Answer:
The answer is - 4x² + 8x - 8
Step-by-step explanation:
ƒ(x) = 3x – 1
g(x) = 4x2 – 5x + 7
(ƒ – g)(x) = 3x - 1 - ( 4x² - 5x + 7)
That's
3x - 1 - 4x² + 5x - 7
Group like terms
- 4x² + 3x + 5x - 1 - 7
The final answer is
- 4x² + 8x - 8
Hope this helps you.
Find the range of the given function y = 5x + 2, where x > -2.
Answer:
Its -3,2,7
Step-by-step explanation:
Simply put, you plug in all values greater than -2. Which is what thst function tells you.
John who is 5 ft tall is standing 20 feet away from a tree, and you measure the angle of elevation to be 38∘. How tall is the tree? Find your answer to the nearest tenth.Instructions: Find the missing length indicated.
Answer:
5√17=
20.6
Step-by-step explanation:
[tex]adj \: = 5 \\ opp \: = 20 \\ hyp \: = \: \\ pythagoras \: theorem \: \: = \\ {hyp}^{2} = {opp}^{2} + {adj}^{2} [/tex]
[tex] {hyp \:}^{2} = {20}^{2} + {5}^{2} \\ {hyp }^{2} = 400 + 25 \\ {hyp}^{2} = 425 \\ \sqrt{ {hyp}^{2} } = \sqrt{425} [/tex]
[tex]hypotenuse \: = 5 \sqrt{17} [/tex]
The tangent or tanθ in a right-angle triangle is the ratio of its perpendicular to its base. The height of the tree is 20.6257 feet.
What is Tangent (Tanθ)?The tangent or tanθ in a right-angle triangle is the ratio of its perpendicular to its base. it is given as,
[tex]\rm Tangent(\theta) = \dfrac{Perpendicular}{Base}[/tex]
where,
θ is the angle,
Perpendicular is the side of the triangle opposite to the angle θ,
The base is the adjacent smaller side of the angle θ.
The digram for the given condition is given below. Now, in ΔABC, the tangent value for ∠A can be written as,
tan(38°) = BC/AB
tan(38°) = 5 feet / AB
AB = 6.3997 feet
Now, in ΔABC and ΔADE for ∠A the value of the tangent can be written as,
tan(38°) = BC/AB = ED/AD
5/6.3997 = ED/(20 + 6.3997)
ED = 20.6257 feet
Hence, the height of the tree is 20.6257 feet.
Learn more about Tangent (Tanθ):
https://brainly.com/question/10623976
#SPJ2
Mrs smith invests £30,000 (some in a 5% account, some in an 8% account). After the year shes earned £2100. How much did she put in each account? PLEASE HELP!!
Answer:
She deposited £10,000 in the 5% yield account and deposited £20,000 in the 8% yield account
Step-by-step explanation:
Let the amount she put in each account be £x and £y respectively
Total amount deposited is ;
x + y = 30,000 ••••••(i)
Now, let’s look at the earnings:
in the £x , amount earned would be;
5/100 * x = 5x/100
For the £y, amount earned would be;
8/100 * y = 8y/100
Adding both gives the total which is £2,1000
5x/100 + 8y/100 = 2,100
Multiply through by 100
5x + 8y = 210,000 ••••••••(ii)
From the first equation, we know that
x = 30,000 -y
Let’s put this into the second
5(30,000-y) + 8y = 210,000
150,000-5y + 8y = 210,000
3y = 210,000 -150,0000
3y = 60,000
y = 60,000/3
y = £20,000
So mathematically;
x = 30,000-y
x = 30,000 -20,000
x = £10,000
Gwendolyn shot a coin with a sling shot up into the air from the top of a building. The graph below represents the height of the coin after
x seconds.
Answer: A
Step-by-step explanation:
HELP ASAP Linear Relations Question
Answer:
8.8
Step-by-step explanation:
set up a system
let x be sour keys and y be chocolate bars
2.65=15x+2y
3.35=10x+3y
then solve
X turns out to be 0.05
y turns out to be 0.95
multiply : 24*0.05=1.2
multiply : 0.95*8=7.6
add : 1.2+7.6 = 8.8
Please help ASAP Payton collected data to show the relationship between the number of hours he practices and the number of errors he makes when playing a new piece of music. The table shows his data. Which is the approximate slope of the line of best fit for the data? –5.5 –4.5 –2.0 –1.0
Answer:
Option B.
Step-by-step explanation:
The general equation of best fit line is
[tex]y=ax+b[/tex]
where, a is the slope of best fit line and b is y-intercept.
Using graphing calculator a=-4.54762 and b=43.7143. So equation of best fit line is
[tex]y=-4.54762x+43.7143[/tex]
Here,
[tex]Slope=-4.54762[/tex]
[tex]Slope\approx -4.5[/tex]
Note: In alternate method, you can use the below formula to find slope.
[tex]m=\dfrac{\overline{x}\cdot \overline{y}-\overline{xy}}{(\overline{x})^2-\overline{x^2}}[/tex]
Therefore, the correct option is B.
Answer:
B: -4.5
Step-by-step explanation:
edg2021
y ≈ -4.548x + 43.714 is the entire equation. So -4.548 or -4.5 is the slope.
Use the graph to complete the given statements. Enter the letters A, B, C, or D in the boxes.
The function with the lowest output values as x approaches infinity is _. The function with the greatest output values as x approaches infinity is _.
The function with the lowest output values as x approaches infinity is A.
The function with the greatest output values as x approaches infinity is B
HELP ME PLEASE PLEASE IM BEGGING
Answer:
a, No
Step-by-step explanation:
We can just substitute the numbers (x, y) into the inequality to see if the inequality is valid.
y=40
5(4) + 8 = 28
"<" means the number on the left is smaller than the number on the right.
40 is not smaller than 28, so in this inequality,
(4, 40) is not valid in y<5x+8
From the information given, what is the biggest flaw in the study? A health researcher randomly selected 500 high school students from the city of Oak Grove. In a private interview the researcher asked the students whether they had ever used drugs. She concluded that only 8% of the high school students of Oak Grove have ever used drugs.
Answer:
The correct answer is - The setting may discourage honest responses.
Step-by-step explanation:
In this particular setting of research and interview regarding this research may not produce hones results as the question is too direct to ask students if they had ever used drugs.
Research should be anonymous and should avoid the questions that can lead to bias results like this case that may lead to dishonest results.
Thus, the correct answer is : The setting may discourage honest responses.
Given that y is directly proportional tox, and when y = 8 when x=
10.
(a) Write down the equation of y in terms of x.
(b) Find the value of y when x = 25.
8
(c) Find the value of x when y==
25
Answer:
see explanation
Step-by-step explanation:
(a)
Given that y is directly proportional to x then the equation relating them is
y = kx ← k is the constant of proportion
To find k use the condition y = 8 when x = 10. then
8 = 10k ( divide both sides by 10 )
0.8 = k
y = 0.8k ← equation of proportion
(b)
when x = 25, then
y = 0.8 × 25 = 20
(c)
when y = 25, then
25 = 0.8x ( divide both sides by 0.8 )
x = 31.25
Find the area of this triangle..
Answer:
39.936 ( not rounded )
Step-by-step explanation:
Use Pythagorean theorem
a^2 + 6.4^2 = 9^2
height = 6.24 (rounded to nearest hundredth)
1/2 * base * height = area
1/2 * 12.8 * 6.24
= 39.936 ( not rounded )
An equation of the form 2x4 + 3x3 – 7x2 + 3x – 2 = 0 is called a/an ____________ equation.
Answer:
Polynomial Equation(fourth degree polynomial)
Step-by-step explanation:
A fourth degree polynomial equation is written in the form
ax^4 + bx^3 + cx^2 + dx + e=0
Just as written in the question
2x4 + 3x3 – 7x2 + 3x – 2 = 0
From the question:
a=2
b=3
c= -7
d=3
e= -2
Fourth degree polynomial equation are also known as QUARTIC POLYNOMIAL.
They have the following characteristics:
1. Zero to four roots.
2. No general symmetry.
3. 0ne,two or three extrema.
4. Roots are solved by radicals.
Malachy, Sushil and Fiona share some sweets in the ratio 1:3:1. Malachy gets 5 sweets. How many did Sushil get?
Answer:
Sushil got 15 sweets
Step-by-step explanation:
we can use law of indices property as shown below
a:b:c = ax:bx:cx
that if we multiply each term of ratio by same number , the ratio does not change
____________________________
given
Malachy, Sushil and Fiona share some sweets in the ratio 1:3:1.
let
Malachy gets 1x sweets
sushil gets 3x sweets
Fiona gets 1x sweets
but given that
Malachy got 5 sweets
thus
1x = 5
x = 5
Sushil got 3x sweets = 3*5 = 15 sweets.
Sushil got 15 sweets.
A mural inspired by a photograph measures 108 inches by 180 inches. The scale of the photograph to the mural is 1 in.:12 in. What are the dimensions of the photograph?
Answer:
9x9
Step-by-step explanation:
Divide 108/12
108/12=9
you have a 9x9 photo
hope this helps!
29:PLEASE HELP Solve the inequality x+6<-2
Answer:
x<-8
Step-by-step explanation:
x+6<-2
subract 6 from both sides
x+6-6<-2-6
x<-8
Sonya made a graph showing the first ten minutes of her drive to the movies. A graph with time on the x-axis and speed on the y-axis. The graph increases, increases rapidly, and then remains constant. Which description is the best interpretation of the graph? Sonya left her house and accelerated as she drove toward the highway entrance. She increased her speed as she drove up the ramp to the highway and then drove a constant speed on the highway. Sonya backed out of her driveway at a constant speed and then accelerated until she reached the street where the movie was playing. She stopped the car. Sonya drove down her driveway at a constant speed until she reached the street. She turned and drove down the street at a constant speed. Her car went slower as she drove up a hill. At the top of the hill she drove into the parking lot of the movie theater. Sonya accelerated as she drove down her driveway. She accelerated on the street on her way to the highway entrance. She waited for a red light, then accelerated onto the highway.
Answer:
Sonya left her house and accelerated as she drove toward the highway entrance. She increased her speed as she drove up the ramp to the highway and then drove a constant speed on the highway.
Step by step explanation:
The first scenario is the best match for the increasing slope, (leaving the house and accelerating) rapidly increasing slope (increasing speed on ramp) and level line (constant speed on the highway).
The best interpretation of the graph is,
Sonya left her house and accelerated as she drove toward the highway entrance. She increased her speed as she drove up the ramp to the highway and then drove a constant speed on the highway.
What is Acceleration?When a point or an object moving in a straight line , the acceleration is the rate at which velocity changes with time, in terms of both speed and direction.
Here, we have,
The first scenario is the best match for the increasing slope, (leaving the house and accelerating) rapidly increasing slope (increasing speed on ramp) and level line (constant speed on the highway).
Hence, The best interpretation of the graph is,
Sonya left her house and accelerated as she drove toward the highway entrance. She increased her speed as she drove up the ramp to the highway and then drove a constant speed on the highway.
To learn more on Acceleration click:
https://brainly.com/question/2303856
#SPJ3
If y varies jointly as x and z and inversely as the square of w, and y =3 when x=3, z=10 and w=2, then y=4 when x=4 z=20 w=4
Answer:
0.4 ; 0.8
Step-by-step explanation:
Given that :
y varies jointly as x and z and inversely as the square of w
y ∝ xz ∝ 1/w^2
y = kxz/w^2 - - - - (1)
Given that y =3 when x=3, z=10, w=2
Inputting the values into (1)
3 = (k*3*10) / 2^2
3 = 30 × k / 4
k × 30 = 3 × 4
k × 30 = 12
k = 12/30
k = 0.4
B.) Given that ;
y=4 when x=4 z=20 w=4
Input values into (1)
y = kxz/w^2
4 = ( k * 4 * 20) / 4^2
4 = (k * 80) / 16
k * 80 = 16 * 4
k * 80 = 64
k = 64 / 80
k = 0.8
Answer:
False
Step-by-step explanation:
Took the test and got it wrong
PLEASE HELP ME Logan has twice as many contacts in his phone as Marcus. Janet has 8 more then 1/3 of the number of contacts that Marcus has. Marcus has 243 contacts in his phone. How many more contacts does Logan have than Janet?
A new hockey stick costs $57.00 at the sporting goods store. If there is a 6%
sales tax, what is the actual cost of the hockey stick?
Answer:
$60.42
Step-by-step explanation:
0.06 x $57 = $3.42
$57 + $3.42 = $60.42
Hope this helped! :)
Which of the sets of ordered pairs represents a function? (1 point)
A = {(2, 7), (1, −5), (7, 2), (2, −9)}
B = {(5, 3), (−2, −9), (−3, 8), (9, 3)}
Answer:
B = {(5, 3), (−2, −9), (−3, 8), (9, 3)}
Step-by-step explanation:
A function has no repeating inputs (x-values). One input is assigned to exactly one output.
In set 'A', the input of two is repeated.
A = {(2, 7), (1, −5), (7, 2), (2, −9)}
In set 'B', there are no repeating inputs.
Set 'B' is a function.
Brainilest Appreciated.
(17x10)-(17x4)=(17 x ?)
Answer:
6
Step-by-step explanation:
6 is the answer
? =6
Answer:
6
Step-by-step explanation:
1. 17 * 10 = 170
2. 17 * 4 = 68
3. 170 - 68 = 102
4. 102 / 17 = 6
PLEASE HELP!!!
The model below represents 4x+(-4) -- 2x+8
What is the value of x when solving the equation 4x+(-4) --2x+8 using the algebra tiles?
X-2
Answer:
x=6
Step-by-step explanation:
4x-4=2x+8
Get all x's to one side. Subtract 2x from both sides.
2x-4=8
Isolate x. Add 4 to both sides.
2x=12
Divide both sides by 2 to get x.
12/2=6
x=6
Answer:
2 A.K.A. C. this answer is really late i think but for people in the future this is the answer lol
PLZ HELP ASAP--------->
NEED HELP ASAP ‼️‼️I BELIEVE ANSWER IS C
Answer:
I agree with your answer C!!
Step-by-step explanation:
Find the value of x in the triangle
shown below.
Answer: 55
Step-by-step explanation:
There are two sides that are equal (5 and 5). That means that this is an isoceles triangle. The unmarked angle and the x angle are equal to each other because isoceles triangles have also have two equal angles. Because every triangle has 180 degrees, that means that all three angles added up should equal 180.
Since the unmarked and x angle are equal you can write the equation out as 180=70+2x. Subtract 70 from both sides to get the variable and nonvariable on different sides.
110=2x. Divide both sides by 2(in order to isolate the variable). X is 55
Hope this helped you:)
ƒ(x) = -(-x), when x = -3?
Answer:
-3
Step-by-step explanation:
Substitute negative 3 as x and you get this -(--3). Then the two negatives make a positive and it's -(3) which becomes -3.
What is one of the zeros of the function shown in this graph?
Answer:
-4 or 2Step-by-step explanation:
the x-intercepts of the graph are the zeros of the quadratic function
This service is NOT important when comparing banks: a: Debit card design. b:Hours of operation. c:Convenience of location. D:Monthly fees and minimum balance required.
Answer:
A.
Step-by-step explanation:
Debit card design really has nothing to do with banks but has to do with personal preference. If you are comparing banks, you would want to see when they are open, how much you would need to deposit to start an account, that kind of stuff.
*QUICK HELP PLEASE
Which pairs of angles are adjacent? Select all that apply.
Answer:
1 and 3; 1 and 4; 2 and 3; 2 and 4
Step-by-step explanation:
Adjacent angles are those with a common side and common vertex (corner point). Of your choices, the ones provided above are the ones that meet the needs of adjacent angles.
Which answers are equivalent to the fraction below? Check all that apply
12/16
A.1/2 B.6/8 C2/3 D.2/6 E.3/4 F.6/4
Answer: e
Step-by-step explanation: 12/16 6/8 3/4
Answer:
B and E.
Step-by-step Explanation:
B: 6/8
6*2=12
8*2=16
12/16
E: 3/4
3*4=12
4*4=16
12/16
Hope this helps!!!!!