Mathematics, 04.12.2020 22:10 kendalljanae

4x^2-15x-4

factorise please

Answers: 2

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Answer from: hannahkharel2

$\boxed{4x^2-15x-4=(x-4)(4x+1)}$ Solution Steps:

______________________________

1.) Change the equation using factored transformation: 4x^2-15x-4=0

- Quadratic polynomial can be factored using the transformation $ax^2+bx+c=a(x-x_{1})(x-x_{2})$ , where $x_{1}$ and $x_{2}$ are the solutions of the quadratic equation ax^2+bx+c=0 .

- This steps basically means change you current equation using the formula ax^2+bx+c=0 .

2.) Turn the factored form into the quadratic equation form: $x=\frac{-(-15)\frac{+}{}\sqrt{(-15)^2-4\bold{x}4(-4)}}{2\bold{x}4}$

- All equations of the form ax^2+bx+c=0 can be solved using the quadratic formula: $\sqrt{\frac{-b\frac{+}{}\sqrt{b^2-4ac}}{2a} }$ .

- The quadratic equation formula gives two solutions, one when $\frac{+}{}$ is addition and one when it is subtraction.

3.) Square -15: -15^2=225

Equation at the end of Step 3:

$x=\frac{-(-15)\frac{+}{}\sqrt{225-4\bold{x}4(-4)}}{2\bold{x}4}$

4.) Multiply −4 times 4:

Equation at the end of Step 4:

$x=\frac{-(-15)\frac{+}{}\sqrt{225-16(-4)}}{2\bold{x}4}$ 5.) Multiply −16 times −4:

Equation at the end of Step 5:

$x=\frac{-(-15)\frac{+}{}\sqrt{225+64}}{2\bold{x}4}$ 6.) Add 225 to 64: 225+64=289

Equation at the end of Step 6:

$x=\frac{-(-15)\frac{+}{}\sqrt{289}}{2\bold{x}4}$ 7.) Take the square root of 289: $\sqrt{289}=17$

Equation at the end of Step 7:

$x=\frac{-(-15)\frac{+}{}17}{2\bold{x}4}$ 8.) Change -15 to positive 15: -15=15

Equation at the end of Step 8:

$x=\frac{15\frac{+}{}17}{2\bold{x}4}$ 9.) Multiply 2 by 4:

Equation at the end of Step 9:

$x=\frac{15\frac{+}{}17}8}$ 10.) Now Solve:

Now solve the equation $x=\frac{15\frac{+}{}17}8}$ when $\frac{+}{}$ is plus.

Add 15 to 17:

$x=\frac{32}{8}$

Divide 32 by 8:

Now solve the equation $x=\frac{15\frac{+}{}17}8}$ when $\frac{+}{}$ is minus.

Subtract 15 by 17:

$x=\frac{-2}{8}$

Reduce the fraction to lowest terms by extracting and canceling out 2:

$x=-\frac{1}{4}$ 11.) Factor the expression:

Factor the original expression using $ax^2+bx+c=a(x-x_{1})(x-x_{2})$ . Substitute 4 for $x_{1}$ and $-\frac{1}{4}$ for $x_{2}$ :

$4x^2-15x-4=4(x-4)(x-(-\frac{1}{4}))$

Simplify all the expressions of the form p-(-q) to p+q :

$4x^2-15x-4=4(x-4)(x+\frac{1}{4})$

Add $\frac{1}{4}$ to x by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible:

$4x^2-15x-4=4(x-4)\bold{x}(\frac{4x+1}{4})$

Cancel out 4, the greatest common factor in 4 and 4:

______________________________

Answer from: Quest

c. x=2.4cm

step-by-step explanation:

similar triangles are triangles which have the same shape but not the same size. this means their angle measures are equal but their side lengths are not instead they are proportional. to solve, we will set up a proportion and solve.

a proportion is two equal ratios set equal to each other. we form the ratios by finding corresponding sides (sides which match to each other on both triangles by their position). out ratios will be one side of the small triangle over the corresponding side on the big triangle as shown below:

$\frac{little}{big} =\frac{side mn}{side ab}=\frac{side on}{side cb}$ .

$\frac{0.96}{1.2}=\frac{x}{3}$

to solve the proportion, we'll cross multiply by multiplying numerator with denominator across the equal sign.

$0.96(3)=1.2(x)\\2.88=1.2x\\\frac{2.88}{1.2}=\frac{1.2x}{1.2} \\2.4=x$

Answer from: Quest

the correct answer is a) "catholic church".

the proposals that liberals in mexico made during 1855 were particularly focused on a person's individual rights, such as the freedom of speech, the freedom of conscience, freedom of assembly, and the right to possess weapons.

when the constitution was formally published 2 years later (1857). it also contained an article which permitted education free from any religious influence, the removal of the catholic church institutional privileges, and the sale of property belonging to the church. all of these provisions were clearly against the catholic church interests.

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