5. Solve for x in the parallelogram below.

Answer:

-25

Step-by-step explanation:

[tex]y=-\dfrac 14 x~~....(i)\\\\x+2y = 4~~...(ii)\\\\\text{Substitute}~~ y= -\dfrac 14 x ~~ \text{in equation (ii):}\\ \\ \\x+2\left(-\dfrac 14 x \right) = 4\\\\\implies 4x -2x = 16~~~~;\left[\text{Multiply both sides by 4} \right]\\\\\implies 2x = 16\\\\\implies x =\dfrac{16}2 \\ \\\implies x =8\\\\\text{Substitute x = 8 in equation (i);}\\\\y= -\dfrac 14 \cdot 8 = -2\\\\\text{Hence,}~ (x,y) = (8,-2)[/tex]

Answer:

[tex]y = - \frac{1 }{4} x \\ [/tex]

[tex]x + 2y = 4 \\ [/tex]

[tex]x + 2( - \frac{1}{4} x) = 4 \\ [/tex]

[tex]x + ( - \frac{2}{4} x) = 4 \\ [/tex]

[tex]x - \frac{1}{2} x = 4 \\ [/tex]

[tex] \frac{2x - 1x}{2} = 4 \\ [/tex]

[tex]2x - x = 8[/tex]

[tex]x = 8[/tex]

[tex]x + 2y = 4 \\ [/tex]

[tex]8 + 2y = 4[/tex]

[tex]2y = 4 - 8[/tex]

[tex]2y = - 4[/tex]

[tex]y = - 2[/tex]

a. Given that y = f(x) and f(0) = -2, by the fundamental theorem of calculus we have

[tex]\displaystyle \frac{dy}{dx} = 3x^2 + 4x + k \implies y = f(0) + \int_0^x (3t^2+4t+k) \, dt[/tex]

Evaluate the integral to solve for y :

[tex]\displaystyle y = -2 + \int_0^x (3t^2+4t+k) \, dt[/tex]

[tex]\displaystyle y = -2 + (t^3+2t^2+kt)\bigg|_0^x[/tex]

[tex]\displaystyle y = x^3+2x^2+kx - 2[/tex]

Use the other known value, f(2) = 18, to solve for k :

[tex]18 = 2^3 + 2\times2^2+2k - 2 \implies \boxed{k = 2}[/tex]

Then the curve C has equation

[tex]\boxed{y = x^3 + 2x^2 + 2x - 2}[/tex]

b. Any tangent to the curve C at a point (a, f(a)) has slope equal to the derivative of y at that point:

[tex]\dfrac{dy}{dx}\bigg|_{x=a} = 3a^2 + 4a + 2[/tex]

The slope of the given tangent line [tex]y=x-2[/tex] is 1. Solve for a :

[tex]3a^2 + 4a + 2 = 1 \implies 3a^2 + 4a + 1 = (3a+1)(a+1)=0 \implies a = -\dfrac13 \text{ or }a = -1[/tex]

so we know there exists a tangent to C with slope 1. When x = -1/3, we have y = f(-1/3) = -67/27; when x = -1, we have y = f(-1) = -3. This means the tangent line must meet C at either (-1/3, -67/27) or (-1, -3).

Decide which of these points is correct:

[tex]x - 2 = x^3 + 2x^2 + 2x - 2 \implies x^3 + 2x^2 + x = x(x+1)^2=0 \implies x=0 \text{ or } x = -1[/tex]

So, the point of contact between the tangent line and C is (-1, -3).

Answer:

Step-by-step explanation:

each pencil costs $8.33.

12÷$1.44=$8.33.

hope this helps!

mark me brainliest as well please.

Answer:

B

Step-by-step explanation:

if you divide the 2/88 you should get a price of 44. So Mechanic B charges $44 while Mechanic A charges $36. Subtract 44-36 and get 8. Since Mechanic B charges more, it would give you the answer listed in B.

The equation satisfies option B, Mechanic B charges $8 more per hour then mechanic A.

a collection of all points whose coordinates satisfy a given relation (such as a function) a diagram that represents the variation of a variable in comparison to that of one or more other variables, such as a series of one or more points, lines, line segments, curves, or areas

The fundamental subject of graph theory is graphs.

Given the Equation for cost charged by Mechanic A

y = 36x

where y = total cost and x = hours worked

graph shows the  total cost charged by Mechanic B

from graph we the coordinates (0, 0) and (2, 88)

when x = 0, y = 0 and when x = 2,  y  =  88

the equation satisfy the condition is

y = 44x

cost for one hour for Mechanic A

y = 36x (x = 1)

y = $36

cost for one hour for Mechanic B

y = 44x (x = 1)

y = $44

Mechanic B is $8 more than Mechanic A

Hence Mechanic B charges $8 more per hour then mechanic A.

Learn more about graph;

https://brainly.com/question/17267403

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Answer:

m∠Z=146

m∠X=34

Step-by-step explanation:

Since this is an Isosceles Trapezoid, we can assume that m∠Z=m∠Y, because an isosceles trapezoid has two pairs of congruent angles, therefore m∠Z=146.

Since angle Y and Angle X are same side interior and line ZY║WX, we can assume that m∠X+m∠Y=180. Substitute values:

[tex]146+X=180\\Y=34[/tex]

The awse is b) :B...... ur welcum

Answer:

A

Step-by-step explanation:

m( n+ p)

it's also known as m × n + p

Answer:

1 hotdog is $3.5.

1 drink is $2.

Step-by-step explanation:

18.50= 3x+4y(times 5)

25.50=5x+4y(times -3)

92.5=15x+20x

-76.5=-15x+-12y

16=-8y

2=y

18.50=3x+4(2)

10.50=3x+8

10.50=3x

3.5=x

Answer:

w - 10

Step-by-step explanation:

Substract 10 from W --> w - 10

Step-by-step explanation:

q3) if the given sequence is 1, 2, 4, 8, 16..., then it is not arithmetic one. The common ratio is 2: 16/8=8/4=4/2=2/1.

q4) if it is given -34; -64; -94; -124; -154..., then it is arithmetic sequence, where the difference is -64--34=-94--64=-124--94=-154--124= -30

Answer:

S₁₁ = 88573

Step-by-step explanation:

the sum to n terms of a geometric sequence is

[tex]S_{n}[/tex] = [tex]\frac{a_{1}(r^{n}-1) }{r-1}[/tex]

where a₁ is the first term and r the common ratio

here a₁ = 1 and r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{3}{1}[/tex] = 3 , then

S₁₁ = [tex]\frac{1(3^{11}-1) }{3-1}[/tex] = [tex]\frac{1}{2}[/tex] (177147 - 1) = [tex]\frac{1}{2}[/tex] × 177146 = 88573

Answer:

science

Step-by-step explanation:

k12 test

Answer:

6 options

Step-by-step explanation:

hes got 3 event options

and 2 time slots so

3 times 2 is 6

Answer:

Step-by-step explanation:

y(y+2)=y²-6

y²+2y=y²-6

2y=-6

y=-3

2[x-(1-3x)]=3(x+1)

2[x-1+3x]=3x+3

2(4x-1)=3x+3

8x-2=3x+3

8x-3x=3+2

5x=5

x=1

Answer:

224 ÷ 4 = 56

Step-by-step explanation:

14 × 4 = 56

56 × 4 = 224

224 ÷ 4 = 56

Answer:

The X-coordinates will decrease by 6 units because, anytime you move something to the left on a coordinate plane you are decreasing the x value

Answer:

The x-coordinates will decrease by 6.

Step-by-step explanation:

So when you look at a graph, the left side has smaller numbers than the right side because as you go down it becomes negative and the right means it is going positive. So if you are moving to the left you are getting smaller so you are decreasing. The other options with y-axis is not true because the y-axis is vertical.

Answer:

Here,

We know that cosD= b/h

=21/75

=7/25

Answer:

2.56

Step-by-step explanation:

(3+2+2+5+1+3+2+0+5)/9=2.55555555556...

Answer:

see below

Step-by-step explanation:

Move R side to the L side to get

2y^2 -4y +3  = 0

Use quadratic formula to find y = 1 +- i sqrt (2) / 2

Answer:

6

Step-by-step explanation:

[tex]h \sqrt{28 } \\ \sqrt{28} = \sqrt{4 \times 7} \\ \sqrt{28} = \sqrt{4} \times \sqrt{7} \\ 2 \sqrt{7} \\ 8 \sqrt{7} - 2 \sqrt{7} = 6 \sqrt{7} [/tex]

hope this helps :D have a good day

Answer:

Mean is all the numbers add up and divide how many number were there. The Median is to line up all in order and the middle on.

Step-by-step explanation:

Answer:

Mean =19.142857142857

Median =19.5

Step-by-step explanation:

Answer:

21300

Step-by-step explanation:

120∑n=13n−4

Split the summation into smaller summations that fit the summation rules.

120∑n=1 3n−4=3120∑n=1 n+120∑n=1 −4

Evaluate

3120∑n=1 n.

21780

Evaluate  

120∑n=1 −4 −480

Add the results of the summations.

21780−480

Subtract 480 from 21780.

21300

Answer:

42 minutes

Step-by-step explanation:

there are 60 minutes in one hour.

from 12 pm, 1 hour and 35 minutes have passed to get to 1:35 pm

from 12 pm, 2 hours and 17 minutes have passed to get to 2:17 pm

we are trying to figure out the start to end time, or the difference between the times

2 hours and 17 minutes - 1 hour and 35 minutes

1 hour = 60 minutes

if we convert everything to minutes we can get a definitive time in one single unit

2 hours = 1 hour * 2 = 60 minutes * 2 = 120 minutes

1 hour = 60 minutes

plug these in

(120 + 17) minutes - (60 + 35) minutes

= 137 minutes - 95 minutes

= 42 minutes as our answer

Answer: 50, 208 mm²

Step-by-step explanation:

    The lateral area is the surface area excluding the bottom, also known as the base. This means we will be solving for two rectangles and two triangles.

[The Rectangles]

    They are both congruent, so I will do the following;

A = 2(L * W)

A = 2(7 mm * 24 mm)

A = 2(168 mm)

A = 336 mm²

[The Triangles]

    The area of a triangle is [tex]\frac{B * H}{2}[/tex] However, they are both congruent. I will do the following;

A = B * H

A = 24 mm * 2,078 mm

A = 49,872 mm²

[The Total]

     Lastly, I will add them together.

336 mm² + 49,872 mm² = 50, 208 mm²

Answer:

B

Step-by-step explanation:

if it's one plant it's b, if it means more than one then probably D

Answer:

D) Volume of a rectangular prism

Step-by-step explanation:

Answer:

We need to find Factors of 14 that will also add and equal to 5

Step-by-step explanation:

Trinomial factorising

Answer:

see explanation

Step-by-step explanation:

p² - 5p - 14

We need to find the factors of the constant term (- 14) that will also add to give the coefficient of the p- term (- 5)

the factors are - 7 and + 2 , since

- 7 × + 2 = - 14 and - 7 + 2 = - 5

then

p² - 5p - 14 = (p - 7)(p + 2) ← in factored form