Practice Question:
f(x)= 3x^2 + 4x - 6
g(x)= 6x^3 - 5x^2 - 2
Find (f + g)(x)
Answer Options (Choose one):
A. (f+g)(x) = -6x^3 + 8x^2 + 4x -4
B. (f+g)(x) = 6x^3 + 3x^2 - x - 8
C. (f+g)(x)= 6x^3 - 2x^2 + 4x - 8
D. (f+g)(x)= 9x^3 - x - 8
The correct option of the function is C. (f+g)(x)= 6x^3 - 2x^2 + 4x - 8.
What is a function?The function is a type of relation, or rule, that maps one input to specific single output.
Given;
f(x)= 3x^2 + 4x - 6
g(x)= 6x^3 - 5x^2 - 2
So,
(f + g)(x) = (3x^2 + 4x - 6) + (6x^3 - 5x^2 -2)
(f + g)(x) = 3x^2 + 4x - 6 + 6x^3 - 5x^2 - 2
Now, like terms and in order of exponent
(f + g)(x) = 6x^3 - 2x^2 + 4x - 8
Therefore, the correct option is C. (f+g)(x)= 6x^3 - 2x^2 + 4x - 8.
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What is the relationship between \blueD{\angle a}∠astart color #11accd, angle, a, end color #11accd and \greenD{\angle b}∠bstart color #1fab54, angle, b, end color #1fab54?
Answer:
C
Step-by-step explanation:
supplementary because it adds to 180
Answer:C
Step-by-step explanation:
khan
{x + 8y = -16
{x-3y = -5
Answer: y= -1 and x=-8
x+8y=-16
x=-8y-16
so x-3y=-5
-8-16-3y=-5
-11y-16=-5
-11y=-5+16
-11y=11
y=-1
x-3y=-5
x+3=-5
x=-8
Solve 2( 32x-5) -4 =11
PLS When You Answer Type In The Number Of The Question With The Answer
The solution has a positive answer (True).
What is the solution to the arithmetic operators and fractions?
Arithmetic operators are those signs such as addition, subtraction, multiplication, and division that are used to solve mathematical expressions such as fractions and linear equations.
1.
The solution to the expression:
= (-1)(1)(-1)(-1)(1)(-1)(-1)(-1)(-1)(1)(-1)(1)
= 1
Thus, the solution has a positive answer(True)
2.
The solution to the improper fraction:
[tex]\mathbf{\dfrac{5}{7}+(-\dfrac{2}{7})= \dfrac{3}{7} }[/tex]
3.
= -52.31 -(-7.44)
= -52.31 + 7.44
= -44.87
= - 4487/100
4.
The solution to the improper fraction is:
[tex]\mathbf{\dfrac{3}{5}\div -\dfrac{6}{15}=-\dfrac{3}{2} }[/tex]
5.
The given equation is:
-(-6.6) (-20) = 132 which is incorrect.
The correct solution is:
-(-6.6) (-20) = -132
Eric's mistake is that he forgot to multiply by -1 first.
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Three friends go to a store to rent games and movies. Calvin rents 3 movies and 2 video games and spends a total of $25. Samantha rents 2 movies and 1 video game and spends a total of $14.75.
If the rental fee for each game is the same and the rental fee for each movie is the same, determine how much their friend, Keith, will spend at the rental store to rent 1 movie and 2 video games. Explain your answer.
The Keith will spend $16 to rent 1 movie and 2 video games from the store.
How to solve the equation of two variable?Let's assume the rental fee for each movie is "m" and the rental fee for each game is "g".
From the given information, we can form the following system of equations:
3m + 2g = 25 (Calvin's rental)
2m + g = 14.75 (Samantha's rental)
We can solve for "m" and "g" by using elimination or substitution method. Here, we will use substitution method.
From the second equation, we can solve for "g" in terms of "m":
g = 14.75 - 2m
Substituting this into the first equation, we get:
3m + 2(14.75 - 2m) = 25
Simplifying this, we get:
3m + 29.5 - 4m = 25
-m + 29.5 = 25
-m = -4.5
m = 4.5
Now that we know the rental fee for each movie is $4.50, we can find the rental fee for each game by substituting "m" into either of the original equations:
2(4.5) + g = 14.75
g = 14.75 - 9 = 5.75
So the rental fee for each game is $5.75.
To find how much Keith will spend to rent 1 movie and 2 video games, we can simply add up the rental fees:
1(4.5) + 2(5.75) = 16
Therefore, Keith will spend $16 to rent 1 movie and 2 video games from the store.
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what is the angle between a=7i+3j and b=4i-j
[tex]a\cdot b=(7)(4)+(3)(-1)=25\\\\|a|=\sqrt{7^{2}+3^{2}}=\sqrt{58}\\\\|b|=\sqrt{4^{2}+(-1)^{2}}=\sqrt{17}\\\\\cos \theta=\frac{25}{\sqrt{58}\sqrt{17}}\\\\\theta=\cos^{-1} \left(\frac{25}{\sqrt{58}\sqrt{17}} \right) \approx 37.235^{\circ}[/tex]
Can you solve this question and explain it for me? Thank you
By direct observation on the graph and concept of relative minimum, we conclude that the relative minimum of the graph is contained by the point (x, y) = (3, - 17).
How to determine the relative minimum of a given graph
Let be f a function that exists in a interval [a, b], there is a value c such that f(c) < f(x), for x ≠ c and x ∈ [a, b]. In this case, f(c) is the relative minimum of f. By direct observation, we find that the relative minimum of the graph is contained by the point (x, y) = (3, - 17).
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The circumference of a circle is 19 ft.
What is the area, in square feet? Express
your answer in terms of T.
Answer:
The area is approximately 28.73ft²
Step-by-step explanation:
Given: Circumference = 19 ft
The necessary formula area,
Area: A = πr²
Circumference: C = 2πr
Combine:
A = [tex]\frac{C^{2} }{4\pi }[/tex]
A = [tex]\frac{19^{2} }{4\pi } \\\\ \frac{361 }{4\pi }[/tex]
A = 28.72747
What is the aquare root of 0.00053361
Step-by-step explanation:
no calculator ? or what is the problem ?
I had to use the calculator too.
so, the square root of 0.00053361 is 0.0231.
Please Someone help with this !!!
Answer:
[tex]45[/tex]
Step-by-step explanation:
[tex]\tan 45^{\circ} = \dfrac{\sin 45^{\circ}}{ \cos 45^{\circ} }\\\\\\~~~~~~~~~~=\dfrac{\sin 45^{\circ}}{\sin\left(90^{\circ} - 45^{\circ} \right)}\\\\\\~~~~~~~~~~=\dfrac{\sin 45^{\circ}}{\sin 45^{\circ}}\\\\\\~~~~~~~~~~=1[/tex]
how to solved theses question (4.2×7)-10.4÷2²+2.9×3-6 explain
Answer:
29.5
Step-by-step explanation:
Use PEDMAS
P - Paraenthesis
E -Exponents
D - Divsion
M - Multiplication
A and S - Addition and subtraction respectively.
First multiply 4.2 and 7 as they are inside the parenthesis
Then find 2² which 4
(4.2 *7) - 10.4 *2² + 2.9*3 - 6 = 29.4 - 10.4 ÷2² + 2.9*3 - 6 {Parenthesis}
= 29.4 - 10.4÷4 + 2.9*3 - 6 {Exponents}
= 29.4 - 2.6 + 2.9*3 - 6 {Division}
= 29.4 - 2.6 + 8.7 - 6 {Multiplication}
= 29.5
Six girls and four boys have entered the science fair. first, second, and third place awards are to be given out. what is the probability that a girl wins the first place award while boys will receive the second and third place awards? express your answer as a percent.
Answer:
the probability is 10%
Step-by-step explanation:
(Giving 80 points, Please do not answer if you don't know. The second and third answer are not 4 btw)
Point A is on the point −6 and Point B is on the point 0. Let's use the Ruler Postulate to find the length of AB¯¯¯.
AB=|a−b|
AB=|−6−0|
AB=|−6|
AB=6
The length of AB¯¯¯¯ is 6. We can also write this as AB=6 or mAB¯¯¯¯=6.
Find the Length of CD¯¯¯¯
Now, let's find the length of CD¯¯¯¯. Point C is on the point 4 and Point D is on the point 8.
CD=|c−d|
CD=|4−8|
CD=|−4|
CD=4
The length of CD¯¯¯ is 4. We can also write this as CD=4 or mCD¯¯¯=4
Your Turn
1. What is the length of BC¯¯¯? 4
2. What is the length of AC¯¯¯¯?
3. What is the length of AD¯¯¯¯?
Answer:
1. 4
2. 10
3. 14
Step-by-step explanation:
A = -6
B = 0
C = 4
D = 8
1. BC = |0 - 4| = 4
2. AC = |-6 - 4| = |-10| = 10
3. AD = |-6 - 8| = |-14| = 14
Answer:
1. BC = 4
2. AC = 10
3. AD = 14
Step-by-step explanation:
Ruler Postulate
The distance between any two points on a number line is their difference.
Question 1
Given:
Point B = 0Point C = 4Therefore, using the Ruler Postulate:
⇒ BC = |b - c|
⇒ BC = |0 - 4|
⇒ BC = |-4|
⇒ BC = 4
Question 2
Given:
Point A = -6Point C = 4Therefore, using the Ruler Postulate:
⇒ AC = |a - c|
⇒ AC = |-6 - 4|
⇒ AC = |-10|
⇒ AC = 10
Question 3
Given:
Point A = -6Point D = 8Therefore, using the Ruler Postulate:
⇒ AD = |a - d|
⇒ AD = |-6 - 8|
⇒ AD = |-14|
⇒ AD = 14
Quadrilateral ABCD is translated 7 units down and 2 units to the right.
The length of side AB of the original quadrilateral is
units. After the translation, the length of side AB will
.
ABCD is a quadrilateral that has been translated 2 units to the right and 7 units down. The length of side AB will not change following the translation. Option C is correct.
What is translation?Each point in a figure is moved the same distance in the same direction using a sort of transformation known as translation.
The complete question is
"Quadrilateral ABCD has translated 7 units down and 2 units to the right.
The length of side AB of the original quadrilateral is_____ units. After the translation, the length of side AB will___________ .
2
3
3.5
4
----------------------------
Increase
Decrease
Remain the same"
Quadrilateral ABCD has translated 7 units down and 2 units to the right. After the translation, the length of side AB will remain the same.
Hence option C is correct.
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The largest pyramid at Giza is a square pyramid. It has a base of 756 feet and a slant height of 612 feet. Which represents the two-dimensional net of this pyramid?
The two-dimensional net of this pyramid that is surface area will be 34,416 square feet.
What is the surface area of the pyramid?Suppose the base of the pyramid has length = L units, width = W units, slant height = K units, and the height of the pyramid is of H units.
The surface area of the pyramid will be
SA = 2(1/2 × B × K) + 2(1/2 × L × K) + (L × B)
The largest pyramid at Giza is a square pyramid. It has a base of 756 feet and a slant height of 612 feet.
We have
L = W = 27.5 feet
Then the two-dimensional net of this pyramid that is surface area will be
SA = 2(1/2 × B × K) + 2(1/2 × L × K) + (L × B)
SA = 4(1/2 × 27.5 × 612) + 756
SA = 33,660 + 756
SA = 34,416 square feet
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25:50=4x:8. What is the value of X
Answer: X = 1
Step-by-step explanation:
25/50 = 4x/8
First, multiply both sides by 8, therefore, the 8 on the right side will be canceled out.
25*8/50 = 4x*8/8
25*8/50 = 4x
25*8 = 200
200 divided by 50 = 4
4 = 4x
After that, you just need to divide 4 on both sides, therefore, the 4 on the right side will cancel out.
4/4 = 4x/4
1 = x
X = 1
Hope I helped! :]
Please help me i would really appreciate it, worth 11 points
The number of seconds it takes for the waste to hit the ground for the given function is: 5 seconds.
How to Evaluate a Function?We are given the function of height to time as, h(t) = -16t² + initial height, and we have the following:
h(t) = 0 (height of the ground is 0)t = seconds the waste takes to height the groundInitial height = 400 feetPlug in the values into the equation of the function
0 = -16t² + 400
Solve for t
0 - 400 = -16t²
-400 = -16t²
-400/-16 = t²
400/16 = t²
√(400/16) = t
20/4 = t
5 = t
t = 5
The number of seconds it takes is: 5 seconds.
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Which of the following is equivalent to the expression?
Answer:
d
Step-by-step explanation:
- 5 (3x - 7) ← multiply each term in the parenthesis by - 5
= - 15x + 35
Answer: d.) -15x + 35
Given expression:
⇒ -5(3x - 7)
Apply distributive method: a(b + c) = ab + ac
⇒ -5(3x) -5(-7)
multiply the variables
⇒ -15x + 35
this is hard for me could smone help me ASAP please?
Answer:
x is 90°
y is 56°
Step-by-step explanation:
Concepts used :
The angle subtended by a diameter inside the circle is always 90° .
Sum of interior angles of a triangle is 180°.
Here x is the angle subtended by the diameter of the circle therefore ,
x is 90°.
let the end points of diameter as A , B
and the point where the it subtends the 90° angle be C
using interior angle property on the triangle ΔABC
90° + 62° + ∠A = 180°
152° + ∠A = 180°
∠A = 180° - 152°
∠A = 28°
now let he midpoint of diameter as D
as the sides DC and DA are radius of circle and therefore equal
so using isosceles triangle property which states that angle opposite to equal sides are equal
so the angle ∠ACD = 28°
now using exterior angle property on ΔADC
y = 56°
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$10,000 is invested at 7% annual interest which is compounded continuously what is the balance after eight years with no deposits or withdrawals are made
Answer:
$17,506.73
Step-by-step explanation:
Continuous Compounding Formula
[tex]\large \text{$ \sf A=Pe^{rt} $}[/tex]
where:
A = Final amountP = Principal amounte = Euler's number (constant)r = annual interest rate (in decimal form)t = time (in years)Given:
P = $10,000r = 7% = 0.07t = 8 yearsSubstitute the given values into the formula and solve for A:
[tex]\sf \implies A=10000e^{(0.07 \times 8)}[/tex]
[tex]\sf \implies A=10000e^{0.56}[/tex]
[tex]\implies \sf A=17506.725...[/tex]
Therefore, the value of the account after 8 years is $17,506.73 to the nearest cent.
Solve the quadratic function by factoring.
y = 4x² 13x + 10
Answer: [tex]x=-\frac{5}{4}[/tex] and [tex]x=-2[/tex]
Step-by-step explanation:
To factor an equation in the form of [tex]ax^2+bx+c[/tex] you need to find the value of [tex]ac[/tex]. So first solve for that
[tex](4)(10) = 40[/tex]
Now we need to find two numbers that add up to b and multiply together to make ac. In this case those numbers are 5 and 8 since 5+8=13 and (5)(8)=40
Now split 13x into 5x+8x and solve by grouping
[tex]4x^2+5x+8x+10\\(4x^2+5x)+(8x+10)[/tex]
Factor out the GCF in each quantity
[tex](4x^2+5x)+(8x+10)\\x(4x+5)+2(4x+5)[/tex]
Now group x+2 together
[tex](x+2)(4x+5)[/tex]
Finally, set each factor equal to 0 and solve for x
[tex]x+2=0\\x+2-2=0-2\\x=-2\\\\\\4x+5=0\\4x+5-5=0-5\\4x=-5\\\frac{4x}{4} =\frac{-5}{4} \\x=-\frac{5}{4}[/tex]
Points A, B, and C, form a triangle. The distance between point A and point B is 15 yards. The distance between point B and point C is 25 yards. Pete walks directly from point A to point C, without passing through point B. What is the direct distance from A to C?
How far would Pete walk if he went from A to B to C? yards
The direct distance from A to C is more than yards.
The inequality w < represents the distance, w, that Pete might save by taking the direct path.
The total distance if Pete walks from A to B to C is 40 yards, the direct distance from A to C is more than 10 yards, and an inequality w < 30
What is inequality?It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.
We have:
Points A, B, and C, form a triangle. The distance between point A and point B is 15 yards. The distance between point B and point C is 25 yards.
Total distance if Pete walks from A to B to C:
= 15 + 25 = 40 yards
As we know in the triangle the sum of the two sides is greater than the third side.
25 + 15 > AC
The direct distance from A to C is more than 10(25-15) yards.
The inequality w < 30 represents the distance, w, that Pete might save by taking the direct path.
Thus, the total distance if Pete walks from A to B to C is 40 yards, the direct distance from A to C is more than 10 yards, and an inequality w < 30
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Answer:
40 yards, 10 yards, and 30 yards.
Was correct for me on edge 2023
Solve the inequality for x and identify the graph of its solution.
|x+ 2|>2
Answer:
A. x < -4 or x > 0Step-by-step explanation:
[tex]|x+2| > 2\iff x+2 > 2\ \vee\ x+2 < -2[/tex]
subtract 2 from both sides
[tex]x > 0\ \vee\ x < -4[/tex]
Choose the quadratic model for the situation.
d(v) =2.14v^/.039
d(v) =2.15v^/64.79
d(v) =2.15v^/25.116
Answer:
d(v) =2.15v^/25.116
Step-by-step explanation:
Answer:
first 1 is .39
second one is C
Step-by-step explanation:
Find the value of x
Answer:
11
Step-by-step explanation:
Consider figures 1 and 2 shown on the coordinate plane. Figure 1 has been transformed to produce figure 2. Graph shows 2 quadrilaterals plotted on a coordinate plane. Quadrilateral 1 in quadrant 1 has vertices at (1, 3), (2, 5), (5, 5), (5, 3). Quadrilateral 2 in quadrant 4 has vertices at (1, minus 3), (5, minus 3), (5, minus 5), (2, minus 5). Describe the transformation. This transformation can be described by?
Using translation concepts, it is found that this transformation can be described as a reflection across the x-axis.
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
In this problem, considering the vertices of quadrilateral 1 and quadrilateral 2, the transformation from quadrilateral 1 to quadrilateral 2 has the following format:
(x,y) -> (x, -y).
Which means that it can be described as a reflection across the x-axis.
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This year, a small business had a total revenue of $40,700. If this is 26% less than their total revenue the previous year, what was their total revenue the previous year?
Describe the solution of f(x) shown in the graph. a parabola opening up passing through 0 comma 2, 1 comma zero and 2 comma zero All real solutions All solutions that lie on f(x) All positive solutions All whole number solutions
A quadratic equation is in the form of ax²+bx+c. The correct option is C, All the positive solutions.
What is a quadratic equation?A quadratic equation is an equation whose leading coefficient is of second degree also the equation has only one unknown while it has 3 unknown numbers. It is written in the form of ax²+bx+c.
The graph of the question is given below. Since a quadratic equation has only two solutions, and this two solutions can be found by observing the graph. The coordinate at which the graph of the equation intersect the x-axis are the solution of the equation.
As it can be observed in this graph, that the graph intersect the x-axis at (1,0) and (2,0).Therefore, the solutions of the graph are 1 and 2.
Thus, both the solutions are positive or it can be concluded that all the solutions are positive.
Hence, the correct option is C, All the positive solutions.
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Answer:
B. All solutions that lie on f(x)
Step-by-step explanation:
Hope this helps!
If not, I am sorry.
What is 5 ones , 38 tens , 27 hundreds , and 5 thousands? Write the number in word form and expanded form
Answer:
Eight thousand eighty five, 8000 + 80 + 5
Explanation:
Five ones, thirty-eight tens, twenty-seven hundreds, and five thousands equal to:
5 + 380 + 2700 + 5000
This is 8085 when added or eight thousand eighty-five in word form. This is also 8000 + 80 + 5 in expanded form.