Evaluating the function in x = -1, we get:
H(-1) = 7
How to evaluate a function?
When we have a function:
y = f(x)
Evaluating the function in a value, like x = a gives:
y = f(a).
This means that we need to replace all the "x" in the equation by the number "a".
In this case:
H(x) = 6 - x
And we want to get:
H(-1)
So we need to replace the x by -1.
H(-1) = 6 - (-1) = 7
H(-1) = 7
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Which composition of transformations maps figure EFGH to figure E"F"G"H"?
a reflection across line k followed by a translation down
a translation down followed by a reflection across line k
a 180° rotation about point G followed by a translation to the right
a translation to the right followed by a 180° rotation about point G
The composition of transformations maps figure EFGH to figure E"F"G"H" is Option A.a reflection across line k followed by a translation down.
What is translation?A translation can be explained as the movement of a shape in a direction which could be up, down but the appearance of the figure remain unchanged in any other way.
And from the figure, we can see that a translation is used, because of the movement of EFGH to figure E"F"G"H" which occurred in the same direction.
Hence, composition of transformations maps figure EFGH to figure E"F"G"H" is Option A.a reflection across line k followed by a translation down.
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Pls help! Geometry
What is the area of the square?
Area of the circle?
Area of the blue section?
(a) By the formula for the area of a square, the answer is [tex]16^2 = 256[/tex] square km
(b) By the formula for the area of a circle, the answer is [tex](\pi)\left(\frac{16}{2} \right)^2 =64\pi[/tex] square km
(c) Subtracting areas, we get [tex]256-64\pi[/tex] square km
f(x)=(2x−1)(3x+5)(x+1) has zeros at x= -5/3, x= -1 and x= 1/2 What is the sign of f on the interval -5/3
The sign of f on the interval -5/3 is negative
How to determine the sign?The function is given as:
f(x)=(2x−1)(3x+5)(x+1)
The zeros of the function are
x= -5/3, x= -1 and x= 1/2
Next, we plot the graph of the function
At x = -5/3, the function approaches negative infinity
This means that the sign of f on the interval -5/3 is negative
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find the area of a triangle whose sides are 5 m, 6 m and 9m,( use root 2 =-1.41 m)
The area of the triangle is 14.1 square meters
How to determine the triangle area?The side lengths are given as:
5m, 6m and 9m
Calculate the semi-perimeter (s) using
s = (5 + 6 + 9)/2
Evaluate
s = 10
The area is then calculated as:
[tex]Area = \sqrt{s(s -a)(s-b)(s-c)[/tex]
This gives
[tex]Area = \sqrt{10 * (10 -5)(10-6)(10-9)[/tex]
Evaluate the products
[tex]Area = \sqrt{200[/tex]
Evaluate the exponent
Area = 14.1
Hence, the area of the triangle is 14.1 square meters
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Help!
The parallel circuit works if one connector works or both work.
Suppose that connectors work independently of each other and, further,
the probability of each component working is 0.84 and 0.72 respectively. What is the probability the parallel circuit works?
Now A and B are independent
Both connectors must work together to make the parallel circuit work
P(A and B)
P(A)*P(B)(0.84)(0.72)0.6048Connectors be C1 and C2
P(C1)=0.84P(C2)=0.72We need P(C1.C2)
Note the formula
For independent events
[tex]\boxed{\sf P(AB)=P(A)P(B)}[/tex]
[tex]\\ \tt{:}\dashrightarrow P(C1C2)=P(C1)P(C2)[/tex]
[tex]\\ \tt{:}\dashrightarrow 0.84(0.72)[/tex]
[tex]\\ \tt{:}\dashrightarrow 0.6[/tex]
Johnny earns $2334.50 from his job each month. he pays $1437 for monthly expenses Johnny is planning a vacation in 3-month times that he estimates will cost $1750 total. how much will Johnny have leftovers from 3 months of saving once he pays for his vacation?
1) $948.50
2) $584.50
3) $852.50
4) $942.50
The amount of money left from 3 months of saving once he pays for his vacation is $942.50
SavingsNumber of months = 3Amount earned per month = $2334.50Total earned = 3 × $2334.50= $7,003.50
Monthly expenses = $1437
Total expenses = 3 × $1437
= $4,311
Cost of vacation = $1750
Total balance = $7,003.50 - ($4,311 + $1750)
= 7,003.50 - 6061
= $942.50
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How many solutions exist for the system of equations in the graph?
Answer:
Two
Step-by-step explanation:
Solutions are when the two graphs intersect
Which inequalities would have a closed circle when graphed? check all that apply. x > 2.3 5.7 less-than-or-equal-to p one-half greater-than y m greater-than-or-equal-to 10 s < –7.6
Option B and D would have closed circles when graphed
The domain and range of a function are the components of a function. The domain is the set of all the input values of a function and range is the possible output given by the function.
At the endpoints of the domain, we draw open circles to indicate where the endpoint is not included because of a less-than or greater-than inequality; we draw a closed circle where the endpoint is included because of a less-than-or-equal-to or greater-than-or-equal-to inequality.
∴ Option B and D that are 5.7 ≤ p and [tex]\frac{1}{2}[/tex] ≥ y respectively would have closed circles
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A ______ of two linear _______ can have one solution, an infinite number of solutions, or no solution.
Answer:
system
equations
Step-by-step explanation:
Answer:
A system of two linear equations can have one solution, an infinite number of solutions, or no solution.
===================================================
Explanation:
An equation is something like [tex]\text{y} = 2\text{x}+5[/tex] and [tex]\text{y} = 3\text{x}+7[/tex]
When we combine two such equations to form a group (of sorts), we consider this to be a system of equations.
We use a single curly brace to write the system
[tex]\begin{cases}\text{y} = 2\text{x}+5\\\text{y} = 3\text{x}+7\end{cases}[/tex]
Here are the three cases mentioned when it comes to solutions.
If the two lines intersect at exactly one point, then the system has exactly one solution. This system is consistent and independent.If the two lines are the same, they intersect at infinitely many points along that line. One line perfectly overlaps the other. Therefore, this scenario leads to infinitely many solutions. The system is dependent because one line depends on the other (since they are one in the same). This system is also consistent because it has at least one solution. Lastly, if the two lines are parallel, then they never cross. The lack of crossing points means there aren't any solutions. We call this an inconsistent system.Side note: Any solution is of the form (x,y)
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.
Using the transformation T: (x, y) (x + 2, y + 1), find the distance named.
Triangle ABC was translated using the rule (x, y) (x + 2, y + 1) to form congruent triangle A'B'C' with AA' = √5 units
What is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, reflection, translation and dilation.
Point A is at (0, 0). Using the transformation T: (x, y) (x + 2, y + 1), point A' = (2, 1). Hence:
[tex]AA'=\sqrt{(1-0)^2+(2 - 0)^2}=\sqrt{5}[/tex]
Triangle ABC was translated using the rule (x, y) (x + 2, y + 1) to form congruent triangle A'B'C' with AA' = √5 units
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After five science tests, Sonya's average score
is 89. If she gets a 95 on the sixth test, what is
her new average?
A. 89.50
B. 89.90
C. 90.00
D. 90.50
Answer:
C
Step-by-step explanation:
The sum of Sonya's 5 initial tests = 89*5 = 445.
445 + 95 = 540 (sum of the 6 tests)
Average = 540/6 = 90
Hence C
Answer:
C. 90.00
Step-by-step explanation:
We find average by adding up all values in a data set and dividing by the total number of values we have
We can say that Sonya got 89 for each test (it doesn't matter what each test score exactly was--you'll see why in a second)
So, we can add up 89 five times (5 tests have occured)
*I say add up, because that's what average is, but you can find this number by multiplying 89 · 5
89 · 5 = 445
(89 + 89 + 89 + 89 + 89 = 445)
Now, we need to add up our new value: 95
445 + 95 = 540
So, we can now divide 540 (sum of all values) by 6 (total number of values)
540 ÷ 6 = 90
So, C (90.00) is her new average
hope this helps! have a lovely day :)
You obtain a 60-day note from a bank for $5200. The loan takes place on November 20, and the costs include $73.38 for interest and $29.12 in other charges. How much, in dollars, is due at the end of 60 days?
Answer:=102.5
Step-by-step explanation:
A sample of 4 different calculators is randomly selected from a group containing 12 that are defective and 33 that have no defects. What is the probability that at least one of the calculators is defective?
The probability that at least one of the calculators is defective is : 0.725
What is probability?Probability is the likelihood of an event happening or not.
if there is certainty that the event would happen probability is 1.
Analysis:
probability = required outcome/possible outcome
for 33 good calculators and 12 defective calculators, total calculators = 45
4 calculators were chosen, possible outcome = 45C4 = 148995
Required outcome = 33C3 . 12C1 + 33C2 . 12C2 + 33C1 . 12C3 + 33C0 . 12C4
= 65472 + 34848 + 7260 + 495 = 108075
Probability = 108075/148995 = 0.725
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What is another name for Angle 2? Lines E H and D F intersect at point G. Angle 2 is formed by line segments D G and G E and angle 1 is formed by line segments E G and G F. Angle D G E Angle G E D Angle E G F Angle G E F
When two straight lines or rays intersect at a shared endpoint, an angle is generated. The correct option is A.
What is an angle?When two straight lines or rays intersect at a shared endpoint, an angle is generated. An angle's vertex is the common point of contact. Angle is derived from the Latin word angulus, which means "corner."
The diagram for the given problem can be made as shown below. Therefore, the other name for angle 2 will be ∠DGE.
Hence, the correct option is A.
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Answer:
a
Step-by-step explanation:
got it right
Geometry
Find the area of the shaded region
Answer:
Area = 1125mi
Step-by-step explanation:
Area of sector = [tex]r^2 *\frac{\alpha }{2}[/tex]
[tex]r^{2} =5^{2} =25[/tex]
[tex]25*\frac{\alpha}{2}[/tex]
[tex]25*\frac{90}{2} =25*45=1125[/tex]
[tex]\alpha[/tex] = angle
[tex]r[/tex] = radius
radius is 5mi
in this case the angle is 90°
A = 1125mi
you can also solve by using circle area which is [tex]\pi r^{2}[/tex]
then divide by 4 because this is 1/4 of the circle.
Hope this helps
the mean value of land and buildings per acre from a sample of farms is $1400 with a standard deviation of $300 the data set has a bell shaped distribution assume the number of farms in the sample is 72 use empirical rule to estimate the number of farms whose land and building values per acre are between $1100 and $1700
Using the Empirical Rule, it is found that 49 farms in the sample have land and building values per acre between $1100 and $1700.
What does the Empirical Rule state?It states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.Approximately 95% of the measures are within 2 standard deviations of the mean.Approximately 99.7% of the measures are within 3 standard deviations of the mean.Considering the given mean and standard deviation, values between $1100 and $1700 are within 1 standard deviation of the mean, which is a percentage of 68%.
Hence, the number of farms out of 72 is:
0.68 x 72 = 49 farms.
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Help with exercise
The number of calories in a 1.5-ounce chocolate bar is 225. Suppose that the distribution of calories is normally distributed with the standard deviation o = 10. a) What is the probability that a randomly selected chocolate bar will have between 200 and 220 calories? Show all your steps.
Hint use the z table and z score and formula Also use less than and grater sign correctly
b) What is the probability that a randomly selected chocolate bar will have less than 190 calories? Show all your steps.
The probability that a randomly selected chocolate bar will have between 200 and 220 calories is 3.97%
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
The zscore is given a:
z = (raw score - mean) / standard deviation
mean = 225, standard deviation o = 10.
a) For x = 200:
z = (200 - 225) / 200 = -0.125
For x = 220:
z = (220 - 225) / 200 = -0.025
P(-0.125 < z < -0.025) = P(z < -0.025) - P(z < -0.125) = 0.4880 - 0.4483 = 3.97%
b) For x = 190:
z = (190 - 225) / 200 = -0.175
P(z < -0.025) = P(z < -0.175) = 0.4286
The probability that a randomly selected chocolate bar will have between 200 and 220 calories is 3.97%
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A particular plant root grows 1.5 inches per month. How many centimeters is the plant root growing per month? (1 inch = 2.54 centimeters). I WILL MARK BRAINLIEST~ PLEASE ITS THE LAST QUESTION!!
[tex]\huge\boxed{3.81\ \text{centimeters}}[/tex]
We simply need to convert 1.5 inches to centimeters.
Use multiplication:
[tex]1.5\cdot2.54=\boxed{3.81}[/tex]
URGENT! PLS ANSWER QUICK!!!!!!!!
Which best describes the relationship between the line that passes through the points (9, –5) and (5, –2) and the line that passes through the points (–4, –2) and (–8, 1)?
Since the lines have the same slopes, hence they are parallel lines
How to determine the relationship between linesWe can determine the relations by knowing the slopes of the line
For the line with coordinates (9, –5) and (5, –2)
Slope = -2+5/5-9
Slope = -3/4
For the line with coordinates (–4, –2) and (–8, 1)
Slope = 1+2/-8+4
Slope = -3/4
Since the lines have the same slopes, hence they are parallel lines
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Use the Divergence Theorem to evaluate
Integral of (9x + 2y + z2) dS
where S is the sphere
x2 + y2 + z2 = 1.
The value of the integral is [tex]\int\limits^{}_s {9x + 2y + z^2} \, dS = \frac{4}{3}\pi[/tex]
How to evaluate the integral?The expression is given as:
[tex]\int\limits^{}_s {9x + 2y + z^2} \, dS[/tex]
[tex]x^2 + y^2 + z^2 = 1[/tex]
Rewrite the integral as:
[tex]\int\limits^{}_s {9x + 2y + z*z} \, dS[/tex]
As a general rule, we have:
[tex]\int\limits^{}_s {Px + Qy + R*z} \, dS[/tex]
By comparison, we have:
P = 9
Q = 2
R = z
By the divergence theorem, we have:
F = Pi + Qj + Rk
So, we have:
F = 9i + 2j + zk
Differentiate
F' = 0 + 0 + 1
F' = 1
The volume of a sphere is:
[tex]V = \frac{4}{3}\pi r^3[/tex]
Where:
r = F' = 1
So, we have:
[tex]V = \frac{4}{3}\pi (1)^3[/tex]
Evaluate
[tex]V = \frac{4}{3}\pi[/tex]
This means that:
[tex]\int\limits^{}_s {9x + 2y + z^2} \, dS = \frac{4}{3}\pi[/tex]
Hence, the value of the integral is [tex]\int\limits^{}_s {9x + 2y + z^2} \, dS = \frac{4}{3}\pi[/tex]
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Find a polynomial function of degree 5 with -3 as a zero of multiplicity 3, 0 as a zero of multiplicity 1, and 3 as a zero of multiplicity 1.
[tex](x+3)^3\cdot x\cdot (x-3)=(x^3+9x^2+27x+27)\cdot (x^2-3x)=\\=x^5-3x^4+9x^4-27x^3+27x^3-81x^2+27x^2-81x=\\=x^5+6x^4-54x^2-81x[/tex]
HELPPP PLS TYSM IF U HELPED <3
The measure of <TRS and angle d are 70 and 43degrees respectively
Triangles and angleThe given triangles are isosceles triangles since they have two equal sides.
14) From he triangle RST
<TRS + 90 + 20 = 180
<TRS + 110. = 180
Subtract 110 from both sides
<TRS = 180 -110
<TRS = 70 degrees
15) For this triangle;
d = 86/2
d = 43 degrees
Hence the measure of <TRS and angle d are 70 and 43degrees respectively
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Tony made 14 { L}14 L14, start text, space, L, end text of lemonade for a party. His guests drank 9,500 { mL}9,500 mL9, 500,m, L, end text of the lemonade.
How many milliliters of lemonade did Tony have left over?
Unit conversion is a way of converting some common units into another without changing their real value. The lemonade left with Tony is 4500ml.
What is unit conversion?Unit conversion is a way of converting some common units into another without changing their real value. for, example, 1 centimetre is equal to 10 mm, though the real measurement is still the same the units and numerical values have been changed.
One litre is equal to 1000 millilitres. Tony made 14 Liter of lemonade, therefore, Tony made 14,000 millilitres of lemonade. His guest drank 9500 millilitres. Therefore, the lemonade left with Tony is,
Lemonade left = 14,000 - 9,500 = 4,500 ml
Hence, the lemonade left with Tony is 4500ml.
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A student hypothesized that in the US adult population, women drank the same amount of water per day as men per kg of body weight as the null hypothesis. The probability value for her null hypothesis was 0.02. Assume the alpha level was 0.05. Which conclusion is justified?
The conclusion that is justified based on the research is that he rejected the null hypothesis that women drank the same amount of water per kg of body weight per day as men.
How to illustrate the research?It should be noted that a research is simply used to get information about a topic.
In this case, it can be deduced that a type 1 error is committed. This implies the rejection of the null hypothesis when it's true.
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I need Help with calculus please, thank you! 10points
3) We have
[tex]f(x) = \sec\left(\dfrac{\pi x}2\right) = \dfrac1{\cos\left(\frac{\pi x}2\right)}[/tex]
which has vertical asymptotes (i.e. infinite discontinuities) whenever the denominator is zero. This happens for
[tex]\cos\left(\dfrac{\pi x}2\right) = 0[/tex]
[tex]\implies \dfrac{\pi x}2 = \cos^{-1}(0) + 2n\pi \text{ or } \dfrac{\pi x}2 = -\cos^{-1}(0) + 2n\pi[/tex]
(where [tex]n[/tex] is any integer)
[tex]\implies \dfrac{\pi x}2 = \dfrac\pi2 + 2n\pi \text{ or } \dfrac{\pi x}2 = -\dfrac\pi2 + 2n\pi[/tex]
[tex]\implies x = 1 + 4n \text{ or } x = -1 + 4n[/tex]
So the graph of [tex]f(x)[/tex] has vertical asymptotes whenever [tex]x=4n\pm1[/tex] and [tex]n\in\Bbb Z[/tex].
4) Given
[tex]h(t) = \begin{cases} t^3+1 & \text{if } t<1 \\ \frac12 (t+1) & \text{if } t\ge1 \end{cases}[/tex]
we have the one-sided limits
[tex]\displaystyle \lim_{t\to1^-} h(t) = \lim_{t\to1} (t^3+1) = 1^3+1 = 2[/tex]
and
[tex]\displaystyle \lim_{t\to1^+} h(t) = \lim_{h\to1} \frac{t+1}2 = \frac{1+1}2 = 1[/tex]
The one-sided limits don't match, so the two-sided limit [tex]L[/tex] does not exist. In other words, the limit does not exist at [tex]x=1[/tex] because the function approaches different values from the left and right side of [tex]x=1[/tex].
Find the next term in the following number pattern: 1, 16, 81, 256, 625, ____
Juanita has 60 horses on her ranch. If 60% of the horses are thoroughbreds, how many are not thoroughbreds?
A.) 45
B.) 22
C.) 21
D.) 24
Answer: d
Step-by-step explanation:
60*0.6=36
60-36=24
24 are not thoroughbreds
Which of the following are solutions to the equation below?
Check all that apply.
x²-2x-24 = 0
Answer:
[tex]x=6, x=-4[/tex]
Step-by-step explanation:
1) Let's solve this quadratic equation by factorizing. We need to find two numbers that multiply to -24 and add up to -2 simultaneously. If we pull out the factors of -24, two of them will be -6 and 4, which multiply to -24 as well as add up to -2.
3) Write [tex]-2x[/tex] as a sum.
[tex]x^2-6x+4x-24=0[/tex]
Now, we can factor them out by grouping.
[tex]x^2-6x+4x-24=0\\x(x-6) + 4(x-6)=0[/tex]
Since, [tex]x -6[/tex] is common in both of the factors, we only take one of the [tex]x -6[/tex] along with [tex]x[/tex] and [tex]4[/tex] and all equated to 0.
[tex](x-6)(x+4) = 0[/tex]
Solve for x: [tex]x-6=0[/tex]
[tex]x=0+6\\x=6[/tex]
Solve for x: [tex]x+4=0[/tex]
[tex]x=0-4\\x=-4[/tex]
Therefore, our solutions to this quadratic equation are [tex]x=6, x=-4[/tex].
Determine if the following relations are functions. If not, explain.
Answer:
Graph 3 represents a function
Graph 4 is not a function
Step-by-step explanation:
By definition :
A function is a rule or law which relates all the elements of one set with some UNIQUE element of another set.
Which means that from a given value of the input x, there will be only one value of y in a function f(x) = y
Graphically it would represent that for a given point x , there would only be one value of y corresponding to that x.
In graph 4, we can see that for one x, there exists two values of y.
Example : at x = 5, we have y=5 AND y= -5; which is not possible in case of a function.
The Jones family bought a refrigerator for $900. They paid installments over 4 years at an add-on rate of 6%. What is the approximate APR? ASAP
The approximate APR for the purchase is 16%
To calculate the annual percentage rate (APR)
We would calculate the interest rate
Add the administrative fees to the interest amount
Divide the loan amount (principal)
Divide by the total number of days in the loan term
Multiply all year
Multiply by 100 to convert to a percentage
Interest= P * R * t
APR= [tex]\frac{\frac{216}{900}}{6 * 4 * 100}[/tex]
APR = 16%
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