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4 years ago

A first number plus twice a second number is 11. Twice the first number plus the second totals 31 find the numbers

1 answer:

5 0

X + 2y = 11
2x + y = 31

x = 11 - 2y

2(11 - 2y) + y = 31
22 - 4y + y = 31
3y = - 9
y = - 3

x = 11 - 2(-3)
x = 11 + 6
x = 17

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I have these factoring questions I need help with.

snow_lady [41]

$f(x)=4x^2+4x-3$

1. Determine y-intercept.

The y-intercept is (0,-3). Substitute x = 0 in the equation as we get f(x) = -3 as the y-intercept.

2. Determine the zeros.

Factor the polynomials first. $(2x-1)(2x+3)$ This is the factored form. The zeros are the roots of equation. Therefore, the zeros are 1/2 and -3/2

3. Determine the Axis of Symmetry

We can solve this by using the formula of $x=-\frac{b}{2a}$ However, I'll be solving the Axis of Symmetry with Calculus instead.

$f'(x)=2(4x^{2-1})+1(4x^{1-1})-0\\f'(x)=8x+4$

Then let f'(x) = 0 to find the Axis of Symmetry.

$8x+4=0\\8x=-4\\x=-\frac{4}{8}\\x=-\frac{1}{2}$

Therefore, the Axis of Symmetry is -1/2

4. Determine the vertex.

Substitute the value of Axis of Symmetry in f(x).

$f(x)=4(-\frac{1}{2})^2+4(-\frac{1}{2})-3\\f(x)=4(\frac{1}{4})-2-3\\f(x)=1-2-3\\f(x)=-4$

Therefore the vertex is at (-1/2, -4)

5. Does the vertex representing max-pont or min-point?

The vertex represents the minimum point. The graph is upward, meaning the minimum point is the point that gives the LOWEST Y-VALUE.

7. Graph f(x)

Unfortunately I won't be able to graph. But I can tell you to graph a parabola that has the most curve at the vertex and intercepts y-axis at (0,-3).

--------------------------- End of Part 1 --------------------------------

2. Write the general form of Quadratic Function in standard form.

$y=ax^2+bx+c$

The graph can be easily determined about the y-intercept and being an upward or downward parabola along with how narrow or wide the parabola is.

For example, c value is the y-intercept as defined. When a > 0, the parabola is upward and when a < 0, the parabola is downward. The more value of | a | is, the more narrow it will be and the less value of | a | it is, the wider it will be.

3. Write in Factored Form

$y=(x+a)(x+b)\\y=(x-a)(x-b)\\y=(x+a)(x-b)\\y=(x-a)(x+b)$

These are factored forms with different types of operators.

The equation can be easily determined about the roots of equation. For example, if the function is in f(x) = (x+2)(x-1) Then the roots would be x = -2 and 1 as the graph will intercept x-axis at (-2,0) and (1,0)

4. Write in Vertex Form.

$y=a(x-h)^2+k$

The equation can be easily determined for the vertex, axis of symmetry and the same narrow/wide/upward/downward parabola again.

The vertex is at (h,k) and the axis of symmetry is at x = h.

For example, $y=(x-2)^2+3$

The vertex would be at (2,3) and the axis of symmetry is x = 2.

3 0

3 years ago

The question was not clear for me! Help :(

Vsevolod [243]

Answer:

0.1 , 0.2 , 0.05

Step-by-step explanation:

*each column adds to 1*

20 x 1/2 = 10

1/2 x 20 x 0.1 = 1

top left box = 0.1

; 5 x 2 x 0.1 = 1

1/2 x 10 = 5

; 0.2 x 1/2 x 10 = 1

bottom middle box = 0.2

; 5 x 1 x 0.2 = 1

; 2 x 10 x 0.05 = 1

middle right box = 0.05

; 20 x 1 x 0.05

5 0

3 years ago

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In what shape are lateral faces of a pyramid?

atroni [7]

congruent isosceles triangles

7 0

3 years ago

Anyone solve these questions plz

LuckyWell [14K]

Answer:

5)7:8=180

84:96=180

6)4:5=90

40:50=90

7)a). q=135

p=45

b).a=70

b=110

supplementary angle=sum of two angle 180°

complementary angle=sum of two angle 90°

3 0

3 years ago

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Every

maw [93]

Answer: $66.7

Step-by-step explanation:

Answer:The equation for inverse proportion is calculated as xy=k.

When 20 people attend the picnic, the cost for each person was $50, then k will be= 20 × 50 = 1000

Recall that k = xy

For the second aspect of the question, x= 15, k= 1000.

k= xy

y = k/x

= 1000/15

= 66.7

If 15 people attend the picnic instead, the cost per person will be $66.7

8 0

4 years ago