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3 years ago

What is the value of c in the equation y = 4x^2 -10x + c if the y-coordinate of the vertex is -7

Mathematics

1 answer:

love history [14]3 years ago

6 0

Answer: $c=-\frac{3}{4}$

Step-by-step explanation:

Find the x-coordinate of the vertex with this formula:

$x=\frac{-b}{2a}$

In this case:

$a=4\\b=-10$

Substituting values, we get:

$x=\frac{-(-10)}{2(4)}=\frac{5}{4}$

Now we can substitute the coordinates of the vertex into the equation $y = 4x^2 -10x + c$ and then solve for "c".

Then:

$-7 = 4(\frac{5}{4})^2 -10(\frac{5}{4}) + c\\\\-7+\frac{25}{4}=c\\\\c=-\frac{3}{4}$

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Work out m and c for the line: 2x + 3y +1=0 m= c =

Sergio [31]

Answer:

m = - $\frac{2}{3}$ , c = - $\frac{1}{3}$

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Given

2x + 3y + 1 = 0 ( subtract 2x + 1 from both sides )

3y = - 2x - 1 ( divide terms by 3 )

y = - $\frac{2}{3}$ x - $\frac{1}{3}$ ← in slope- intercept form

with m = - $\frac{2}{3}$ and c = - $\frac{1}{3}$

4 0

2 years ago

Is 593÷6 is a little less than 10 a little more than 10 a little less than 100 a little more than 100 explain

DerKrebs [107]

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Hope this helps!

4 0

3 years ago

Factor Trinomials:

notka56 [123]

Answer:

1. $2(x+2)(x+5)$

2. $8(x+4)^{2}$

Step-by-step explanation:

Problem #1:

1. Find the GCF (Greatest Common Factor)

$GCF = 2$

2. Factor out the GCF and simplify.

$2(x^{2} +7x+10)$

3. Factor $x^{2} +7x+10$

Which two numbers add up to 7 and multiply to 10?

2 and 5

Rewrite the expression using the above.

$(x+2)(x+5)$

4. Done!

$2(x+2)(x+5)$

Problem #2:

1. Find the GCF (Greatest Common Factor)

$GCF=8$

2. Factor out the GCF and simplify.

$8(x^{2} +8x+16)$

3. Use the perfect square formula. $a^{2} +2ab+b^{2} =(a+b)^{2}$

$a = x\\b=4$

$(x+4)^{2}$

4. Done!

$8(x+4)^{2}$

8 0

2 years ago

Help please:Suppose that x and y inversely, and x=10 when y=8 write the function that models the inverse variation

jarptica [38.1K]

SOLUTION

From the question, we are told that y varies inversely as x

This is mathematically written as

$\begin{gathered} y\propto\frac{1}{x} \\ \propto\text{ is a sign of proportionality } \end{gathered}$

Now, we will remove the proportionality sign and replace it with equal to sign =

If we do this, we will intoduce a constant k

$\begin{gathered} y\propto\frac{1}{x} \\ y=k\times\frac{1}{x} \\ y=\frac{k}{x} \end{gathered}$

So we have the formula

$y=\frac{k}{x}$

We will substitute the values of x for 10 and y for 8 into the formula to get k, we have

$\begin{gathered} y=\frac{k}{x} \\ 8=\frac{k}{10} \\ k=8\times10 \\ k=80 \end{gathered}$

Now, we will substitute k for 80 back into the formula to get the inverse function, we have

$\begin{gathered} y=\frac{k}{x} \\ y=\frac{80}{x} \end{gathered}$

Hence the answer is option C

7 0

1 year ago

7th Grade Math Please help -7 = 1/3 a Find the value of a

julsineya [31]

Answer:

$\huge\boxed{a=-21}$

Step-by-step explanation:

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4 0

3 years ago