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3 years ago

Find two consecutive integers whose sum is 123

Mathematics

1 answer:

Helen [10]3 years ago

8 0

I believe it is 61 and 62 I'm not 100% positive tho

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Prudie needs $90 or more to be able to take her family out to dinner. She has already saved $30 and wants to take her family out

Aleks [24]

90≤4x+30

Yes she will have enough. 4 multiplied by 18 is 72. 72+30=102.

Hope this helped.

7 0

3 years ago

Angle 1 and angle 2 form a linear pair.if m angle =5x+9 and m angle 2=3x+11,find the measures of both angels.

lbvjy [14]

Answer: ∠1 = 109° ∠2 = 71°

<u>Step-by-step explanation:</u>

If the two angles form a linear pair, then their sum is 180°

∠1 + ∠2 = 180°

(5x + 9) + (3x + 11) = 180

8x + 20 = 180

8x = 160

x = 20

∠1 = 5x + 9

= 5(20) + 9

= 100 + 9

= 109

∠2 = 3x + 11

= 3(20) + 11

= 60 + 11

= 71

<u> CHECK:</u>

∠1 + ∠2 = 180°

109° + 71° = 180°

180° = 180° $\checkmark$

7 0

3 years ago

Kendra dives off a diving board into the water and then comes back up to the surface. Her dive can be modeled by the equation: ,

MAVERICK [17]

Answer:

1. 6 feet

2. 6.25 feet

3. 1 feet

4. 6 feet

Step-by-step explanation:

The equation is : $h(x)=x^2-7x+6$

1. The diving board is where Kendra dives off. Here, the horizontal distance, x from the diving board is 0.

So, substituting x = 0 in the equation, we get

$h(0)=0^2-7(0)+6$

$=0-0+6$

$=6$

So, the diving board is 6 feet above the surface of the water.

2. From the equation, we known that it is a parabola and the vertex is minimum.

It is the minimum height which represents the depth Kendra dives into the water.

So the $x$ coordinate of the vertex is = $\frac{-b}{2a}$

Here, a and b are the coefficients of linear term and the quadratic terms in the equation. Therefore,

a = 1 and b = -7

∴ x coordinate = $\frac{-(-7)}{2 \times 1}$

$\frac{7}{2}=3.5$

Now substituting to find f(x),

$h(3.5)=(3.5)^2-7(3.5)+6$

= -6.25

Therefore, the diver dives 6.25 feet below the water surface.

3. The horizontal distance from the board the diver enters into the water.

This is the y-intercept and it is the value of x when h(x)=0.

∴ $0=x^2-7x+6$

Factorizing, we get $(x-1)(x-6)=0$

∴ $x=1 \text{ or}\ x=6$

So there are two solutions that are the two x intercepts of the function. Here at x = 1 shows the horizontal distance from the board from where Kendra dives into the water.

4. We know that the equation given has $\text{two}$ x intercepts. These two x intercepts are the points where the parabola crosses the x-axis, which is the height $h(x)=0$ . The height is the water surface level.