MATHEMATICS MIDDLE SCHOOL

WILL MARK BRAINLIST!!!!

Just need question 1 (i) and 2 (i), (ii)
WILL MARK BRAINLIST!!!! Just need question 1 (i) and 2 - 1

Answers

Answer 1
Answer: 2i
y=4-2x and 4x+2y = 5 can be rewritten as:

 y = -2x + 4
2y = -4x + 5

Multiply all 3 terms of the first eq'n by 2:    2y = -4x + 8

Note that 2y = -4x shows up in both equations.  This is enuf info on which to conclude that the 2 lines have the same slope.

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The line tangent to the graph of g(x) = x^{3}-4x+1 at the point (2, 1) is given by the formulaL(x) = 8(x - 2) + 1.


Which of the following statements are true? Select all that apply.
A. The functions are approximately equal on the interval 1.9 smaller than or equal to x larger than or equal to 2.1.
B. The functions have the same y-intercept.
C. The slope of the line equals g'(0).
D. The functions are approximately equal on the interval 0.5 smaller than or equal to x larger than or equal 1.0.
E. The graphs intersect at the point (2,1).
F. The slope of the line equals g'(2).
G. None of the above are true.

Answers

Using function concepts, it is found that the correct options are:

  • A. The functions are approximately equal on the interval 1.9 smaller than or equal to x larger than or equal to 2.1.
  • E. The graphs intersect at the point (2,1).
  • F. The slope of the line equals g'(2).

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  • The value of x we are interested is x = 2, thus, considering a margin, the functions are approximately equal between x = 1.9 and x = 2.1, which means that option A is correct, while option D is not.
  • The y-interceptof g is g(0) = 0^3 - 4(0) + 1 = 1, while the y-intercept of L is L(0) = 8(0 - 2) + 1 = -16 + 1 = - 15. Not the same, thus, option B is not correct.
  • The slope of the tangent line to g at x = 2 is the derivative of g at x = 2, that is, g'(2), thus option F is correct while option C is not.
  • At (2,1), the g(x) and L(x) intersect, thus, option E is correct.

A similar problem is given at brainly.com/question/22426360

well, about A and D, I just plugged the values on the slope formula of

\bf \begin{array}{llll} g(x)=x^3-4x+1\n L(x) = 8(x-2)+1 \end{array} \qquad \begin{cases} x_1=1.9\n x_2=2.1 \end{cases}\implies \cfrac{f(b)-f(a)}{b-a}

for A the values are 8.01 and 8.0, so indeed those "slopes" are close. \textit{\huge \checkmark}

for D the values are -2.25 and 8.0, so no dice on that one.

for B, let's check the y-intercept for g(x), by setting x = 0, we end up g(0) = 0³-4(0)+1, which gives us g(0) = 1.

checking L(x) y-intercept, well, L(x) is in slope-intercept form, thus the +1 sticking out on the far right is the y-intercept, so, dice. \textit{\huge \checkmark}

for C, well, the slope if L(x) is 8, since it's in slope-intercept form, the derivative of g(x) is g'(x) = 3x² - 4, and thus g'(0) = -4, so no dice.

for E, do they intercept at (2,1)?  well, come on now, L(x) is a tangent line to g(x), so that's a must for a tangent. \textit{\huge \checkmark}

for F, we know the slope of the line L(x) is 8, is g'(2) = 8?  let's check

recall that g'(x) = 3x² - 4, so g'(2) = 3(2)² - 4, meaning g'(2) = 8, so, dice. \textit{\huge \checkmark}

A freight elevator has a capacity of just under 3,000 pounds . A group of movers wants to move a piano that weighs 900 pounds and several crates of electronic that weigh 300 pounds each Part A : Write an inequality that shows how many crates of electronics can go on the freight elevator with the piano . Part B : Solve the inequality from Part A to find how many crates of electronics can go on the freight elevator

Answers

Freight elevator's capacity will be defined as c.

Pounds (weight) will be defined as w.

So we can say that:

c<3000w

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Piano will be defined as 900w.

Number of crates of electronics will be defined as n300w, as we don't know how many crates there are.

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So, with this information we can say that:

900w+n300w<3000w

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Now let's find out how many crates (n) can go on that elevator with the piano...

900w+n300w<3000w\n \n n300w<3000w-900w\n \n n300w<2100w

\n \n \frac { 1 }{ 300w } \cdot n300w<2100w\cdot \frac { 1 }{ 300w } \n \n n<\frac { 2100 }{ 300 } \cdot \frac { w }{ w } \n \n n<7

The elevator won't be able to accommodate a piano and 7 crates of electronics but it will be able to accommodate a piano and 6 crates of electronics.
part A + B  if you subtract 3,000 - 900 ( piano ) = 2,100 then if you keep subtracting 300 ( 1 crate of electronics ) soon you will get down to 0 then you can count how many times you subtracted 300 which in my answer 6 crates will fit with the piano part A ( 3,000 - 900) - 300 until 0  because it's 6 crates it said it was just under 3,000 pounds not on the exact weight.

 

Passes through ( -4, -5), slope = 3/4

Answers

Answer:

y= .75x

Step-by-step explanation:

first, you take the fraction and make it into a decimal

Then, you make an equation

What is 2x2?
Pease help

Answers

Two times two is four (4), if that is what you need. 
You just add that same number to the base when it comes to multiplication. For example, if you had 4x2, then that would be 4 + 4, which is 8. 

Hi there, 2*2 is 4. Multiplication is repeated addition. I hope this helps, have a good day/evening. :)

The table shows the outputs y for different inputs x:Input
(x) 2 4 6 8
Output
(y) 1 2 3 4


Part A: Do the data in this table represent a function? Justify your answer. (3 points)
Part B: Compare the data in the table with the relation f(x) = 3x – 10. Which relation has a greater value when x = 8? (2 points)
Part C: Using the relation in Part B, what is the value of x if f(x) = 80? (5 points)

PLEASE HELP!!!!!!!!!!!

Answers

A.   The data in the table represent a function. y=x/2. This is seen as for every value of x in the table, y=x/2(half of it). You can show this further by trying this fact on each value.

B.   For the original function, when x =8, y=x/2=4
For the function given in this part, when x=8, y=3(8)-10
                                                                 y=24-10                                                                                                            y=14
     This means the relation given in this part has a greater value when x=8

C. When x=80, f(x)=3(80)-10
                           =240-10
                           =230 

Photo above! Find the area of this triangle (It says the answer is 405 but all I get when I do it is 810) please help!

Answers

So, the area of a triangle is base x height, divided by 2. 

When you calculated the area, you forgot to divide the answer by 2, which left you with 810. 

27 x 30 = 810 
Answer/2 is equal to the answer:
810/2 is 405. 

Hope this helps! 
the formula for the area of a triangle is 1/2(base×height)
30×27=810
810×1/2=405
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