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3 years ago

Which is the best estimate of the solution to this system of equations ?

Mathematics

2 answers:

mafiozo [28]3 years ago

7 0

Answer:

A. Close to (4,2)

Step-by-step explanation:

When solving a system of equations by setting them equal to one another, the resulting co-ordinates models the coordinates at which the lines intersect. In this case, from the graph, it looks like the lines cross at about 4 on the x-scale, and about 2 on the y-scale.

Ket [755]3 years ago

6 0

The answer is (4,2). The solution to a system of equations is when there is an intersection.

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15x^2 + 41x + 28 <br><br>STEP BY STEP ANSWER PLSSS

maria [59]

Answer:

(3x+4)(5x+7)

Step-by-step explanation:

15x^2 +41x+28

Factor the expression by grouping. First, the expression needs to be rewritten as 15x^2 +ax+bx+28. To find a and b, set up a system to be solved.

a+b=41

ab=15×28=420

Since ab is positive, a and b have the same sign. Since a+b is positive, a and b are both positive. List all such integer pairs that give product 420.

1,420

2,210

3,140

4,105

5,84

6,70

7,60

10,42

12,35

14,30

15,28

20,21

Calculate the sum for each pair.

1+420=421

2+210=212

3+140=143

4+105=109

5+84=89

6+70=76

7+60=67

10+42=52

12+35=47

14+30=44

15+28=43

20+21=41

The solution is the pair that gives sum 41.

a=20

b=21

Rewrite 15x^2 +41x+28 as (15x^2 +20x)+(21x+28).

(15x^2 +20x)+(21x+28)

Factor out 5x in the first and 7 in the second group.

5x(3x+4)+7(3x+4)

Factor out common term 3x+4 by using distributive property.

(3x+4)(5x+7)

7 0

3 years ago

Read 2 more answers

A savings account that pays interest every six months is said to have a ___ Interest period.

Doss [256]

Answer:

C. Semiannual

8 0

3 years ago

The height of a rectangle is increasing at a rate of 3 centimeters per hour and the width of the rectangle is decreasing at a ra

n200080 [17]

Answer:

Rate of change of the area of the rectangle at that instant = 7 cm²/hr.

Step-by-step explanation:

Area of rectangle = Height x Width

A = hw

The height of a rectangle is increasing at a rate of 3 centimeters per hour and the width of the rectangle is decreasing at a rate of 4 centimeters per hour.

$\texttt{Rate of change of height = }\frac{dh}{dt}=3cm/hr\\\\\texttt{Rate of change of width = }\frac{dw}{dt}=-4cm/hr$

Differentiating area with respect to time,

$\frac{dA}{dt}=h\frac{dw}{dt}+w\frac{dh}{dt}$

We need to find rate of change of area when the height is 5 centimeters and the width is 9 centimeters.

$\frac{dA}{dt}=h\frac{dw}{dt}+w\frac{dh}{dt}\\\\\frac{dA}{dt}=5\times (-4)+9\times 3=-20+27=7cm^2/hr$

Rate of change of the area of the rectangle at that instant = 7 cm²/hr.

5 0

4 years ago

in 1990 automobile dealership sold certain model car for $14 and 649 cents in 2000 so the same model car for $23 and 609 cents f

Virty [35]

The original prize: 14.649

New prize: 23.609

(the years here are not relevant, just to confuse you with more numbers)

the increase is 23.609-14.649=8.960

If we want to know the percentage, we need to know what percentage of the original prize is 8.960.

this is calculated like this:

$\frac{8960}{14609}= 0.61164$

ti make it into percentage, we multiply by 100%: 61.164%

3 0

3 years ago

Find the distance between to points given?

kondor19780726 [428]

<h3>Answer: 29 goes in the box</h3>

===============================================

Explanation:

The two endpoints are (-3,1) and (-1,-4)

Apply the distance formula

$d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(-3-(-1))^2 + (1-(-4))^2}\\\\d = \sqrt{(-3+1)^2 + (1+4)^2}\\\\d = \sqrt{(-2)^2 + (5)^2}\\\\d = \sqrt{4 + 25}\\\\d = \sqrt{29}\\\\d \approx 5.3851648\\\\$

So the approximate distance is roughly 5.38 units and the exact distance is $\sqrt{29}$ units.

--------------

As a slight alternative, you can plot the point (-3,-4) and draw a right triangle. Then apply the pythagorean theorem to find the length of the hypotenuse. The vertical and horizontal legs are 5 and 2 units respectively.

It turns out that the distance formula is essentially a modified form of the pythagorean theorem.

5 0

3 years ago