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3 years ago

180 red marbles to 145 blue marbles write the ratio in simplest form

Mathematics

1 answer:

slamgirl [31]3 years ago

4 0

The ratio of red marbles to blue marbles in simplest form is 36:29

Step-by-step explanation:

Given,

Number of red marbles = 180

Number of blue marbles = 145

Ratio;

Red marbles : Blue marbles

$180:145$

As both are multiples of 5;

$\frac{180}{5}:\frac{145}{5}\\36:29$

The ratio of red marbles to blue marbles in simplest form is 36:29

Keywords: multiples, ratio

Learn more about ratio at:

#LearnwithBrainly

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Sonbull [250]

Answer:

$-6 < k < 2$

Step-by-step explanation:

Given

$y = x^2 - 2x$

$y =kx -4$

Required

Possible values of k

The general quadratic equation is:

$ax^2 + bx + c = 0$

Subtract $y = x^2 - 2x$ and $y =kx -4$

$y - y = x^2 - 2x - kx +4$

$0 = x^2 - 2x - kx +4$

Factorize:

$0 = x^2 +x(-2 - k) +4$

Rewrite as:

$x^2 +x(-2 - k) +4=0$

Compare the above equation to: $ax^2 + bx + c = 0$

$a = 1$

$b= -2-k$

$c =4$

For the equation to have two distinct solution, the following must be true:

$b^2 - 4ac > 0$

So, we have:

$(-2-k)^2 -4*1*4>0$

$(-2-k)^2 -16>0$

Expand

$4 +4k+k^2-16>0$

Rewrite as:

$k^2 + 4k - 16 + 4 >0$

$k^2 + 4k - 12 >0$

Expand

$k^2 + 6k-2k - 12 >0$

Factorize

$k(k + 6)-2(k + 6) >0$

Factor out k + 6

$(k -2)(k + 6) >0$

Split:

$k -2 > 0$ or $k + 6> 0$

So:

$k > 2$ or k $> -6$

To make the above inequality true, we set:

$k < 2$ or $k >-6$

So, the set of values of k is:

$-6 < k < 2$

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3 years ago

Please help me with this! Very much appreciate

Setler [38]

Answer:

The answers for your two problems, can be found below in the attached images.

Problem 1

Graph

The graph was plotted using a calculator. We can see that the graph opens up.

f(x) = x^2 + 4x +3

Vertex

The vertex is the minimum point of the equation

In this case Vertex (V) = (-2,-1)

Axis of symmetry

The x axis corresponding to the vertex component

x = -2

y intercept

Interception with the y-axis

From the first attached image, we can see that they y intercept occurs

at x = 0, y = 3

(0,3)

Problem 2

Graph.

The graph was plotted using a calculator. We can see that the graph opens up.

f(x) = 2x^2 + 3x +1

Vertex

The vertex is the minimum point of the equation

In this case Vertex (V) = (-0.75,-0.125)

Axis of symmetry

The x axis corresponding to the vertex component

x = -0.75

y intercept

Interception with the y-axis

From the second attached image, we can see that they y intercept occurs

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Ash company reported sales of $580,000 for year 1, $630,000 for year 2, and $680,000 for year 3. Using year 1 as the base year,

Elenna [48]

Answer:

Year 2: 109.4%

Year 3: 118.9%

Step-by-step explanation:

<h3>Given;</h3>

Ash company reported sales of $580,000 for year 1
$630,000 for year 2,
$680,000 for year 3.

Now,

For the revenue trend percent for year 2

Year 2: $580,000 / $530,000 × 100 = 109.4%

For the revenue trend percent for year 3

Year 3: $630,000 / $530,000 × 100 = 118.9%

Thus, The answer is 109.4% and 118.9%.

<u>-TheUnknownScientist 72</u>

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