A function assigns the value of each element of one set to the other specific element of another set. The correct option is D.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
Given that a function, h, has a domain of -3 ≤ x ≤ 11 and a range of 1 ≤ h(x) ≤ 25 and that h(8) = 19 and h(-2) = 2.
1.) h(8) = 21
Since the value of h(8) is 19. This can not be the correct option.
2.) h(-3) = -1
Since the range is from 1 to 25. Therefore, this is not the correct option.
3.) h(13) = 18
Since the domain is from -3 to 11. Therefore, this is not the correct option.
4.) h(2) = 16
This is the only option that is feasible. Thus, this is the correct option.
Hence, the correct option is D.
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A tub of water is emptied at a rate of 3 gallons per minute. The equation y –12 = –3(x – 1) models the amount of water remaining, where x is time (in minutes) and y is the amount of water left (in gallons). Analyze the work shown below to determine the initial amount of water. 1. Solve for the y-variable. y – 12 = –3(x – 1) y – 12 = –3x + 3 y = –3x +15 2. Write the equation using function notation. f(x) = –3x +15 The tub started with gallons of water.
The equation in the function form is f(x) = -3x + 15 and the tub started with 15 gallons of water.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have an equation:
y –12 = –3(x – 1)
We can write the above equation as follows:
y = 12 - 3(x - 1)
y = 12 - 3x + 3
y = -3x + 15
or
f(x) = -3x + 15
Plug x = 0
f(0) = 15
The tub started with 15 gallons of water.
Thus, the equation in the function form is f(x) = -3x + 15 and the tub started with 15 gallons of water.
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I need the answer to this question
Answer:
See attached image.
Step-by-step explanation:
In an Italian class, 65 percent of the students were women. At the end of the class, 52 percent of the men and 44 percent of the women received a certificate. What percentage of those who received a certificate were men
47% of those who received a certificate were men
It is given that in an Italian class, 65 percent of the students were women. At the end of the class, 52 percent of the men and 44 percent of the women received a certificate.
Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty.
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What is the following product?
(√14-√3)(√12+√7)
O 2√√42+7√√2-6-√√21
O√√14-6+√√7
O√26+ √21-√15-/10
O2√42-√√21
Answer: [tex]3\sqrt{21}+7\sqrt{2}-6[/tex]
Step-by-step explanation:
[tex](\sqrt{14}-\sqrt{3})(\sqrt{12}+\sqrt{7})\\\\=(\sqrt{2}\sqrt{7}-\sqrt{3})(2\sqrt{3}+\sqrt{7})\\\\=4\sqrt{21}+7\sqrt{2}-6-\sqrt{21}\\\\=\boxed{3\sqrt{21}+7\sqrt{2}-6}[/tex]
The product on the equation is A = 2√42 - 6 + 7√2 - √21
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
A = ( √14 - √3 ) ( √12 + √7 )
On simplifying , we get
A = √14 ( √12 ) - √3 ( √12 ) + √14 ( √7 ) - √3 ( √7 )
A = √168 - √36 + √98 - √21
On further simplification , we get
A = 2√42 - 6 + 7√2 - √21
Therefore , the value of A is 2√42 - 6 + 7√2 - √21
Hence , the product is A = 2√42 - 6 + 7√2 - √21
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Terms:
Length of lease = 48 months
• MSRP of the car = $32,100
Purchase value of the car after lease = $26,200
Down payment = $4400
Monthly payment = $450
$435 security deposit
$530 acquisition fee.
●
The total cash that's due at signing will be $5365.
How to calculate the cash?It should be noted that security deposit on acquisition are paid at the begining.
The total cash that's due at signing:
= Down payment + Security deposit + Acquisition fee
= 4400 + 435 + 530
= $5365
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Tina baked a batch of 40 cupcakes. daisy baked 4/5 as many cupcakes as tina. miko baked 1/2 as many cupcakes as daisy. how many cupcakes did the 3 girls bake altogether?
The three girls baked 88 cupcakes altogether.
Cupcakes Baked by Each
Number of cupcakes baked by Tina, T = 40
It is given that Daisy baked 4/5 as many cupcakes as Tina.
Therefore, number of cupcakes baked by Daisy, D = (4T/5) (Applying fractions)
⇒ D = (4/5)×40
⇒ D = 4 × 8
⇒ D = 32
Also, it is given that Miko baked 1/2 as many cupcakes as Daisy.
Thus, number of cupcakes baked by Miko, M = D/2 (Applying fractions)
⇒ M = 32/2
⇒ M = 16
Calculating Total Number of Cupcakes Baked
Cupcakes baked by the three girls altogether = T + D + M
= 40 + 32 + 16
= 88
Hence, the girls together baked 88 cupcakes.
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What is the equation of the line parallel to 3x + 2y = -4 that goes through the point (4, -1)?
y =
2x+4
y =
2³x + 5
y =
¾x + 5
Oy = =
x +5
=
Answer:
y = - [tex]\frac{3}{2}[/tex] x + 5
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
given
3x + 2y = - 4 ( subtract 3x from both sides )
2y = - 3x - 4 ( divide terms by 2 )
y = - [tex]\frac{3}{2}[/tex] x - 2 ← in slope- intercept form
with slope m = - [tex]\frac{3}{2}[/tex]
• Parallel lines have equal slopes , then
y = - [tex]\frac{3}{2}[/tex] x + c ← is the partial equation
to find c substitute (4, - 1 ) into the partial equation
- 1 = - 6 + c ⇒ c = - 1 + 6 = 5
y = - [tex]\frac{3}{2}[/tex] x + 5 ← equation of parallel line
Solve. Set up the Table.
$2,000 at 2.50% for 50 years.
$2,000 at 5.00% for 50 years.
Answer:
can you explain more i dont get what u mean if you mean 2,000 a year and you get 2.50% or 5.00% and you get it for 50 years your answer for each would be 50 and 100
Use the grouping method to factor the polynomial below completely.
x3-5x2+3x-15
A. (x²+5)(x-3)
B. (x² - 3)(x + 5)
O C. (x² - 5)(x+3)
D. (x²+3)(x - 5)
The factored expression of x^3 - 5x^2 + 3x - 15 is (x^2 + 3)(x- 5)
How to factor the polynomial?The polynomial is given as:
x^3 - 5x^2 + 3x - 15
Group the terms
(x^3 - 5x^2) + (3x - 15)
Factorize each group
x^2(x - 5) + 3(x - 5)
Factor out x - 5
(x^2 + 3)(x- 5)
Hence, the factored expression of x^3 - 5x^2 + 3x - 15 is (x^2 + 3)(x- 5)
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A quadratic polynomial with real coefficients and leading coefficient is called if the equation is satisfied by exactly three real numbers. Among all the disrespectful quadratic polynomials, there is a unique such polynomial for which the sum of the roots is maximized. What is
p(1) = 1
Let p(x) = x2 + bx = c
then, p(p(x)) = (x2 + bx + c)² + b(x2 + bx + c) + c
Sum of roots of p(p(x)) is given by = - (coefficient of x3/constant term)
= -2b/c2+bc+c = f(a,b) (say)
For critical points,
∂f/∂c = 0 and ∂f/∂b = 0
= 2b(2c+b+1)/c2+bc+c = 0 and - {( c2+bc+c)²- 2b (c)/ ( c2+bc+c)²}= 0
= b(2c+b+1) =0
= b= 0 or b= - (1+2c) = -(2c(c+1))/c2+bc+c = 0
If c=0 , b= -1 => c= 0 or c=-1
If c = -1 ,b = 1
thus we have the following possibility for (b,c)
(0,0) , (0,-1) , (-1,0) ,(1,-1).
At (0,0) f(0,0) = not defined
(0,-1) f(0,-1) = 0
(1,-1) f(1,-1) = 2
(-1,0) is not possible.
p(x) = (x2 +x-1)² + (x2 +x-1) -1
= p(1) = (1+1-1)² + (1+1-1) -1
= 1
Hence, p(1) = 1
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pythagoras theorem application
Answer:
A squared plus B squared equal C squared
Step-by-step explanation:
Determine the seating capacity of an auditorium with 34 rows of seats if there are 16 seats in the first row, 20 seats in the second row, 24 seats in the third row, and so on.
Answer:
2788.
Step-by-step explanation:
This is represented by an arithmetic series with first term 16 and common difference 4.
The number of rows n = 34.
The capacity
= sum of 34 terms
= (34/2)[2*16 + 4(34-1)]
= 2788.
Answer:
2788
Step-by-step explanation:
16,20,24,.. This is a arithmetic progression with common difference of 4
Sn=? , d=4 , a =16 , n=34[tex]Sn=\frac{34}{2}[2(16)+(34-1)4] \\\\Sn=17[32+33(4)]\\\\Sn=17[164]\\\\Sn=2788[/tex]
whats the distance between -3 and -12
Answer:
9
Step-by-step explanation:
We can just count from -3 to -12 and get 9 as the distance
which expression is a sum of cubes?
Answer:
Step-by-step explanation:
A more complicated expression such as 64x3+27y3 64 x 3 + 27 y 3 is also a sum of cubes since 64x3=(4x)3 64 x 3 = ( 4 x ) 3 and 27y3=(3y)3 27 y 3 = ( 3 y ) 3 . Please note, that expressions such as 2x3 2 x 3 are not perfect cubes.
Currently, Netflix has 93 000 subscribers. Netflix subscriptions are decreasing by 2.2% per day. How many subscribers are there after 5 days?
There are 83210 subscribers after 5 days
How to determine the number of subscribers?The given parameters are:
Initial, a = 93000Rate, r = 2.2%The number of subscribers each day is calculated as:
f(n) = a * (1-r)^n
This gives
f(n) = 93000 * (1 - 2.2%)^n
Evaluate the difference
f(n) = 93000 * 0.978^n
At 5 days, we have:
f(5) = 93000 * 0.978^5
Evaluate
f(5) = 83210
Hence, there are 83210 subscribers after 5 days
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Which table represents a proportional relationship?
how do u not know this
Step-by-step explanation:
my guy
3 metres of material cost £1.56
Work out the cost of 5 metres of the same material.
Answer:
2.6
Step-by-step explanation:
1.56 ÷3 = 0.52 ( cost of 1 meter of material )5 × 0.52 = 2.6 ( cost of 5 meter of material )If one dozen bananas cost is Rs.30 how many dozens can be purchased for 2,67,003 Rs
Answer:
67
Step-by-step explanation:
sorry if wrong
help me please eeeeeeeeee
Answer:
A
Step-by-step explanation:
Fundamental Theorem of Algebra:
This states that any polynomial with degree n will have n solutions which are real or complex.
Since this function you gave has 4 zeroes, this function has to have at at least a degree of 4. The reason I say at least, is because of something called multiplicity. When a zero has an even multiplicity it will have a turning point at the zero, if it has an odd multiplicity it will pass the x-axis. So assuming each zero only has a multiplicity of 1, then this will have at least a degree of 4. It also might have complex zeroes which still count as zeroes.
End Behavior of Polynomial Functions:
So this is pretty easy to remember, but if the leading coefficient is positive, then the end behavior to the right will go up, if it's negative it will go down. Now the next thing to know is an odd degree means that the end behavior will go in opposite directions. So if the right goes up, then the left side will be going down and vice verse. if it's an even degree then the two opposite sides will go in the same direction.
In this case both ends are going down, in the same direction. This means that the leading coefficient is negative and the degree is even.
Using these two things, we can exclude answers
B can't be the answer, it only has 3 zeroes, this has at least 4.
C can't be the answer, it has an odd degree so the end behaviors would go in opposite directions
D can't be the answer, it has a positive leading coefficient so the right side would be going up
This means the only possible equation is A which has at least a degree of 4, negative leading coefficient, and even degree.
HELP ASAP!!!
When the polynomial 2x^3 + mx^2 + nx – 2 is divided by x – 3, the remainder is 4. When
divided by x – 2, the remainder is 2. What are the values of m and n?
The values of m and n are -29/3 and 40/3 respectively
Factor and remainder theoremA polynomial is a function that has a leading degree of 2 and greater. Given the polynomial
P(x) = 2x^3 + mx^2 + nx – 2
If it is divided by x – 3, the remainder is 4 and divided by x – 2, the remainder is 2, hence;
4 = 2(3)^3 + 9m + 3n - 2
4 = 54 + 9m + 3n - 3
9m + 3n = -47
Similarly
2 = 2(2)^3 + 4m + 2n - 2
4m + 2n = -12
Solve simultaneously
9m + 3n = -47 * 2
4m + 2n = -12 * 3
______________
18m + 6n = -94
12m + 6n = -36
Subtract
6m = -58
m = -58/6 = -29/3
For the value of n
4m + 2n = -12
2m + n = -6
2(-29/3) + n = -6
n = -6 + 58/3
n = 40/3
Hence the values of m and n are -29/3 and 40/3 respectively
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14.
the function y=-16t^2+ 50t +4 describes the height (in feet) of a discus t seconds after it is released. describe the domain and range of the function. find the maximum height of the discus.
The domain is t=0 to t=3.2 and range is y = 0 to 57.125 feet.
What are Domain and range of a Function?
The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values. The y values are those.A function can be compared to a piece of equipment on an assembly line. A few screws and nuts are located on one end of the assembly line, while a car is located on the other. The function is the device in the center. The domain is the screws and bolts that we insert into the machine. The car at the other can be thought of as the range.Given function is : y = -16t^2 + 50t + 4
It hits the ground when y=0
0 = -16t^2 + 50t + 4
8t^2 -25t -2 = 0
t = 25/16 + (1/16)sqrt(625+64) = (25+26.25)/16 = 51.25/16 = 3.2 seconds
domain is t=0 to t=3.2 [3.2]
take the derivative and set it equal to zero to find maximum height
-32t +50 = 0
t = 50/32 = 25/16 = 1.5625 seconds
-16(25/16) + 50(25/16) + 4 = 34(25/16) + 64/16 = (17(25)+32)/8 = 57.125 = maximum height
range is y = 0 to 57.125 feet. the discus goes from 4 feet to 57 1/8 feet and back down to 0 feet.
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Convert from Decimal Notation to Scientific Notation
In the following exercises, write each number in scientific notation.
553. 1,290,000
Answer:
Hence, 12,90,000 can be expressed as [tex]$1.29 \times 10^{6}$[/tex].
Step-by-step explanation:
- Given 12,90,000
- Use given, move the decimal point so that first factor is greater than or equal to 1 but less than 10 .
- Then count n and write in scientific notation.
Step 1 of 1
Consider 12,90,000
1.29
So, 1.29 lies between 1 & 10.
Now, Decimal moved to 6 places at left.
[tex]$1.29 \times 10^{6}$[/tex]
So, [tex]$12,90,000=1 \cdot 29 \times 10^{6}$[/tex].
What are the exact solutions of x2 − 5x − 7 = 0, where x equals negative b plus or minus the square root of b squared minus 4 times a times c all over 2 times a? (1 point)
x = the quantity of negative 5 plus or minus the square root of 3 all over 2
x = the quantity of 5 plus or minus the square root of 3 all over 2
x = the quantity of negative 5 plus or minus the square root of 53 all over 2
x = the quantity of 5 plus or minus the square root of 53 all over 2
Answer: [tex]x=\frac{5 \pm \sqrt{53}}{2}[/tex]
Step-by-step explanation:
[tex]x^2 - 5x-7=0\\\\x=\frac{-(-5) \pm \sqrt{(-5)^2 - 4(1)(-7)}}{2(1)}\\\\x=\frac{5 \pm \sqrt{53}}{2}[/tex]
if one-sixth of a number is 1 1/3, find the number.
Answer:
8
Step-by-step explanation:
Since one-sixth was multiplyed be 1 1/3, we just have to find the opposite, six-ones. We multiply that by 1 1/3 and we get 8!
Can someone help please?
Triangle not drawn to scale
Given: m&A= 62°,m&C=28°,c=24cm. Then a
_?__cm to the nearest hundredth.
Answer:
a = 45.14
Step-by-step explanation:
First we need to determine whether this is a non-right triangle or a right triangle.
Since we have two angles already, we can determine whether the third angle is a right or non-right angle:
The sum of all the angles in a triangle will always add up to 180, so we have
180 - (62 + 28) = 180 - 90 = 90
Since we have a right triangle and only one side, we can use trigonometry to find the measure of a.
If we use ∠A as the reference angle, side a is our opposite angle and side c is our adjacent angle.
This means we must use tangent as [tex]tan=\frac{opposite}{adjacent}[/tex]:
[tex]tan (62)=\frac{a}{24}\\ 24*tan(62)=a\\45.137=45.14 = a[/tex]
Select the correct answer from each drop-down menu.
Consider triangles ABC and QPRshown.
Triangle ABC is
triangles are
B
triangle QPR. Since the transformations
Reset
Next
, the
Triangle ABC is similar to triangle QPR due to the transformations reflection, the triangles are similar by side-angle-side similarity theorem.
How to Identify similar triangles?Transformations are changes done in the shapes on a coordinate plane by rotation, reflection or translation.
- Rotation means that it rotates or turns the pre-image around an axis with no change in size or shape
- Reflection means that it flips the pre-image and produces the mirror-image with no change in size or shape or orientation
- Translation means that it slides or moves the pre-image with no change in size or shape but has changes in only the direction of the shape
- Dilation means that it stretches or shrinks the pre-image.
Two triangles are said to be similar if they have the same shape and the ratio of their corresponding sides are in the same proportion. It should be noted that, corresponding angles are congruent.
Thus, we conclude that triangle ABC and triangle QPR are similar triangle based on the side-angle-side similarity theorem.
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Answer: reflected and then translated onto only involve rigid motions
congruent
Step-by-step explanation:
Triangle abc
is
reflected and then translated onto
triangle qpr
. Since the transformations
only involve rigid motions
, the triangles are
congruent
.
Brainliest + 25, Urgent
For all values of x, there is a function h such that 4h(x) = h(4x). What is the value of h(6) if h(24) = 20 ?
Ty!
The value of h(6) = 5
What is a Function ?A function is a mathematical statement used to relate two variables .
It is given that
4h(x) = h(4x)
It is also given that
h(24) = 20
now to determine the value of h(6)
4* h(6) = h(6 *4)
4* h(6) = h(24)
4 * h(6) = 20
h(6) = 5
Therefore the value of h(6) = 5.
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In the equation y=kx, where k is a constant. when y=12, then x=5. when y=60, what does x equal?
Answer:
If y = 60 then x = 25
Step-by-step explanation:
You know that when y = 12 then x = 5
So when y = 60, x = 25
The reason for this is because 12 * 5 = 60.
Which means that since the y = 12 was multiplied by 5, the x = 5 should be multiplied by 5 too.
Since 5 * 5 = 25, then we know that if y = 60, then x will equal 25.
Hope this helped! :D
look at image.............
Answer:
answer is -3 ....is this correct
Jack and Diane are jogging back and forth along a one-mile path.They started out at 9:00 am from opposite ends of the path.they passed each other in 10 minutes when Diane has gone 1/3 mile.what time will they first meet at one end of the path?you have to assume they keep jogging at the same speed.
Answer:
Step-by-step explanation:
30 minutes
Step-by-step explanation:
that problem description is imprecise.
I think what is meant here : they each keep jogging at their own same speed.
Diane’s speed is 1/3 miles / 10 min.
Jack’s speed is 2/3 miles / 10 min.
now, to bring this to regular miles/hour format, we need to find the factor between 10 minutes and an hour (60 minutes) and multiply numerator and denominator (top and bottom of the ratio) by it.
60/10 = 6.
so, we need to multiply both speeds up there by 6/6 to get the miles/hour speeds.
Diane : (1/3 × 6) / hour = 2 miles / hour
Jack : (2/3 × 6) / hour = 4 miles / hour
since Jack is running twice as fast as Diane, she will finish one length in the same time he finishes a round trip (back and forth).
Diane running 1 mile going 2 miles/hour takes her 30 minutes.
Jack running 2 miles (back and forth) going 4 miles/hour will take him also 30 minutes.
so, they will meet at his starting point after 30 minutes.