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3 years ago

1) How is unit rate related to slope or rise over run?

Mathematics

1 answer:

quester [9]3 years ago

8 0

The unit rate is a ratio of change in y and into the change on x. It can also be the rise to run or the slope.

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One of the roots of the quadratic equation dx^2+cx+p=0 is twice the other, find the relationship between d, c and p

scZoUnD [109]

Answer:

$c^2 = 9dp$

Step-by-step explanation:

Given

$dx^2 + cx + p = 0$

Let the roots be $\alpha$ and $\beta$

So:

$\alpha = 2\beta$

Required

Determine the relationship between d, c and p

$dx^2 + cx + p = 0$

Divide through by d

$\frac{dx^2}{d} + \frac{cx}{d} + \frac{p}{d} = 0$

$x^2 + \frac{c}{d}x + \frac{p}{d} = 0$

A quadratic equation has the form:

$x^2 - (\alpha + \beta)x + \alpha \beta = 0$

So:

$x^2 - (2\beta+ \beta)x + \beta*\beta = 0$

$x^2 - (3\beta)x + \beta^2 = 0$

So, we have:

$\frac{c}{d} = -3\beta$ -- (1)

and

$\frac{p}{d} = \beta^2$ -- (2)

Make $\beta$ the subject in (1)

$\frac{c}{d} = -3\beta$

$\beta = -\frac{c}{3d}$

Substitute $\beta = -\frac{c}{3d}$ in (2)

$\frac{p}{d} = (-\frac{c}{3d})^2$

$\frac{p}{d} = \frac{c^2}{9d^2}$

Multiply both sides by d

$d * \frac{p}{d} = \frac{c^2}{9d^2}*d$

$p = \frac{c^2}{9d}$

Cross Multiply

$9dp = c^2$

$c^2 = 9dp$

Hence, the relationship between d, c and p is: $c^2 = 9dp$

8 0

3 years ago

Use the substitution method to solve the system of equations. Choose the

Hatshy [7]

Answer:

(3, 2) is the ordered pair for the given system of equations.

Step-by-step explanation:

Given:

2 x+ y = 8.......................(i)

y = - x + 5........................(ii)

Put y = - x + 5 in equation (i)-

2 x + ( - x+ 5) = 8

2 x - x + 5 = 8

x = 8 - 5

x = 3

Now put x = 3 in equation (ii)-

y = - 3 + 5

y = 2

Hence the (3, 2) is the correct ordered pair.

4 0

3 years ago

Lesson 1 Homework

Nonamiya [84]

128

This question requires us to solve an infinite GP

As we can see the first unit is 16 wide, then 8, then 4 and so on; this can be written as

$64(1,0.5,0.25,0.125,....$ $\infinity$ ∞ $)$ (64 used as 16*4 = 64 is the area of the first rectangle)

We have $S$ ∞ $=a/(1-r)$ where a is the first term and r is the common ratio of the GP for summing an infinite GP.

here we have

$a=64 \\ r=0.5$

Therefore

$S$ ∞ $=\frac{64}{1-0.5} \\\\=\frac{64}{0.5} \\\\=128$

Learn more about GP here

brainly.com/question/16954106

#SPJ9

5 0

2 years ago

Y = 3x – 5 y= 1/2x + 5 Solve

Varvara68 [4.7K]

Answer:

(4, 7 )

Step-by-step explanation:

y = 3x - 5 → (1)

y = $\frac{1}{2}$ x + 5 ( multiply through by 2 to clear the fraction )

2y = x + 10 → (2)

Substitute y = 3x - 5 into (2)

2(3x - 5) = x + 10 ← distribute parenthesis on left side

6x - 10 = x + 10 ( subtract x from both sides )

5x - 10 = 10 ( add 10 to both sides )

5x = 20 ( divide both sides by 5 )

x = 4

Substitute x = 4 into (1) and evaluate for y

y = 3(4) - 5 = 12 - 5 = 7

solution is (4, 7 )

3 0

3 years ago

Read 2 more answers

How many mL (milleters) are in 12.9 liters?

Umnica [9.8K]

The answer is 3. 12, 900

5 0

3 years ago