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antiseptic1488 [7]
3 years ago
9

8/7 = 12/k solve for k

Mathematics
2 answers:
Serjik [45]3 years ago
7 0

Answer:

k = 10.5

Step-by-step explanation:

8/7 = 12/k

Using cross products

8k = 7*12

8k = 84

Divide each side by 8

8k/8 = 84/8

k = 10.5

devlian [24]3 years ago
5 0

Answer:

k= 10.5

Step-by-step explanation:

We can solve this by using cross multiplication

We multiply the values across from each other

8k=7(12)

Then we multiply 7 and 12, and then divide by 8

8k=84

k= 10.5

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What is the slope of y = 2x + 4
Tamiku [17]

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Step-by-step explanation:

The slope intercept form states that y=mx+b

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Solve the equation by graphing. If exact roots cannot be found, state the consecutive integers between which the roots are locat
eimsori [14]

Answer:

There are NO real roots for this equation. The only roots have imaginary parts and therefore cannot be represented on the real x-axis.

Step-by-step explanation:

We notice that the expression on the left of the equation is a quadratic with leading term 2x^2, which means that its graph is that of a parabola with branches going up.

Therefore, there can be three different situations:

1) if its vertex is ON the x axis, there would be one unique real solution (root) to the equation.

2) if its vertex is below the x-axis, the parabola's branches are forced to cross it at two locations, giving then two real solutions (roots) to the equation.

3) if its vertex is above the x-axis, it will have NO real solutions (roots) but only non-real ones.

So we proceed to examine the vertex's location, which is also a great way to decide on which set of points to use in order to plot its graph efficiently.

We recall that the x-position of the vertex for a quadratic function of the form  f(x)=ax^2+bx+c is given by the expression:

x_v=\frac{-b}{2a}

Since in our case a=2 and b=-3, we get that the x-position of the vertex is:

x_v=\frac{-b}{2a}\\x_v=\frac{-(-3)}{2(2)}\\x_v=\frac{3}{4}

Now we can find the y-value of the vertex by evaluating this quadratic expression for x = 3/4:

y_v=f(\frac{3}{4})=2( \frac{3}{4})^2-3(\frac{3}{4})+4\\f(\frac{3}{4})=2( \frac{9}{16})-\frac{9}{4}+4\\f(\frac{3}{4})=\frac{9}{8}-\frac{9}{4}+4\\f(\frac{3}{4})=\frac{9}{8}-\frac{18}{8}+\frac{32}{8}\\f(\frac{3}{4})=\frac{23}{8}

This is a positive value for y, therefore we are in the situation where there is NO x-axis crossing of the parabola's graph, and therefore no real roots.

We can though estimate a few more points of the parabola's graph in order to complete the graph as requested in the problem. For such we select a couple of x-values to the right of the vertex, and a couple to the right so we can draw the branches. For example: x = 1, and x = 2 to the right; and x = 0 and x = -1 to the left of the vertex:

f(-1) = 2(-1)^2-3(-1)+4= 2+3+4=9\\f(0)=2(0)^2-3(0)+4=0+0+4=4\\f(1)=2(1)^2-3(-1)+4=2-3+4=3\\f(2)=2(2)^2-3(2)+4=8-6+4=6

See the graph produced in the attached image.

4 0
3 years ago
Need help with number 7
tatyana61 [14]

Since she runs 6\frac{1}{2} miles each day and there 7 days per week, you will have to multiply 6\frac{1}{2} times 7.

But since you have to use distributive properties, multiply like this (6\frac{1}{2})(7)

6\frac{1}{2} is equal to \frac{13}{2}

Now turn 7 into a fraction, so its \frac{7}{1}

Now multipy (6\frac{1}{2})(\frac{7}{1})

Multiply the numerators, so its 7 * 13 which gives you 91 and multiply the denominators so its 1 * 2 which gives you 2.

Put that back into a fraction as \frac{91}{2}

Divde it to change it to a mixed number and the answer is 45\frac{1}{2}

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soldi70 [24.7K]

Answer:

Translate right 7 units (x+7)

Reflect over x-axis (-y) and translate down 6 units (-y - 6)

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