The value of the functions are:
a. g(-4) + f(-2) = 24
b.. f(1) - g(0) = 1
What is a function?A function can be defined as an expression showing the relationship between two variables.
Given the functions;
f (x) = 3x - 1 g (x) = x² + 1g(-4); substitute the value of x as - 4 in g(x)
g(-4) = (-4)² + 1
g(-4) = 16 + 1
g(-4) = 17
f(-2); substitute the value of x as - 2 in f(x)
f(-2) = 3(-2) - 1
f(-2 = -7
a. g(-4) + f(-2) = 17 -(-7)
g(-4) + f(-2) = = 24
f(1) = 3(1) - 1
f(1) = 2
g(0) = (0)² + 1
g(0) = 1
b. f(1) - g(0) = 2 - 1
f(1) - g(0) = 1
Thus, the value of g(-4) + f(-2) and f(1) - g(0) are 24 and 1 respectively.
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a swimming pool is 20m wide and has a diagonal length of 52m. how much shorter is it than a 50m long pool?
-3x+29=17 would it be 3 , 4 5 6 7 8 9
Answer:
x=4
Step-by-step explanation:
[tex]-3x+29-29=17-29 < - Subtract[/tex]
[tex]-3x=-12[/tex]
[tex]\frac{-3x}{-3}=\frac{-12}{-3} < - Divide[/tex]
[tex]x=4[/tex]
Evaluate f(x) = -2x + 5 when x = 8
PLS ASAP AND TY IF U ANSWERED
Answer:
3.5 un
Step-by-step explanation:
to find the new length of the square using a scale factor of 1/7 you can just multiply 24.5 by 1/7
this is basically dividing 24.5 by 7
24.5 / 7 = 3.5
that is your answer
At a fish fry fundraiser, the math club raised $277.50. child plates were sold for $2.25 and adult plates were sold for $4.75. if there were twice as many child plates sold than adult plates, how many adult plates were sold?
The number of adult plates sold are 30.
It is given in the question that:-
Total money raised by math club = $277.50
Cost of a child plate = $2.25
Cost of an adult plate = $4.75
There are twice as many child plates sold than adult plates.
Let the number of adult plates be x.
Hence, according to the question,
Number of child plates = 2x
Using this data, we can form a linear equation,
2.25*2x + 4.75*x = 277.50
4.50x + 4.75x = 277.50
9.25x = 277.50
x = 277.50/9.25
x = 30
Hence, the number of adult plates sold are 30.
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Please help.
The diagram is placed on a coordinate plane in Quadrant 1, with the origin (0,0) at the intersection of North Street and Wilson Street.
Using linear function concepts, it is found that:
a) They intersect at (0,20).
b) They intersect at (14,0).
c) They intersect at (0,3).
d) The equation is: y = -10/7x + 20.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.The intersections are the points where they cross, hence:
North and Main: (0,20).Wilson and Main: (14,0).North and New: (0,3).Main Street goes through points (0,20) and (14,0), hence the intercept is of b = 20 and the slope is found as follows:
(0 - 20)/(14 - 0) = -10/7.
Hence the equation is:
y = -10/7x + 20.
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what is difference between fraction and rationals
Answer:
fraction is any number of the form a/b where both a,b are whole numbers
rational number is which is in the form of p/q where people q are integers.mark me brainlist thank you!
What is the perimeter of the triangle
The perimeter of the triangle is 40 units
Perimeter of a triangleFrom the question, we are to determine the perimeter of the given triangle
From the given diagram, we can observe that the triangle is a right triangle
The vertical length of the triangle is 15 units
and the horizontal length of the triangle is 8 units
Thus,
We can find the hypotenuse by using the Pythagorean theorem
Let the hypotenuse be h
Then,
h² = 15² + 8²
h² = 225 + 64
h² = 289
h = √289
h = 17 units
Now, for the perimeter of the triangle
The perimeter of a triangle is the sum of all its three sides
Thus,
The perimeter. P, of the triangle is
P = 15 + 8 + 17
P = 40 units
Hence, the perimeter of the triangle is 40 units
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answer this question
Answer:
[tex]g(x)=|x+8|-2[/tex]
Step-by-step explanation:
The vertex is at (-8, 2), so g(x)=a|x+8|+2.
Considering g(-6),
[tex]g(-6)=4=a|-6+8|+2 \\ \\ 2=2a \\ \\ a=1 \\ \\ \therefore g(x)=|x+8|-2[/tex]
The sequence below shows the number of raffle tickets that Samantha sold each day during a month.
3,7,11,15…
Which one explicit formula models the number of tickets Samantha sold on day x?
Answer:
C
Step-by-step explanation:
You are looking for the arithmetic sequence.
[tex]a_{n}[/tex] = [tex]a_{1}[/tex] + (n-1)d
In this case the formula is written:
t(x) = 3 + 4(x-1)
The 3 is the first term. The 4 is how much the sequence is increasing each time. (x-1) stands for the term we are looking for. If we were looking for the 15th term, we would have (15-1) in the parentheses.
Jamal loves his dog, Rupert. On sunny days, Jamal keeps Rupert on a 12-foot leash
in the backyard. He secures the leash to a stake in the ground.
> Answer each question and use 3.14 for T.
1 Determine the diameter, circumference, and area of Rupert's play area.
Diameter = 24 foot, circumference = 75.36 foot, Area = 452.16 square foot
As the leash is 12 feet, and dog Rupert will form a circle in the backyard.
As the leash is of 12 feet, so it is the radius(r) of the circle.
Diameter = 2r
= 2×12
= 24 foot
Circumference = 2πr
=2×3.14×12
= 75.36 foot
Area of the circle = π[tex]r^{2}[/tex]
= 3.14×[tex]12^{2}[/tex]
=3.14 × 144
= 452.16 [tex]foot^{2}[/tex]
Therefore we get diameter = 24foot, circumference = 75.36 foot and area = 452.16 square foot.
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Find the velocity, acceleration, and speed of a particle with the given position function. r(t) = t i t2 j 2 k
The velocity of a particle = i + 2t j
The acceleration of a particle = 2 j
The speed of a particle = [tex]\sqrt{1 + 4t^{2} }[/tex]
Here,
The position function is, [tex]r (t ) = ti + t^{2} j +2k[/tex]
We have to find, the velocity, acceleration, and speed of a particle with the given position function.
What is Velocity of a particle with the given position function?
The instantaneous velocity v(t) of a particle is the derivative of the position with respect to time. That is, v(t)=dx/dt.
Now,
The position function is, [tex]r (t ) = ti + t^{2} j +2k[/tex]
The velocity of a particle = [tex]\frac{d r(t)}{dt}[/tex]
[tex]r (t ) = ti + t^{2} j +2k[/tex]
[tex]\frac{d r(t)}{dt} = i + 2t j[/tex]
The acceleration of a particle = [tex]\frac{d^{2} r(t)}{dt^{2} }[/tex]
[tex]r (t ) = ti + t^{2} j +2k[/tex]
[tex]\frac{d r(t)}{dt} = i + 2t j[/tex]
[tex]\frac{d^{2} r(t)}{dt^{2} }= 2j[/tex]
The speed of a particle = [tex]| \frac{d r(t)}{dt}| = |v(t)|[/tex]
[tex]\frac{d r(t)}{dt} = i + 2t j[/tex]
[tex]|v(t)|=\sqrt{1 + 4t^{2} }[/tex]
Hence, The velocity of a particle = [tex]i + 2t j[/tex]
The acceleration of a particle = [tex]2 j[/tex]
The speed of a particle = [tex]\sqrt{1 + 4t^{2} }[/tex]
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Evan wants to leave an 18% tip for the server at a restaurant. Which expression does not show how to calculate the tip if b is the total bill?
Answer:
(b*.18)
Step-by-step explanation:
In terms of tips, 18% of $1.00 is $0.18. So for every dollar in the total (b) we can assume that it is going to be 18% of the overall total. 18% is 18/100 or .18, so we know the tip will be .18 of b (b*.18).
Answer:
7 major of system units defination and function
Translate the sentence into an equation.
Four times the sum of a number and 3 is 2.
Use the variable w for the unknown number.
letter j, i need help i don’t really understand it doesn’t explain good enough
Answer:
3/5 < 3/4 (The symbol you need is <.)
Step-by-step explanation:
The problem is asking you to compare the fractions 3/5 and 3/4. You need to supply a comparison symbol, one of {<, =, >}.
Comparing valuesIn general, when you are asked to compare two values, you are being asked which one is greater (or smaller). Sometimes, you are being asked for the amount by which one is greater than the other (their difference), and sometimes you are being asked for the factor by which one is greater than the other (their ratio).
You can do the arithmetic to find the appropriate difference or ratio, or you can use your number sense to identify the larger (or smaller) number.
FractionsAs you know, the denominator of a fraction tells you how many pieces the pie has been divided into.
In the fraction 3/5, the 5 tells you each piece is 1/5 of the whole, that there are 5 equal pieces.
In the fraction 3/4, the 4 tells you each piece is 1/4 of the whole, that there are 4 equal pieces.
A pie divided into 5 pieces instead of 4 has smaller pieces. That is ...
1/5 < 1/4
When there are 3 pieces of each, this relation still holds:
3×(1/5) < 3×(1/4) ⇒ 3/5 < 3/4
__
Additional comment
Here, the numerators are the same, so we only need to compare the denominators to find the relationship. If the denominators are the same, we can compare the numerators.
If neither is the same, it is often useful to multiply one or the other or both of the fractions by some value so they will have a common numerator or denominator. The usual recommendation is to give the fractions a common denominator.
Here, the denominators can be made to be 20 in each case.
[tex]\dfrac{3}{5}=\dfrac{3}{5}\cdot\dfrac{4}{4}=\dfrac{12}{20}\\\\\dfrac{3}{4}=\dfrac{3}{4}\cdot\dfrac{5}{5}=\dfrac{15}{20}[/tex]
The denominators are now the same, so we can compare values by comparing the numerators. 12 < 15, so 12/20 < 15/20 and 3/5 < 3/4.
The measure of two supplementary angles, ls and lt, are in the ratio of 7:3. find the value of mls.
The value of measure of ls is 126 degrees.
It is given in the question that the measure of two supplementary angles, ls and lt, are in the ratio of 7:3.
We have to find the value of measure of ls.
Let the measure of two supplementary angles ls and lt be 7x and 3x respectively.
We know that, the sum of measure of two supplementary angles is 180 degrees.
Hence, according to the data given in the question, we can write,
7x + 3x = 180 degrees
10x = 180
x = 180/10
x = 18 degrees
Hence,
mls = 7x = 7*18 = 126 degrees.
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f(-6)=3(3-2x). What is the evaluating function?
Step-by-step explanation:
or,(-6)=3(3-2x)
or,(-6)=9-6x
or,-6-9=-6x
or,-15=-6x
or,-15+6=x
or,-9=x
x=-9
Ronald wants to rent a car to take a trip and has a budget of $60. there is a fixed rental fee of $25 and a daily fee of $5. write an inequality that would be used to solve for the maximum number of days for which ronald can rent the car on his budget. 25 5x ≤ 60 25 5x ≥ 60 25x 5 ≤ 60 25x 5 ≥ 60
Answer:
60>x>25
Step-by-step explanation:
Ms. Jordan bought a box of 32 granola bars. Every day each of her three children ate one granola bar for lunch. Now there are only 11 bars left. Which equation can be used to find the number of days, n, that the children ate the bars for lunch? 32 = -11 32 = 3n - 11 32 = +11 O 32 3n+ 11
The calculation for calculating the number of days the youngsters ate the bars for lunch is 11 = 32 - 3x.
What exactly does it mean to "solve an equation"?An equation is a mathematical expression that represents the equivalence of two or more mathematical expressions.
When someone asks you to solve an equation, they typically want to determine the unknown values for which the equation is true (the equality between expressions should hold true for those values).
An equation's solutions are the values of the variables involved in the equation for which the equation holds true.
Given that Ms Jordan purchases a box of 32 granola bars every day, each of her three children consumes one granola bar for lunch, there are only 11 bars remaining.
The algorithm for calculating the number of days the youngsters ate the bars for lunch;
11 = 32 - 3x
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When a three-digit number written in base 10 has its final digit moved to the beginning, the result is the same number written in base 7. find all such numbers
There is no such number that has the result is the same number written in base 7 and base 10.
Decimal and Octal numbers:
Decimal system is most familiar number system to the general public. It is base 10 which has only 10 symbols − 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.
Whereas octal system is one of the number systems to represent numbers. It is base 8 which has only 8 symbols − 0, 1, 2, 3, 4, 5, 6, and 7.
Given,
When a three-digit number written in base 10 has its final digit moved to the beginning, the result is the same number written in base 7.
Here we need to find all such numbers.
Let abc be the starting number, where the catenated letters represent digits, and not factors like in the product
=> a x b x c
And each of a,b, and c can be elements of the list,
=> {1,2,3,4,5,6,7,8,9,0}
Except a≠0.
Since abc is a base-10 numeral, we can also write it as
=> 10²a + 10¹b + 10⁰c
Which can be expanded as,
=> 100a + 10b + c ----------------------(1)
Moving the last digits to the first slot makes the new number,
=> 100c + 10a + b------------------------(2)
So, here the value c≠0.
We know that, the digits in the base-10 numeral cab are identical to those of the base-7 numeral that is written as cab₇.
In the equation form it is equal to,
=> 7²c + 7¹a + 7⁰b
=> 49c + 7a + b ---------------------(3)
but since we're working in base 7 now, the digits a,b, and c cannot exceed 6.
Now, we want to solve for a, b, and c such that
By equalizing the equations 2 and 3,
=> 100c + 10a + b = 49c + 7a + b
=> 100c + 10a + b - 49c - 7a - b
=> (100 - 49)c + (10 - 7)a
=> 51c + 3a
=> 3 (17c + a)
Both a and c must be positive, but this equation has solution,
=> a = -17c
So there are no positive integers solutions, and hence no such number.
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If f(x) = 2x + 1 and h(x) = 3x - 5, find f(h(2)).
Answer:
f(h(2)) = 3.
Step-by-step explanation:
Replace the x in f(x) by h(2).
h(2) = 3(2) - 5
= 1,
so, f(h2) = 2(1) + 1
= 3.
round the following numbers to the nearest ten thousands: 1. 57,342 2. 76,564 3. 95,634 4. 85,756 5. 63,526
Answer:
1. 60,000
2. 80,000
3. 100,000
4. 90,000
5. 60,000
Step-by-step explanation:
Remember if the thousands digit is 5 or greater, round up, if the thousands digit is 4 or less, round down.
57342 (up) 76564 (up) 95634 (up) 85756 (up) 63526 (down)
which of the following is equivalent to 5x-x+3x=30
In linear equation , 7x=30 is equivalent to 5x-x+3x=30.
What in mathematics is a linear equation?
A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."A linear equation with one variable is one that contains just one variable. It has the formula Ax + B = 0, with A and B being any two real numbers and x being an ambiguous variable with only one possible value. One such linear equation in one variable is 9x + 78 = 18.5x -x + 3x =30, first you combine like terms 5x + 3x-x=30
8x-x =30
7x=30
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∠A and \angle B∠B are complementary angles. If m\angle A=(x-19)^{\circ}∠A=(x−19) ∘ and m\angle B=(3x+1)^{\circ}∠B=(3x+1) ∘ , then find the measure of \angle B∠B.
Answer:
∠ B = 82°
Step-by-step explanation:
complementary angles sum to 90° , then
∠ A + ∠ B = 90 , that is
x - 19 + 3x + 1 = 90
4x - 18 = 90 ( add 18 to both sides )
4x = 108 ( divide both sides by 4 )
x = 27
Then
∠ B = 3x + 1 = 3(27) + 1 = 81 + 1 = 82°
What is the equation in slope-intercept form of the line that passes through the points (12, -34) and (10, -28)?
Answer:
[tex]y=-2x+2[/tex]
Step-by-step explanation:
1) Determine Slope
[tex]\frac{y_2-y_1}{x_2-x1}[/tex] = [tex]\frac{-28-(-34)}{10-12}[/tex] = [tex]\frac{6}{-2}[/tex] = -3
2) Use point slope form to create equation
[tex]y-y_1=m(x-x_1)[/tex]
[tex]y-(-28)=-3(x-10)[/tex]
[tex]y+28=-2x+30[/tex]
[tex]y=-2x+2[/tex]
Help, Theres a time limit!
Answer:
The answer is 2.72 * 10^8 sec.
Step-by-step explanation:
Distance between Earth and Sirius is 5.062 * 10^13 miles.
Time taken = Distance travelled/speed
5.062*10^13 miles/sec/1.86*10^5 miles.
=2.72 * 10^8 sec.
So this means that the time taken to travel light from Sirius to Earth is 2.72*10^8.
The sum of 4 consecutive odd integers is -24. What are they?
Step-by-step explanation:
4 consecutive odd integers means we start with x, then have x+2, x+4 and then x+6.
and then we have
-24 = x + x+2 + x+4 + x+6 = 4x + 12
4x = -36
x = -9
x+2 = -7
x+4 = -5
x+6 = -3
so, in sequence from small to large these 4 numbers are
-9, -7, -5, -3
Create a very long sentence with at least four phrases using only three propositions. identify the propositions and create logic sentences.
(q ∨ (¬r ∧ ¬q)) → ¬p is the propositions and create logic sentences.
What is propositions ?
An axiom is a mathematical assertion that is predicated on a proposition, such as "3 is greater than 4," "an infinite set exists," or "7 is prime."
If you are more than 18 years old or if you are above 18 but lack identification proving your age, you are not permitted to to watch cartoon.
Prepositions -
p = You are allowed to watch cartoon.
q = your age is more than 18 years old
r = you have age proof
(q ∨ (¬r ∧ ¬q)) → ¬p
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what is the estimate of 3,182x5
Step-by-step explanation:
15,910 like what said of calculator
What is 7 greater than 15 multiplied by 2?
After solving we get that 7 greater than 15 multiplied by 2 is indeed 37.
Follow the PEMDAS/BODMAS (Parentheses/Brackets, Exponents/Orders, Multiplication and Division, Addition and Subtraction) sequence of operations to solve this problem:
1. Begin by performing a multiplication operation: 2 times 15 results in 30.
2. To get the answer to the multiplication, add 7: 30 + 7 = 37.
Therefore, multiplying 7 by 2 and adding 15 is equivalent to 37.
The steps are broken down as follows:
Step 1: 15 × 2 = 30
Step 2: 30 + 7 = 37
The answer is 37 since 7 is more than 15 when multiplied by 2.
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