How to find an equation for the line that passes through the points (-6, 2) and (2, 4)

-12x2 + 45x + 12

bazaltina [42]

Answer:

3(4x + 1)(x - 4) Answer choice B

Step-by-step explanation:

-12x^2 + 45 + 12

You would take out the -3 in the equation.

-3(4x^2 -15x - 4)

You can then multiply the first 4 and the last -4 and get a -16. You can then find two numbers that would multiply to -16 and add to -15.

You would do this by listing the factors of -16, which the numbers 1 and -16 would work.

You would then substitute each value in for the 17x and add them together, which this is just separating the value 17x.

3(4x^2 - 16x + x - 4)

3(4x^2 - 16x)(x - 4)

You can then take ou ta four for the first function in the parentheses.

3(4x(x - 4) 1(x - 4))

Then you take the function from the outside and the inside.

3(4x + 1)(x - 4)

The answer to the question would be B.

8 0

3 years ago

1/2x + 1/3y = 7

pashok25 [27]

let's multiply both sides in each equation by the LCD of all fractions in it, thus doing away with the denominator.

$\begin{cases} \cfrac{1}{2}x+\cfrac{1}{3}y&=7\\\\ \cfrac{1}{4}x+\cfrac{2}{3}y&=6 \end{cases}\implies \begin{cases} \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{6}}{6\left( \cfrac{1}{2}x+\cfrac{1}{3}y \right)=6(7)}\\\\ \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{12}}{12\left( \cfrac{1}{4}x+\cfrac{2}{3}y\right)=12(6)} \end{cases}\implies \begin{cases} 3x+2y=42\\ 3x+8y=72 \end{cases} \\\\[-0.35em] ~\dotfill$

$\bf \stackrel{\textit{using elimination}}{ \begin{array}{llll} 3x+2y=42&\times -1\implies &\begin{matrix} -3x \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~-2y=&-42\\ 3x+8y-72 &&~~\begin{matrix} 3x \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~+8y=&72\\ \cline{3-4}\\ &&~\hfill 6y=&30 \end{array}} \\\\\\ y=\cfrac{30}{6}\implies \blacktriangleright y=5 \blacktriangleleft \\\\[-0.35em] ~\dotfill$

$\bf \stackrel{\textit{substituting \underline{y} on the 1st equation}~\hfill }{3x+2(5)=42\implies 3x+10=42}\implies 3x=32 \\\\\\ x=\cfrac{32}{3}\implies \blacktriangleright x=10\frac{2}{3} \blacktriangleleft \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \left(10\frac{2}{3}~~,~~5 \right)~\hfill$

7 0

3 years ago

Seamstress Jane has purchased 50 yards of red fabric and 110 yards of gold fabric to make red and gold curtains. What is the lar

Alisiya [41]

Answer: There are 10 largest number of curtains she can make if she wants all the curtains to be exactly the same length.

There are 5 red fabrics and 11 gold fabrics that would be used for each curtain.

Step-by-step explanation:

Since we have given that

Number of yards of red fabric purchased by Jane = 50

Number of yards of gold fabric purchased by Jane = 110

We need to find the largest number of curtains she can make if she wants all the curtains to be exactly the same length.

For this we will find H.C.F. of 50 and 110.

Factors of 50 = 1, 2, 5, 10, 25, 50.

Factors of 110 = 1, 2, 5, 10, 11, 22, 55, 110.

So, Highest common factor of 50 and 110 is 10.

So, there are 10 largest number of curtains she can make if she wants all the curtains to be exactly the same length.

Number of yards of red fabric is given by

$\frac{50}{10}=5$

Number of yards of gold fabric is given by

$\frac{110}{10}=11$

Hence, there are 5 red fabrics and 11 gold fabrics that would be used for each curtain.

4 0

3 years ago

Which is the best estimate of 11 and one-fifth divided by 2 and three-fourths?

Scrat [10]

Answer:

4 should be the answer to the question

5 0

3 years ago

Read 2 more answers

Please help question in the picture

Tju [1.3M]

We can think of this as a right triangle, where the given lengths are the legs.

So, we can solve using the Pythagorean Theorem.

21² + 28² = c²

441 + 784 = c²

1225 = c²

35 = c

35 miles

8 0

3 years ago