tex]
Solve for t.
[tex]t = (2gh)^{2} [/tex]
[tex]t = 2 \sqrt{gh} [/tex]
[tex]t = \frac{ \sqrt{gh} }{2} [/tex]
[tex]t = \frac{ \sqrt{2hg} }{g} [/tex]
Answers
t must equal √2h/g but I don't see that in the choices above
Answer:
t=2hg√g
Step-by-step explanation:
took the test!
Given right triangle XYZ, which correctly describes the locations of the sides in relation to ∠Y?
Answers
Answer:
Step-by-step explanation: a is adjacent, b is opposite, c is the hypotenuse
Answer:
D
Step-by-step explanation:
solve for b. -1/3b = 9
Answers
Answer:
B=-27
Step-by-step explanation:
Answer:
-27
-1/3b=9
Divide both sides by -1/3 to get b by itself
-1/3b=9
/-1/3 /-1/3
b=-27
Sarah got 16 out of 20 questions correct on a math quiz is each question was worth the same number of pints and the test was worth 50 points total, what was sarah’s score
Answers
The total points could be 50.
It has 20 questions, so each question is worth: 50/20 = 2.5 points each.
She got 16 correct, so her score was: 16 x 2.5 = 40