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Papessa [141]
3 years ago
13

What is the value of x

Mathematics
1 answer:
barxatty [35]3 years ago
3 0
X = 15


X + 90 = 7x

X = 7x - 90

X - 7x = -90

-6x = 90

Divide both sides by -6

X = 15
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Match the parabolas represented by the equations with their vertices. y = x2 + 6x + 8 y = 2x2 + 16x + 28 y = -x2 + 5x + 14 y = -
GaryK [48]

Consider all parabolas:

1.

y = x^2 + 6x + 8,\\y=x^2+6x+9-9+8,\\y=(x^2+6x+9)-1,\\y=(x+3)^2-1.

When x=-3, y=-1, then the point (-3,-1) is vertex of this first parabola.

2.

y = 2x^2 + 16x + 28=2(x^2+8x+14),\\y=2(x^2+8x+16-16+14),\\y=2((x^2+8x+16)-16+14),\\y=2((x+4)^2-2)=2(x+4)^2-4.

When x=-4, y=-4, then the point (-4,-4) is vertex of this second parabola.

3.

y =-x^2 + 5x + 14=-(x^2-5x-14),\\y=-(x^2-5x+\dfrac{25}{4}-\dfrac{25}{4}-14),\\y=-((x^2-5x+\dfrac{25}{4})-\dfrac{25}{4}-14),\\y=-((x-\dfrac{5}{2})^2-\dfrac{81}{4})=-(x-\dfrac{5}{2})^2+\dfrac{81}{4}.

When x=2.5, y=20.25, then the point (2.5,20.25) is vertex of this third parabola.

4.

y =-x^2 + 7x + 7=-(x^2-7x-7),\\y=-(x^2-7x+\dfrac{49}{4}-\dfrac{49}{4}-7),\\y=-((x^2-7x+\dfrac{49}{4})-\dfrac{49}{4}-7),\\y=-((x-\dfrac{7}{2})^2-\dfrac{77}{4})=-(x-\dfrac{7}{2})^2+\dfrac{77}{4}.

When x=3.5, y=19.25, then the point (3.5,19.25) is vertex of this fourth parabola.

5.

y =2x^2 + 7x +5=2(x^2+\dfrac{7}{2}x+\dfrac{5}{2}),\\y=2(x^2+\dfrac{7}{2}x+\dfrac{49}{16}-\dfrac{49}{16}+\dfrac{5}{2}),\\y=2((x^2+\dfrac{7}{2}x+\dfrac{49}{16})-\dfrac{49}{16}+\dfrac{5}{2}),\\y=2((x+\dfrac{7}{4})^2-\dfrac{9}{16})=2(x+\dfrac{7}{4})^2-\dfrac{9}{8}.

When x=-1.75, y=-1.125, then the point (-1.75,-1.125) is vertex of this fifth parabola.

6.

y =-2x^2 + 8x +5=-2(x^2-4x-\dfrac{5}{2}),\\y=-2(x^2-4x+4-4-\dfrac{5}{2}),\\y=-2((x^2-4x+4)-4-\dfrac{5}{2}),\\y=-2((x-2)^2-\dfrac{13}{2})=-2(x-2)^2+13.

When x=2, y=13, then the point (2,13) is vertex of this sixth parabola.

3 0
3 years ago
PLZ HELP!!!!!!!<br>Solve for x​
Lunna [17]

Answer:

100

Step-by-step explanation:

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6 0
3 years ago
1.1
solniwko [45]

Answer:

Cost = 112.266 cent/km

Step-by-step explanation:

Given

Unit\ cost = R17.82/litre

Rate = 6.3litre/100km

Required

The fuel cost in cent\ per\ km

This is calculated using:

Cost = Unit\ cost * Rate

Cost = R17.82/litre * 6.3litre/100km

Cost = R17.82 * 6.3/100km

Cost = R1.12266/km

Multiply by 100 to get the cost in cents

Cost = 1.12266 * 100 cent/km

Cost = 112.266 cent/km

6 0
2 years ago
14) Simplify: -(16 - 5x) A) 5x - 16 B) 5x + 16 C) -5x - 16 D) - 5x + 16
VLD [36.1K]

Answer: 5x-16

<u>Switch operations</u>

Before: -(16 - 5x)

After: 5x-16

Before you switch operation you remove the subtraction sign where -(16) is.

5 0
3 years ago
A square pyramid. The square base has side lengths of 6 inches. The 4 triangular sides have a base of 6 inches and height of 9 i
Marrrta [24]

Answer:

The area of the pyramid’s base is 36 in².

The pyramid has 4 lateral faces.  

The surface area of each lateral face is 27 in².

Step-by-step explanation:

"<u>Lateral</u>" means side, so the lateral faces are <u>triangles</u>.

The <u>base</u> is the bottom, which is a <u>square</u>.

To calculate the <u>area of the base</u>, use the formula for area of a square.

A_{base} = s^{2}

A_{base} = (6 in)^{2}

A_{base} = 36 in^{2}

To calculate the <u>area of a lateral face</u>, find the area of a triangle.

A_{lateral} = \frac{bh}{2}

A_{lateral} = \frac{(6 in)(9 in)}{2}

A_{lateral} = \frac{54 in^{2}}{2}

A_{lateral} = 27 in^{2}

In a pyramid, the number of lateral faces is the same as the number of sides in the base. <u>The square base as 4 sides, so there are 4 lateral faces</u>.

3 0
3 years ago
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