The vertex of the absolute value function f(x) = (-2/3)*|x + 4| is:
(-4, 0)
Which is the vertex of the absolute value function?Here we have the following absolute value function:
f(x) = (-2/3)*|x + 4|
The x-value of the vertex is the one that makes the argument of the absolute value part equal to zero, so we will get:
x + 4 = 0
x = -4
To et the y-value of the vertex we evaluate the function in x = -4, we will get:
f(-4) = (-2/3)*|-4 + 4|
f(-4) = 0
Then the vertex of the absolute value function is (-4, 0).
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NO0000000000000000000000
To determine whether the system of equations is consistent and independent, consistent and dependent, or inconsistent, we need to first solve the system of equations to find the value of x and y that satisfy both equations.
To solve the system of equations, we can first solve the first equation for y:
y = −3x + 1
Next, we can substitute this expression for y into the second equation and solve for x:
2y = −6x + 2
2 * (−3x + 1) = −6x + 2
−6x + 2 = −6x + 2
0 = 0
Since the two equations are equivalent, the system of equations is consistent and dependent, meaning that there is only one possible solution (x = 0, y = 1) that satisfies both equations.
the time it takes to preform a task has a continuous uniform distribution between 43 min and 57 min. what is the the probability it takes between 54.7 and 56 min. round to 4 decimal places.
the time it takes to preform a task has a continuous uniform distribution between 43 min and 57 min. 0.1875 is the the probability it takes between 54.7 and 56 min. round to 4 decimal places.
The probability of any event occurring is given by the formula P(x) = (x-a)/(b-a). In this case, the probability of the task taking between 54.7 and 56 minutes is (56-54.7)/(57-43) = 0.1875. This probability is equal to the area under the uniform distribution graph between 54.7 and 56 minutes. As the graph is a rectangle, the area is simply the width multiplied by the height, so 0.1875. Rounding to 4 decimal places, the probability is 0.1875.
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I need help with A help please
Answer:
x = 12
y = 4
Step-by-step explanation:
Part B
Gradient
Gradient = (y2 - y1) / (x2 - x1)
Gradient = (6 - 3) / (10 - 4)
Gradient = 0.5
Line of equation
y - y1 = m (x - x1)
y - 3 = 0.5 (x - 4)
y - 3 = 0.5x - 2
y = 0.5x - 2 + 3
y = 0.5x + 1
f(x) = mx + b ---> f(x) = 0.5x + 1
m = 0.5
b = 1
Part A
x = 12
y = 4
(Put the values of the graph in the line of equation)
I hope my answer helps you.
Identify the measure of angle x please show work Bc I have too !!
Answer:
x = 145°
Step-by-step explanation:
x and 35° are a linear pair and sum to 180° , then
x + 35° = 180° ( subtract 35° from both sides )
x = 145°
Sarah took the advertising department from her company on a round trip to meet with a potential client. Including Sarah a total of 11 people took the trip. She was able to purchase coach tickets for $180
and first class tickets for $1200. She used her total budget for airfare for the trip, which was $10,140. How many first class tickets did she buy? How many coach tickets did she buy?
number of first class tickets bought=
The number of coach tickets is; 3 coach tickets
The number of first class tickets is; 8 first class tickets
How to solve algebra word problems?We are told that she took 11 people on the trip.
Let the number of first class tickets be f
Let the number of coach tickets be c
Thus;
c + f = 11 -----(1)
She was able to purchase coach tickets for $180 and first class tickets for $1200. She used her total budget for airfare for the trip, which was $10,140. Thus;
180c + 1200f = 10140 -----(2)
Make c the subject in eq 1 to get;
c = 11 - f
Put 11 - f for c in eq 2 to get;
180(11 - f) + 1200f = 10140
1980 - 180f + 1200f = 10140
1020f = 8160
f = 8
Thus;
c = 11 - 8
c = 3
So, 3 coach tickets and 8 first class tickets were bought
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a simple random sample of 64 observations was taken from a population of size 500. the population standard deviation is 16. what is the standard deviation of sample mean?
64 observations were randomly selected at random from a population of 500. the population standard deviation is 16.The standard deviation of the sample mean is 4 (16/√64).
The standard deviation of the sample mean is calculated by dividing the population standard deviation (16) by the square root of the sample size (64).
Consequently, the sample mean's standard deviation is
16/√64 = 4.
This means that the expected spread of the sample means is 4, which is less than the population standard deviation of 16. This is because the sample is smaller than the population, so the sample standard deviation will be smaller than the population standard deviation.
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Which ordered pair does NOT lie on the graph of y = x/4 + 5?
Work out the area of a rectangle with base B= 38mm and perimeter, P = 88mm
Answer: the area of the rectangle is 456 square millimeters.
Step-by-step explanation:
the perimeter is 88 mm, so if we let L be the length of the rectangle and W be the width, we can write the following equation to find the perimeter:
2L + 2W = 88 mm
Since the base of the rectangle is 38 mm, we know that the width of the rectangle is 38 mm, so we can substitute that value into the equation above to get:
2L + 2(38 mm) = 88 mm
Solving for L, we get:
2L = 88 mm - 2(38 mm)
2L = 88 mm - 76 mm
2L = 12 mm
Therefore, the length of the rectangle is 12 mm. Now that we know both the length and the width, we can find the area by multiplying the length and the width:
Area = L * W
Area = 12 mm * 38 mm
Area = 456 mm^2
Thus, the area of the rectangle is 456 square millimeters.
Answer:
A=228mm
Step-by-step explanation:
What formulas do we know?
Parameter= 2(length)+2(width)
Area= length x width
We can just substitute in values for parameters so,
88=2(length) + 2(38)
88=2L + 78 ------> 12=2L -------> L=6
Now we know width (which is just B) and Length (what we calculated)
Now we use area ----> Area= length x width
Area= (38)(6)-----> 228mm
Help me please thank you show your work if you want
Answer:
8) y = 4
9) y = x
Step-by-step explanation:
8) Parallel = Same slope
y = mx + b
m = 0
4 = - 4(0) + b
4 = b
y = 4
9) y = x + b
7 = 7 + b
b = 0
Multiply: (√2x³ +√12x)(2√10x³ + √6x²
2√10x +2√3x³ +4√15x³ +6√2x
2x²√5 +2x√3x + 2x³√30 +3x√2x
4x √√5+2x²√√3x + 4x³√30+ 6x√√2x
x√20+x²√√6x + x³√120 + x√12x
The result of the multiplication of (√2x³ +√12x)(2√10x³ + √6x²) is
[tex]2\sqrt{20}x^6 + \sqrt{12}x^5 + 2\sqrt{120}x^4 + \sqrt{72}x^3[/tex]
What is multiplication?
Multiplication is a mathematical operation in which one number is multiplied by another. It is usually used to calculate the product of two or more numbers. It is an important operation in mathematics and is used in a variety of ways, including calculating the area of a rectangle, the volume of a cube, and the total cost of items purchased at a store. Multiplication is often represented by the multiplication symbol, which is usually an 'x' or an asterisk (*). When two numbers are multiplied, the result is called the product. For example, if two numbers are multiplied together, the product is the answer to the question "what is the result of multiplying these two numbers together?" The answer is the product of the two numbers.
Here the multiplication given is
(√2x³ +√12x)(2√10x³ + √6x²)
[tex]2\sqrt{20}x^6 + \sqrt{12}x^5 + 2\sqrt{120}x^4 + \sqrt{72}x^3[/tex]
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Shirts are on sale for of the original price. If the original price was $16, what is the
sale price?
$4
$16
THINK
$12
$64
CLEAR
CHECK
The sale price of the shirt is equal to $12
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
We are given that Original price of the shirt = $16
The Sale price = 34% of the original price
If original price = $16, then Sales price will be 34% of original price - original price
= 0.34 × 16 - 16
Apply BODMAS multiply before subtracting;
=16 - 0.34 × 16
=$16 - $4
Sales price = $12
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The complete question is
Shirts are on sale for 34 of the original price. If the original price was $16, what is the sale price?
the surface of an ellipsoid is intersection with a plane to form a space curve. find the vector function that represents the space curve of intersection of the ellipsoid and the plane
The vector function that represents the space curve of intersection of the ellipsoid and the plane is given by[tex]$\mathbf{r}(t) = (x(t), y(t), z(t))$[/tex] and [tex]x(t) = a\cos(t)$ y(t) = b\sin(t)$ $z(t) = \frac{-d - ax(t) - by(t)}{c}$$[/tex]
Let [tex]$\mathbf{x} = (x, y, z)$[/tex] be the position vector of a point on the ellipsoid, and [tex]$a, b, c$[/tex] be the corresponding semi-major axes. Then the equation is
[tex]$$\frac{x^2}{a^2} + \frac{y^2}{b^2} + \frac{z^2}{c^2} = 1.$$[/tex]
The equation of the plane is
[tex]$$ax + by + cz + d = 0.$$[/tex]
The vector function that represents the space curve of intersection of the ellipsoid and the plane is given by
[tex]$$\mathbf{r}(t) = (x(t), y(t), z(t)),$$[/tex]
where
[tex]$$x(t) = a\cos(t)$$$$y(t) = b\sin(t)$$$$z(t) = \frac{-d - ax(t) - by(t)}{c}$$[/tex]
The vector function that represents the space curve of intersection of the ellipsoid and the plane is given by [tex]$\mathbf{r}(t) = (x(t), y(t), z(t))$[/tex]where [tex]$x(t)$[/tex]and [tex]$y(t)$[/tex] are the coordinates of points on the ellipsoid, and [tex]$z(t)$[/tex] is determined by the equation of the plane. The vector function allows us to represent the intersection of the ellipsoid and the plane as a space curve.
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Two lines intersect at the point (1, 3).
The y-intercepts of the lines are 1 and 2.
What are the equations of the lines?
The two linear equations can be written as:
y = 2*x + 1
y = x + 2
What are the equations of the lines?
Remember that a general linear equation is written as:
y = a*x + b
Where a is the slope and b is the y-intercept.
First, we know that one of the lines has an y-intercept at y = 1, then:
y = a*x + 1
And the line passes through (1, 3), replacing these values we get:
3 = a*1 + 1
3 - 1 = a
2 = a
That line is y = 2*x + 1
The other line has a y-intercept at y = 2, then:
y = a*x + 2
This line also passes through (1, 3), then:
3 = a*1 + 2
3 = a + 2
3 - 2 = a
1 = a
The line is:
y = a*x + 2
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The science club is taking a trip to a nature preserve. Before the trip, the divide 3 pounds of trail mix equally into 10 bags to have as a snack. How much trail mix went in each bag?
Answer: 0.03 pounds
Step-by-step explanation:
To determine how much trail mix went in each bag, you need to divide the total amount of trail mix by the number of bags.
In this case, you would divide 3 pounds of trail mix by 10 bags to find that each bag contained 0.3 pounds of trail mix.
You can also express this amount in ounces. Since there are 16 ounces in a pound, each bag contained 4.8 ounces of trail mix (0.3 pounds * 16 ounces/pound = 4.8 ounces).
NEED IT ASAP!!! math
The variables x, y, z associated to the parallelogram are equal to 60, respectively.
How to find the measures of the variables associated to the angles of a parallelogram
A parallelogram is a quadrillateral formed by two pairs of parallel sides. The figure shows a parallelogram since the following relationships are met: BC ║ AD, AB ║ CD. We need three equations to determine the values of x, y and z and this can be obtained by means of parallelogram properties:
y = x
y + (x + y) = 180°
z + (x + y) = 180°
First, substitute x on the second and third equations:
3 · y = 180°
z + 2 · y = 180°
Second, find y:
y = 180° / 3
y = 60
Third, find z:
z = 180° - 2 · y
z = 180° - 2 · 60
z = 180° - 120°
z = 60
Fourth, find x:
x = 60
The values of variables x, y, z are 60, respectively.
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You just won the lottery! You now have $25,000! You make a smart decision and invest all $25,000 to earn interest on it over the next 10 years.
You need to find 3 local banks and find their savings interest rates.
Then you need to decide which bank will earn you the most money after investing $25,000 for 10 years. Use the SIMPLE INTEREST FORMULA.
1) Which bank yielded the highest amount of interest earned? Which bank yielded the lowest amount of interest earned?
2) What is the difference in the principal invested for banks that yielded the highest and lowest interests from Question 1? What is the difference in the interest earned for the banks from Question 1?
3) Which bank would you invest your $25,000? WHY?
The difference between the interest compounded daily and the interest compounded annually is $67.13.
To calculate the interest earned by your money annually, you calculate as follows;
To determine the interest, use FV - amount invested
FV = P (1 + r)^n
the above represents,
FV = Future value
P = Present value
R = interest rate
N = number of years
$25,000 (1.0725) = 26,812.50
26,812.50 - $25,000 = $1,812.50
What is the interest earned in your money is compounded on a daily basis?
$25,000x (1 + 0.0725 /365)^365 = 26,879.63
26,879.63 - $25,000 = $1879.63
What is the difference in interest?
$1879.63 - $1,812.50 = $67.13
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A medical clinic is reducing the number of incoming patients by giving vaccines before flu season. during week 5 of flu season, the clinic saw 85 patients. in week 10 of flu season, the clinic saw 65 patients. assume the reduction in the number of patients each week is linear. write an equation in function form to show the number of patients seen each week at the clinic.
You have a piece of fabric with an area of 32 1/3 ft. ² if there are five people in your group what i the area of fabric that each peron can ue
With the mentioned area of fabric, the five person in group will get 6.47 ft² of fabric per person.
Firstly converting the area of fabric from mixed fraction to fraction.
The area of fabric = (32×3 + 1)/3
Performing multiplication and addition on Right Hand Side of the equation
The area of fabric = 97/3 ft²
Amount of fabric each person gets = (97/3)/5
Performing division on Right Hand Side of the equation
Amount of fabric each person gets = 97/(3×5)
Amount of fabric each person gets = 97/15
Amount of fabric each person gets = 6.47 ft²
Thus, each person will get the fabric of area 6.47 ft².
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a menorah holds one candle for each night of hanukkah and and extra candle called the shamash that is used to light the other candles. how many candles does a hanukkah menorah hold?
The primary eight candles or oil lamps must be on a plane that is higher or lower than the shamash.
A nine-branched candelabrum known as a Hanukkah menorah, also known as a hanukkiah, is lighted during the eight-day Jewish festival of Hanukkah. Eight of the nine branches are held up by lights (candles or oil lamps), which stand throughout the eight nights of the festival. One additional light is lighted each night until all eight branches are illuminated on the last night. The candle on the ninth branch, known as the shamash (Arabic for "helper" or "servant"), is used to light the other eight branches.
The seven-branched menorah used in the first Temple in Jerusalem is commemorated by the Hanukkah menorah, which is separate from it. It's one of the most commonly manufactured pieces of Jewish ritual art, along with the Star of David and the menorah with seven branches.
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aahan has a job that guarantees him the same fixed salary increase every year. after 4 years, he makes $56,785; after 9 years, he makes $60,210. what is the equation of the line that would graph his salary over time?
The equation of line that would graph his salary over time will be;
⇒ y = 1/685x - 38.89
What is Equation of line?The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
After 4 years, he makes $56,785; after 9 years, he makes $60,210.
Now,
Since, After 4 years, he makes $56,785; after 9 years, he makes $60,210.
Hence, The equation of line passes through the points (56,785, 4) and
(60,210, 9).
So, We need to find the slope of the line.
Hence, Slope of the line is,
m = (y₂ - y₁) / (x₂ - x₁)
m = (9 - 4) / (60210 - 56785)
m = 5 / 3425
m = 1/685
Thus, The equation of line with slope 1/685 is,
⇒ y - 4 = 1/685 (x - 56,785)
⇒ y - 4 = 1/685x - 42.89
⇒ y = 1/685x - 42.89 + 4
⇒ y = 1/685x - 38.89
Therefore, The equation of line that would graph his salary over time will be;
⇒ y = 1/685x - 38.89
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Solve.
27) The cost of having a car towed is given by the
linear function C(x) = 3x + 65, where C(x) is in
dollars and x is the number of miles the car is
towed. Find the cost of having a car towed 7
miles.
2/2
Answer:
It will cost $86.00 for the care to be towed 7 miles.
Step-by-step explanation:
C(x) = 3x + 65 Substitute in 7 for x
C(7) = 3(7) + 65
C(x) = 21 + 65
C(x) = 86
Answer
86 Dollars
Step-by-step explanation:
It is given that
[tex]c(x) = 3x + 65 \\ [/tex]
Since,x is the number of miles the car is towed which in this case is 7
So, If we input 7 in the function C(x)
[tex]c(7) = 3 \times 7 + 65[/tex]
We know through BODMAS that multiplication is done before addition.
Thus,
[tex]c(7) = 21 + 65 \\ because \: 3 \times 7 = 21 \\ [/tex]
and so,
[tex]c(7) = 86 \\ because \:21 + 65 = 86[/tex]
and so,
c(7) = 86
We also know that C(x) is the cost of having the car towed which is equal to 86 for the case of towing the car 7 miles
Thus,The cost of having the car towed 7 miles is 86 Dollars
write the percent and the decimal shown by the model
percent: __ %
decimal: __
please please please help meee :>
The percentage represented is 72%, and the decimal is 0.72
How to write the percent and the decimal?
First lets find the decimal, it will be equal to the quotient between the total number of shaded squares and the total number of squares.
There are 200 squares in total, and of these 200, there are 144 shaded ones, then the decimal is:
d = 144/200 = 0.72
To find the percentage, you only need to multiply the decimal by 100%, we will get:
p = 100%*0.72 = 72%
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What value of x is in the solution set of the inequality –5x – 15 > 10 20x? –2 –1 0 1
X is an algebraic variable which has no defined value. X is kind of universe variable taken in most of the equations.
The value of x in the solution set of - 5x - 15 > 10 + 20x is x < - 1 and the required value from the solution set is -2.
Solution:
Given: - 5x - 15 > 10 + 20x
Let us solve the inequality by isolating the variable x.
Add 5x on both sides
- 5x - 15 + 5x > 10 + 20x + 5x
- 15 > 10 + 25x
Subtract 10 from both sides
- 15 - 10 > 10 - 10 + 25x
- 25 > 25x
Divide both sides by - 25
-1 > x
x < - 1
The value of x in the solution set of - 5x - 15 > 10 + 20x is x < - 1 and the required value from the solution set is -2.
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Answer:
-2
Step-by-step explanation:
i did it
Here are the first six terms of an arithmetic sequence 3,8,13,18,19,23,28 find the an expression for the nth term
Answer:
nth term = a+(n-1)d
Step-by-step explanation:
where a=first term
n=nth term
d=common difference=2nd term - 1st term=5
Which Of The Following Propositions Is Tautology? Select One: O A. Pv (Q→P) O B B. (P V Q) →Q O C. Pv (Pq) O D. None
The logical statement [tex]$(a \wedge b) \rightarrow(b \vee c)$[/tex] is a tautology. Hence, Option B and Option C is the most appropriate answer to the given question.
A tautology is a logical statement where the conclusion is always equivalent to the premise. No matter what the individual parts are, the result is always a true statement; i.e. a tautology is always true. The opposite of tautology is either a contradiction or a fallacy.
say, "x=y or x≠y".
Similarly, "either the ball is red, or the ball is not red" is always true, irrespective of the color of the ball.
Here, checking the truth tables of each of the options
we can conclude that the truth values of (P v Q)→Q and P v (P→Q) are always true.
So, (P V Q) →Q and P v (P→Q) are tautology statements.
Hence, option B and option C are the correct choices for this question.
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lilyana runs a cake decorating business, for which 10\, percent of her orders come over the telephone. let ccc be the number of cake orders lilyana receives in a month until she first gets an order over the telephone. assume the method of placing each cake order is independent. find the probability that it takes fewer than 555 orders for lilyana to get her first telephone order of the month.
The Probability of getting less than 555 orders = x<555/ccc
What is independent probability?
Suppose we discuss about two events which can be occurred at any time but the occurrence of one event is not dependent on other event. In such case the probability of occurring each event is called independent probability.
How to calcualte independent probability?The probability of two independent events is calculated by the formula
probability of one event × probability of another event
If A and B are two events occurred independently
probability of happening two events = P(A)×P(B)
In our problem, order for cake over telephone is one event
order for cake manually is another event
10 percent order get over telephone
So, percent of probability to get order from phone = 10/100 = 1/10
She got total ccc cake order in a month before getting order over phone
let. X is a number of orders she got before getting her first telephone order.
Therefore, the probability that it takes fewer than 555 orders for Lilyana to get her first telephone order = X<555/ccc
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in a simple regression, which would suggest a significant relationship between x and y? a. large p-value for the f statistic b. large p-value for the estimated slope c. large t statistic for the slope d. small t statistic for the slope
A significant relationship between x and y is b. large p-value for the estimated slope.
Simple linear regression is used to estimate the connection among quantitative variables. You can use easy linear regression whilst you need to know: How robust the connection is among variables (e.g., the connection among rainfall and soil erosion). The fee of the established variable at a positive fee of the impartial variable (e.g., the quantity of soil erosion at a positive stage of rainfall). Simple linear regression is used to version the connection among non-stop variables. Often, the goal is to are expecting the fee of an output variable (or response) primarily based totally at the fee of an input (or predictor) variable.
Thus, option b is the correct choice.
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Joe make tomato auce to ell at a craft fair. He make it in 5 gallon batche. How many pint jar doe he need to hold 5 gallon of auce?
The number of pint jar needed to hold 5 gallon of sauce is 40 jars.
Pint and gallons are both units of volume. The number of pint jars needed to hold 5 gallon of sauces can be determined by changing the unit of volume. Conversion of units refers to the conversion between different units of measurement for the same quantity, typically through multiplicative conversion factors which change the measured quantity value without changing its effects. According to the conversion of units, 1 gallon is equal to 8 pint. Hence, applying the conversion rate to the total volume of tomato sauce made:
5 gallons = 5*8 = 40 pint
If a jar holds 1 pint of sauce, the number of jars to hold the total volume of sauce is 40 pint jar.
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The sum of present ages of a father and his son is 80 years. When the fathers a was equal to the present age of the son. the sum of their ages was 40 years Fin their present ages
The present ages of the father and his son are 50 and 30 years respectively.
What is an algebraic expression?An algebraic expression can be defined as an expression made up of constants, variables, terms, coefficients, and factors.
These expressions are also made up of mathematical or arithmetic operations, which includes;
BracketDivisionAdditionSubtractionMultiplicationParentheses, etcFrom the information given;
Let the son's age be x
Let the father's age be x + y
x + x + y = 80
2x + y = 80
Then, 2x - y = 40
From equation (1), make 'y' the subject
y = 80 - 2x
Substitute the value
2x - (80 - 2x) = 40
2x - 80 + 2x = 40
collect like terms
4x = 120
x = 30
y = 80- 2(30)
y = 20
Hence, their ages are 30 years and 50 years
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Helpppppp pleaseeee thank you