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3 years ago

What is the answer to this equation 4x-9=2x+5

Mathematics

2 answers:

photoshop1234 [79]3 years ago

5 0

4x-9=2x+5
4x-2x=9+5
2x=14
divide both sides by 2
x=7

Amiraneli [1.4K]3 years ago

4 0

X =7 is the answer. To solve one must combine like terms. Because I find it easier to work with positive numbers, I added 9 to both sides of the equation and subtracted 2x from each side, leaving 2x = 14. Then I divided each side of The equation by two, giving me x =7.

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Could someone help me rnnn?

GuDViN [60]

Answer:

vertex = (0, -4)

equation of the parabola: $y=3x^2-4$

Step-by-step explanation:

Given:

y-intercept of parabola: -4
parabola passes through points: (-2, 8) and (1, -1)

Vertex form of a parabola: $y=a(x-h)^2+k$

(where (h, k) is the vertex and $a$ is some constant)

Substitute point (0, -4) into the equation:

$\begin{aligned}\textsf{At}\:(0,-4) \implies a(0-h)^2+k &=-4\\ah^2+k &=-4\end{aligned}$

Substitute point (-2, 8) and $ah^2+k=-4$ into the equation:

$\begin{aligned}\textsf{At}\:(-2,8) \implies a(-2-h)^2+k &=8\\a(4+4h+h^2)+k &=8\\4a+4ah+ah^2+k &=8\\\implies 4a+4ah-4&=8\\4a(1+h)&=12\\a(1+h)&=3\end{aligned}$

Substitute point (1, -1) and $ah^2+k=-4$ into the equation:

$\begin{aligned}\textsf{At}\:(1.-1) \implies a(1-h)^2+k &=-1\\a(1-2h+h^2)+k &=-1\\a-2ah+ah^2+k &=-1\\\implies a-2ah-4&=-1\\a(1-2h)&=3\end{aligned}$

Equate to find h:

$\begin{aligned}\implies a(1+h) &=a(1-2h)\\1+h &=1-2h\\3h &=0\\h &=0\end{aligned}$

Substitute found value of h into one of the equations to find a:

$\begin{aligned}\implies a(1+0) &=3\\a &=3\end{aligned}$

Substitute found values of h and a to find k:

$\begin{aligned}\implies ah^2+k&=-4\\(3)(0)^2+k &=-4\\k &=-4\end{aligned}$

Therefore, the equation of the parabola in vertex form is:

$\implies y=3(x-0)^2-4=3x^2-4$

So the vertex of the parabola is (0, -4)

5 0

3 years ago

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ABCD is a rhombus, where m∠AED = 5x – 10. Use the properties of a rhombus to determine the value of x. Question 10 options: A) x

fomenos

Answer:

A) x = 20

Step-by-step explanation:

ABCD is a rhombus, AC and BD are diagonals which intersect each other at point E.

Since, diagonals of a rhombus are perpendicular bisector.

$\therefore \: m \angle AED = 90 \degree \\ \therefore \: (5x - 10) \degree = 90 \degree \\ \therefore \: 5x - 10 = 90 \\ \therefore \: 5x = 90 + 10 \\ \therefore \: 5x = 100 \\ \\ \therefore \: x = \frac{100}{5} \\ \\ \huge \red{ \boxed{ \therefore \: x =20}}$

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3 years ago

write an equation in slope intercept form for a line that passed through the two points below (-4, -5) (4,1)

topjm [15]

Y= 3/4x - 2
Hope this helps!!!!!

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Answer:

Step-by-step explanation:

It is really easy just subtract the money with the percentage

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Natalka [10]

Answer:

Step-by-step explanation:

Solving inequalities is easy, you just need to follow the standard rules of algebra. Also, when multiplying or dividing by a negative number, the inequality sign is reversed.

Step 1: Divide by 5

x < 2

Step 2: Check

5(1) < 10

5 < 10✔️

Step 3: Check Again

Since an inequality has multiple solutions, it is important to check at least 2, to determine if the entire range of solutions is true.

5(-6) < 10

-30 < 10✔️

Step 4: Verified Answer

x < 2

I'm always happy to help :)

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3 years ago

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