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3 years ago

Graph the system of inequalities presented here on your own paper, then use your graph to answer the following questions:

Mathematics

1 answer:

valentinak56 [21]3 years ago

3 0

Here's a graph.

Part A: The graph is a shaded region with one corner and two edges that goes forever. It's only located on the right side of the y axis.

Part B: It's not a solution because it's not in the graph.

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Which values of x make the equation |x - 7| = x - 7 true? 9 0 3 8 -7

Vlad [161]

-7
I might not be right but that’s what I got.

3 0

3 years ago

Angus has $3,000 he want to invest. What interest rate compounded continuously does an account need to offer so that Angus has $

kaheart [24]

Answer:

The interest rate is 7.58%

Step-by-step explanation:

Compound continuous interest can be calculated using the formula:

A = P $e^{rt}$ , where

A is the future value of the investment, including interest

P is the principal investment amount (the initial amount)

r is the interest rate in decimal

t is the time the money is invested for

∵ Angus has $3,000 he want to invest

∴ P = 3000

∵ The interest rate is compounded continuously

∵ Angus has $5,500 in 8 years

∴ A = 5500

∴ t = 8

→ Substitute them in the rule above to find r

∵ 5500 = 3000 $e^{8r}$

→ Divide both sides by 3000

∴ $\frac{11}{6}$ = $e^{8r}$

→ Insert ㏑ in both sides

∵ ㏑( $\frac{11}{6}$ ) = ㏑( $e^{8r}$ )

→ Remember ㏑( $e^{n}$ ) = n

∴ ㏑( $\frac{11}{6}$ ) = 8r

→ Divide both sides by 8

∴ 0.07576697545 = r

→ Multiply it by 100% to change it to a percentage

∴ r = 0.07576697545 × 100%

∴ r = 7.576697545 %

→ Round it to the nearest hundredth

∴ r ≅ 7.58

∴ The interest rate is 7.58%

3 0

2 years ago

Find the domain and range of the function represented by the graph

lora16 [44]

Answer:

4(b) , 5(a)

Step-by-step explanation:

(4). (b) Domain is {0, 1, 2, 3} and Range is { - 3, - 2, - 1, 0}

(5). (a) Domain is [ - 4, 2] and Range is [ - 4, 4]

domain: - 4 ≤ x ≤ 2 , range: - 4 ≤ y ≤ 4

6 0

3 years ago

Please help!! Thank you so much in advance :)

meriva

Answer:

Step-by-step explanation:

x = 1 - i sqrt(2) ^ y = 10 + i sqrt(2)

x = 1 + i sqrt(2) ^ y = 10 - i sqrt(2)

6 0

2 years ago

Read 2 more answers

Find the vertex point, axis of symmetry, x-intercepts, and y-intercept of the

Bond [772]

Answer:

1) Vertex point (-1.5,-20.25)

2) axis of symmetry: x=-1.5

3) x-intercepts: (-6,0) and (3,0)

4) y-intercept: (0,18)

5) Graph in attachment.

Step-by-step explanation:

1) The given parabola has equation:

$y = {x}^{2} + 3x - 18$

We need to complete the square.

$y = {x}^{2} + 3x + {1.5}^{2} - {1.5}^{2} - 18$

$y = ( {x + 1.5)}^{2} - 20. 25$

This function is in the vertex form:

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

where (h,k) is the vertex, x=h is the axis of symmetry.

By comparing our equation to the general vertex form:

The vertex point is (-1.5,-20.25)

2) The axis of symmetry divides the parabola into two congruent halves.

Since this is a vertical parabola, the axis of symmetry occuring at x=h is a vertical line.

The axis of symmetry is x=-1.5

3) Y-INTERCEPT.

The y-intercept is the point where the graph cross the y-axis.

At this point, the value of x is zero.

To find the y-intercept, we substitute x=0 in the equation of the parabola and simplify.

when x=0,

$y = {(0)}^{2} + 3(0) - 18 = - 18$

The y-intercept is (0,-18).

4) X-INTERCEPT

The x-intercepts are the points where the graph touches or intersect the x-axis.

To find the x-intercept, we substitute y=0.

$( {x + 1.5)}^{2} - 20.25 = 0$

Add 20.25 to both sides;

$( {x + 1.5)}^{2} = 20.25$

Take square root.

$(x + 1.5)= \pm \sqrt{20.25}$

$x = - 1.5\pm 4.5$

$x = - 1.5 - 4.5 \: \: or \: \: x = - 1.5 + 4.5$

$x = - 6 \: or \: x = 3$

The x-intercepts are(-6,0) and (3,0).

4) GRAPH

To graph this function, we can use transformation.

To graph the function,

$y = {(x + 1.5)}^{2} - 20.25$

We shift the parent quadratic function 1.5 units left and 20.25 units down.

See attachment for graph.

5 0

3 years ago