Solve for all values of x by factoring x² + 6x = 0

Answer:

The value of x is 5

Answer:

x = 2, y = - 1

Step-by-step explanation:

Given the 2 equations

y = - 7x + 13 → (1)

y = - 1 → (2)

Substitute y = - 7x + 13 into (2)

- 7x + 13 = - 1 ( subtract 13 from both sides )

- 7x = - 14 ( divide both sides by - 7 )

x = 2

y = - 1 is already given in (2)

Then x = 2, y = - 1

Answer:

[tex]\displaystyle y=-\frac{1}{10}x^2-\frac{4}{5}x-\frac{11}{10}[/tex]

Step-by-step explanation:

By definition, any point (x, y) on the parabola is equidistant from the focus and the directrix.

The distance between a point (x, y) on the parabola and the focus can be described using the distance formula:

[tex]d=\sqrt{(x-(-4))^2+(y-(-2))^2[/tex]

Simplify:

[tex]d=\sqrt{(x+4)^2+(y+2)^2}[/tex]

Since the directrix is an equation of y, we will use the y-coordinate. The vertical distance between a point (x, y) on the parabola and the directrix can be described using absolute value:

[tex]d=|y-3|\text{ or } |3-y|[/tex]

The two equations are equivalent. Therefore:

[tex]\sqrt{(x+4)^2+(y+2)^2}=|y-3|[/tex]

Solve for y. We can square both sides. Since anything squared is positive, we can remove the absolute value:

[tex](x+4)^2+(y+2)^2 = (y-3)^2[/tex]

Expand:

[tex](x^2+8x+16)+(y^2+4y+4)=(y^2-6y+9)[/tex]

Isolate:

[tex]x^2+8x+11=-10y[/tex]

Divide both sides by -10. Hence, our equation is:

[tex]\displaystyle y=-\frac{1}{10}x^2-\frac{4}{5}x-\frac{11}{10}[/tex]

Answer:

There is no common factor

Step-by-step explanation:

Step-by-step explanation:

first number=x

second number=x+2

third number=x+4

(x+2)(x+4)=35

x(x+4)+2(x+4)=35

x²+4x+2x+8=35

x²+6x+8=35

x²+6x=35-8

x²+6x=33

x²+6x-33=0

using that, you can find the first number,

then use the data to find the other two.

Answer:

117 centimeters

Step-by-step explanation:

Since the longest pieces is 72 centimeters and it’s ratio is 8, that means the individual unit of the ratio is 9 (72/8=9). You can multiply each part of the ratio by 9

2x9=18

3x9=27

We already know the third part of the ratio is 72. Add all of it together to get the original length.

18+27+72=117 cm

Answer:

It would be considered stealing.

Step-by-step explanation:

They did willingly give you their card BUT, they trusted you to only spend a certain amount and not go over that certain limit. You went over the limit even though they specifically told you not to go over it so yes, it would be classified as stealing.

Answer: B

Step-by-step explanation:

There are two x-intercepts: x = -√5 and x = √5. The answer is: 2 x-intercepts.

The x-intercept is defined as an intercept that is located at the x-axis of the plane, is the location or coordinate from where the line crosses.

To find the x-intercepts of the polynomial function f(x) = x⁴ - 5x², we set f(x) equal to zero and solve for x.

Setting f(x) = 0:

x⁴ - 5x² = 0

Factoring out the common term x²:

x²(x² - 5) = 0

Now we have two factors: x² = 0 and x² - 5 = 0.

For x² = 0, we have a double root at x = 0.

This means the graph touches the x-axis at x = 0 but does not cross it.

For x² - 5 = 0, we can solve for x by taking the square root:

x² = 5

x = ±√5

Therefore, there are two x-intercepts: x = -√5 and x = √5.

The answer is: 2 x-intercepts.

Learn more about the x-intercept here:

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Answer:

a = 24 ft²

Step-by-step explanation:

Area of 1 side

a = 2 * 2

a = 4 ft²

Cubes have 6 sides

a = 6 * 4

a = 24 ft²

Answer:

A. 24 ft²

Step-by-step explanation:

The faces of a cube are squares. We know that the squares have a side length of 2 ft. Therefore, the area of a square will be 4 ft². There are 6 faces/squares on a cube, so we take the 4 ft² and multiply it by 6. This gives us 24 ft².

2

Hope this helps! :)

______________

Answer:

you can know by the minimum number or the maximum e.g minimum 1 maximum 20 answer 20

Step-by-step explanation:

so in this kind it is 2

hope its useful

Answer:

It would be 9π

Step-by-step explanation:

(x-1)²π

(x-1)(2x-4)

Answer:

∠ B = 61°

Step-by-step explanation:

The inscribed angle B is half the measure of its intercepted arc, then

∠ B = [tex]\frac{1}{2}[/tex] × 122° = 61°

So if you multiply 15 by 6 you get 90 and the 6 is from every years she has saved. So if you take any number 95000 and 15 percent of 95000 is 14250 so try breaking it down and divide as much as you can but not to much and slowly at a time and then when you get that try to get close to 9500 as much as you can cause 90 percent of 95000 is 9500.

Answer: 12.

Step-by-step explanation: Use Pythagorean Theorem. We that a = 9, b = ?, and c = 15. Plugging that in gives us 9^2 + b^2 + 15^2. Solving for b gets us b^2 = 144. Taking the square root of both sides gets us b = 12.

Answer:

The last 3 choices are correct

Step-by-step explanation:

A rotation of 180 degrees has the rule (x,y) →(-x,y) , so the coordinates will not be the same. The shape's size doesn't change.

Answer:

The surveyor is 36.076 kilometers far from her camp and her bearing is 16.840° (standard form).

Step-by-step explanation:

The final position of the surveyor is represented by the following vectorial sum:

[tex]\vec r = \vec r_{1} + \vec r_{2} + \vec r_{3}[/tex] (1)

And this formula is expanded by definition of vectors in rectangular and polar form:

[tex](x,y) = r_{1}\cdot (\cos \theta_{1}, \sin \theta_{1}) + r_{2}\cdot (\cos \theta_{2}, \sin \theta_{2})[/tex] (1b)

Where:

[tex]x, y[/tex] - Resulting coordinates of the final position of the surveyor with respect to origin, in kilometers.

[tex]r_{1}, r_{2}[/tex] - Length of each vector, in kilometers.

[tex]\theta_{1}, \theta_{2}[/tex] - Bearing of each vector in standard position, in sexagesimal degrees.

If we know that [tex]r_{1} = 42\,km[/tex], [tex]r_{2} = 28\,km[/tex], [tex]\theta_{1} = 32^{\circ}[/tex] and [tex]\theta_{2} = 154^{\circ}[/tex], then the resulting coordinates of the final position of the surveyor is:

[tex](x,y) = (42\,km)\cdot (\cos 32^{\circ}, \sin 32^{\circ}) + (28\,km)\cdot (\cos 154^{\circ}, \sin 154^{\circ})[/tex]

[tex](x,y) = (35.618, 22.257) + (-25.166, 12.274)\,[km][/tex]

[tex](x,y) = (10.452, 34.531)\,[km][/tex]

According to this, the resulting vector is locating in the first quadrant. The bearing of the vector is determined by the following definition:

[tex]\theta = \tan^{-1} \frac{10.452\,km}{34.531\,km}[/tex]

[tex]\theta \approx 16.840^{\circ}[/tex]

And the distance from the camp is calculated by the Pythagorean Theorem:

[tex]r = \sqrt{(10.452\,km)^{2}+(34.531\,km)^{2}}[/tex]

[tex]r = 36.078\,km[/tex]

The surveyor is 36.076 kilometers far from her camp and her bearing is 16.840° (standard form).

Answer:

D distance(20)

Step-by-step explanation:

The notation to express a dependent variable is given by :-

, where Y is depending variable which is dependent upon x ( independent variable).

The given statement : The distance an airplane travels depends on how much time it spends flying.

Here , Independent variable : Time

Dependent variable : Distance

Then , the notation to express distance (dependent variable) the airplane flies in 20 minutes is given by :-distance(20).

Answer:

2(6.3) + b = 15.7

12.6 + b = 15.7

b = 3.1

Answer:

9

Step-by-step explanation:

Answer:

d

Step-by-step explanation:

9×2 =18 or 9+9=18 I haven't done this since 6 grade sorry if I got it wrong

Answer:

96

Step-by-step explanation:

80*120=9600 divided by 100

Solution :

Let [tex]$v_0$[/tex] be the unit vector in the direction parallel to the plane and let [tex]$F_1$[/tex] be the component of F in the direction of [tex]v_0[/tex] and [tex]F_2[/tex] be the component normal to [tex]v_0[/tex].

Since, [tex]|v_0| = 1,[/tex]

[tex]$(v_0)_x=\cos 60^\circ= \frac{1}{2}$[/tex]

[tex]$(v_0)_y=\sin 60^\circ= \frac{\sqrt 3}{2}$[/tex]

Therefore, [tex]v_0 = \left<\frac{1}{2},\frac{\sqrt 3}{2}\right>[/tex]

From figure,

[tex]|F_1|= |F| \cos 30^\circ = 10 \times \frac{\sqrt 3}{2} = 5 \sqrt3[/tex]

We know that the direction of [tex]F_1[/tex] is opposite of the direction of [tex]v_0[/tex], so we have

[tex]$F_1 = -5\sqrt3 v_0$[/tex]

    [tex]$=-5\sqrt3 \left<\frac{1}{2},\frac{\sqrt3}{2} \right>$[/tex]

    [tex]$= \left<-\frac{5 \sqrt3}{2},-\frac{15}{2} \right>$[/tex]

The unit vector in the direction normal to the plane, [tex]v_1[/tex] has components :

[tex]$(v_1)_x= \cos 30^\circ = \frac{\sqrt3}{2}$[/tex]

[tex]$(v_1)_y= -\sin 30^\circ =- \frac{1}{2}$[/tex]

Therefore, [tex]$v_1=\left< \frac{\sqrt3}{2}, -\frac{1}{2} \right>$[/tex]

From figure,

[tex]|F_2 | = |F| \sin 30^\circ = 10 \times \frac{1}{2} = 5[/tex]

∴  [tex]F_2 = 5v_1 = 5 \left< \frac{\sqrt3}{2}, - \frac{1}{2} \right>[/tex]

                   [tex]$=\left<\frac{5 \sqrt3}{2},-\frac{5}{2} \right>$[/tex]

Therefore,

[tex]$F_1+F_2 = \left< -\frac{5\sqrt3}{2}, -\frac{15}{2} \right> + \left< \frac{5 \sqrt3}{2}, -\frac{5}{2} \right>$[/tex]

           [tex]$=<0,- 10> = F$[/tex]

Answer:

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