please help in math : lenght of rectangle is width+7m.
and width of this rectangle is 1/3 of lenght. find lenght of rectangle.
....please help and explain....
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Answer:

16

Step-by-step explanation:

Answer:

The answer is B

Step-by-step explanation:

The solution is -3 by the way

Answer:

Part I)

[tex]a=-1\text{ and } c=2[/tex]

Giving the equation:

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

Part II)

(-1, 2)

Step-by-step explanation:

We have the equation:

[tex]y=ax^3+x+c[/tex]

Where a and c are constants.

We are given gradient/slope of the curve at the point (1, 2) is -2.

Part I)

We know that the gradient of the curve exactly at the point (1, 2) is -2.

So, we will differentiate our equation. We have:

[tex]\displaystyle y=ax^3+x+c[/tex]

Differentiate both sides with respect to x:

[tex]\displaystyle y^\prime=\frac{d}{dx}\big[ax^3+x+c\big][/tex]

Expand the right:

[tex]\displaystyle y^\prime=\frac{d}{dx}\big[ax^3]+\frac{d}{dx}\big[x\big]+\frac{d}{dx}\big[c\big][/tex]

Since a and c are simply constants, we can move them outside:

[tex]\displaystyle y^\prime=a\frac{d}{dx}\big[x^3]+\frac{d}{dx}\big[x\big]+c\frac{d}{dx}\big[1\big][/tex]

Differentiate. Note that the derivative of a constant is simply 0.

[tex]\displaystyle y^\prime=3ax^2+1[/tex]

We know that at the point (1, 2), the gradient/slope is -2.

Hence, when x is 1 and when y is 2, y’ is -2.

So (we don’t have a y so we can ignore it):

[tex]-2=3a(1)^2+1[/tex]

Solve for a. Simplify:

[tex]-2=3a+1[/tex]

Subtract 1 from both sides yield:

[tex]-3=3a[/tex]

So, it follows that:

[tex]a=-1[/tex]

Therefore, our derivative will be:

[tex]y=-3x^2+1[/tex]

Now, we can go back to our original equation:

[tex]y=ax^3+x+c[/tex]

Since we know that a is -1:

[tex]y=-x^3+x+c[/tex]

Recall that we know that a point on our curve is (1, 2).

So, when x is 1, y is 2. By substitution:

[tex]2=-(1)^3+1+c[/tex]

Solve for c. Simplify:

[tex]2=-1+1+c[/tex]

Then it follows that:

[tex]c=2[/tex]

Hence, our entire equation is:

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

Part II)

Our derivative is:

[tex]y^\prime=-3x^2+1[/tex]

If the gradient is -2, y’ is -2. Hence:

[tex]-2=-3x^2+1[/tex]

Solve for x. Subtracting 1 from both sides yields:

[tex]-3=-3x^2[/tex]

So:

[tex]x^2=1[/tex]

Then it follows that:

[tex]x=\pm1\\[/tex]

Since we already have the point (1, 2) where x is 1, our other point is where x is -1.

Using our equation:

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

We can see that our second point is:

[tex]y=-(-1)^3+(-1)+2[/tex]

Simplify:

[tex]y=1-1+2=2[/tex]

So, our second point where the gradient is -2 is at (-1, 2).

Answer:

more than 1 step?

Step-by-step explanation:

if there are multiple steps. then theirs more than 1

Answer:

okay, but with what should i help?

Answer:

22%

Step-by-step explanation:

The percentage of tax can be found by calculating the percent change.

new - old / old

6084 - 7800 / 7800

= -0.22 or -22%

This means the price decreased by 22%, meaning you paid 22% in taxes.

please click heart button to give thanks :)

Answer:

it's the one all the way to the right

Answer:

50 and 80 or 65 and 65

Step-by-step explanation:

two angles in an isosceles are the same.

Answer:

bc 0<0.35<1

and 5 is more than 1

Step-by-step explanation:

Answer:

It is less because the number 0.35 has a lower value meaning that it has less value.And the 5 is like a whole.

Step-by-step explanation

Say if you had 5 pizza's that would be more then just having the top of the pizza.

Answer:

1 = 2x      2= -3    4 =3

Step-by-step explanation:

Answer:

1. 5x-3=-15

2. -15/5=-3

3. -15/-3=5

Step-by-step explanation:

Hope this helps :)

Answer:

D

Step-by-step explanation:

Answer:

x=-2

Step-by-step explanation:

same on both sides

Step-by-step explanation:

The interval is -2 <= x <= 3 (A).

Step-by-step explanation:

Sam's rope = 42 inches * (2/7) = 12 inches.

Hi!

The equation we're working with is in slope-intercept form:

[tex]\diamondsuit~\boldsymbol{y=mx+b}[/tex]

Where:

[tex]\diamondsuit[/tex] [tex]\boldsymbol{m- > slope}[/tex]

[tex]\diamondsuit~\boldsymbol{b- > y-intercept}[/tex]

Therefore,

[tex]\stackrel{\heartsuit}{\boxed{\boxed{\textsc{Answers:}\begin{cases}\bold{Slope:4}\\\bold{-5}\end{cases}}}}[/tex]

I hope that helped, have a wonderful rest of your day! :)

The slope of the line is 4 and the y-intercept of the line is -5.

An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.

The general form of the equation of the line:-

y = mx + c

m = slope

c = y-intercept

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

The given equation of the line is y = 4x - 5. Compare the equation with the general form of the equation,

y = mx + c

y = 4x - 5

Slope m = 4

Y-intercept = -5

Therefore, the slope of the line is 4 and the y-intercept of the line is -5.

To know more about an equation of the line follow

https://brainly.com/question/18831322

#SPJ2

Answer:

72.9

Step-by-step explanation:

Multiply your first 2 terms

4.5* (-9) = -40.5

multiply this by -1.8

-40.5*-1.8 = 72.9

Answer:

−72.9 / option B

Step-by-step explanation:

(4.5)(-9)(1.8)

Step 1: (4.5) x (-9) = (-40.5)

Step 2: (-40.5) x (1.8) = (-72.9)

Answer:

the new point would be (1, 10).

Step-by-step explanation:

if you start with the point (6, 7) and go left 5 units and up 3 units, then the new point you land on is (1, 10) as you can see in the picture below. hope this helped!

Answer: 5 pounds

Step-by-step explanation:

80 / 16 = 5

Answer:

5 pounds

Step-by-step explanation:

Hope this helps!

Answer:

I. The point (6, -2) is not a solution for the given equation

II. The slope of the line going through (-4, 1) and (-7, -5) is 2

III. The slope of the line x = -7 is ∞

IV The slope of the line y = -6 is 0

V. The coordinate of the x-intercept is (12.5, 0)

The coordinate of the y-intercept is (0, 25)

VI. The equation of the line is y = 17·x + 59

Step-by-step explanation:

I. The given equation is -4·x - 5·y = 32

The given point = (6, -2)

Therefore;

The x-coordinate value of the point = 6

The y-coordinate value of the point = -2

Plugging in the x and y-coordinate values into the given equation gives;

-4 × (6) - 5 × (-2) = -14 which does not correspond to the given equation, therefore, the point (6, -2) is not a solution for the given equation;

We can also show, by making y the subject of the formula of the given equation, weather the point is a solution of the given equation as follows;

-4·x - 5·y = 32

y = (-4/5)·x - 32/5

For x = -2, we have;

y = (-4/5) × (-2) - 32/5 = - 4.8

Therefore, the point (6, -2) where y = 6 when x = -2 is not a solution of -4·x - 5·y = 32

II. The slope of a straight line, given two points on the line is given as follows;

[tex]Slope, \, m =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

Where the two points are (-4, 1), and (-7, -5), we have;

x₁ = -4, y₁ = 1, x₂ = -7, and y₂ = -5

[tex]Slope, \, m =\dfrac{-5-1}{-7-(-4)} =2[/tex]

The slope, m, of the line going through (-4, 1) and (-7, -5) is m = 2

III. The slope of the line x = -7 = ∞ because, the difference in the x-value which is the denominator of the slope equation = 0 for all differences in the y-coordinate values

IV The slope of the line y = -6 is 0 because, the difference in the y-values which is the numerator of the slope equation = 0 for all differences in the x-coordinate values

V. The x and y-intercept of an equation is found by finding the values of the variable, x or y, in the equation, when the other variable, y or x is equal to zero respectively, which is given as follows;

The given equation is y = -2·x + 25

When y = 0, we have the x-intercept as 0 = -2·x + 25

∴ 2·x = 25

x = 25/2 = 12.5

Therefore, the coordinate of the x-intercept is (12.5, 0)

When x = 0, we have the x-intercept as y = -2·x + 25 = -2 × 0 + 25 = 25

The coordinate of the y-intercept is (0, 25)

VI. The general equation of a straight line is y = m·x + c

Where;

m = The slope of the line

c = The y-intercept

For the  line that goes through the points (-3, 8) and (-4, -9), we have;

[tex]The \ slope, \, m =\dfrac{-9-8}{-4- (-3)} = \dfrac{-9-8}{-4+3} = 17[/tex]

The equation in point and slope form is y - 8 = 17 × (x - (-3))

∴ y  = 17·x + 51 + 8 = 17·x + 59

The equation of the line is y = 17·x + 59

Answer:

g(h(10)) = 43

Step-by-step explanation:

Given: g(x) = 4x – 4 and h(x) = 2x – 8.

We are to find g(h(10))

First we need to get g(h(x))

g(h(x)) = g(2x-8)

Replace x in g(x) with 2x-8 as shown:

g(2x-8) = 4(2x-8)-4

g(2x-8)= 8x-32-5

g(2x-8) = 8x-37

Hence g(h(x)) = 8x-37

g(h(10)) = 8(10)-37

g(h(10)) = 80-37

g(h(10)) = 43

Hence g(h(10)) is 43

Answer:

I will explain each step

3(x-y) / 2 =9

so first you have to make the equation equal to 0 so you can find the intercepts

3(x-y) /2  -9 =0

now simplify

3x-3y/2 -9 =0

2(3x-3y/2 -9)=0(2)

3x-3y-18

we will factor

3(x-y-6)

3=0

(x-y-6)=0

make the x=0 to find y and vise versa

(-y-6)=0

-y=6

y=6/-1 or -6

(x-6)=0

x=6/1 or 6

2/3x +4(y-2)=0

it is already equal to 0 to we simplify and factor

3(2/3x = 4(y-2)= 0(3)

2x+ 4y -8

2(x+y-4)

2=0

as we did in the last problem make x=0 then do the same to y

(y-4)=0

y=4

(x-4)=0

x=4

Step-by-step explanation:

I believe the answer is -12x, so sorry if that is incorrect.

Answer:

12x

Step-by-step explanation:

17x+(-5x)=17x-5x=12x

Answer:

[tex]\angle D= 162\\\\\angle E = 18\\\\\angle F = 162\\\\\angle G = 18[/tex]

Step-by-step explanation:

By properties of parallelograms we know that opposite are the same so we have

[tex]12x=4(x+3)\\\\4(3x)=4(x+3)\\\\3x=x+3\\\\2x=3\\\\x=\frac{3}{2}[/tex]

so for the angles we have

[tex]\angle G=\angle E=12(\frac{3}{2})=18\\\\\angle D=\angle F = 180-\angle G=180-18=162[/tex]

Answer:

24

Step-by-step explanation:

20+20% is equal to 24.

Answer:

3.514 degrees per hour

Step-by-step explanation:

To find change per hour, you find the slope, which is change in output (temperature) over change in input (hours)

y2-y1 / x2-x1

-12.3 - 0 / 3.5

3.514 degrees per hour

Answer:

40°

Step-by-step explanation:

180- (90 + 40) = 50°

Angle 1 = 50°

180 - 50 = 130°

Angle 2 = 130°

180 - 130 = 50°

Angle 3 = 50°

180 - (90 + 50) = 40°

Angle 5 = 40°

OR

the two triangles are similar. Therefore, their angles are congruent. Since the tringle was only flipped and made slightly smaller, angles 9 and 5 are corresponding angles. (Both have the same measure of 40°)

Hope this helps. Have a nice day

Answer:

$6889.89

Step-by-step explanation:

6321/100=63.21

63.21x4.5=284.445

284.445x5=568.89

568.89+6321=$6889.89

Answer:

x=-9

Step-by-step explanation:

x+5^2=16

x+25=16

x=-9

Answer :

x + 5² = 16

x + 25 = 16

x = 16-25

x = -9 is the answwr

Hope it helped

Answer:

Two perpendicular segments are segment AB and segment CD

Step-by-step explanation:

The given construction with the straight edge and the compass gives;

1) A straight line CD

2) A line AE from the center of the circle A, to the line CD

3) The circles A and B constructed from the centers A and B respectively

Therefore

Whereby the points A and B are joint by the line AB, we have;

The line passing through the points C and D is the perpendicular bisector of line AB

Therefore, two perpendicular segments are segment AB and the perpendicular bisector of AB which is segment CD