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jeyben [28]
3 years ago
12

Help ASAP

Mathematics
1 answer:
statuscvo [17]3 years ago
4 0

x = - 6 and x = 7

given x² - x - 42 = 0 ← quadratic in standard form

(x - 7 )(x + 6) = 0 ← in factored form

equate each factor to zero and solve for x

x - 7 = 0 ⇒ x = 7

x + 6 = 0 ⇒ x = - 6


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Question in attachment
ELEN [110]

Answer:

  • $20,000 at 8.5%
  • $10,000 at 10%

Step-by-step explanation:

There are a number of ways to solve mixture problems like this. Some are simple enough you can almost write down the answer. One I like uses a diagram to help you find the ratios of the components of the mix. You can do the same thing with a formula (without the diagram).

The basic idea is that you compute a ratio between two differences. The numerator is the difference between the average interest rate and the lower interest rate. Here, the average interest rate is 2700/30,000 = 0.09 = 9%. Then the numerator is 9% -8.5% = 0.5%

The denominator is the difference between the two interest rates of the investments: 10% -8.5% = 1.5%. And the ratio of these two values is ...

  0.5%/1.5% = 1/3

This is the fraction of the total investment that was invested at the higher interest rate:

  (1/3)×$30,000 = $10,000 . . . . was invested at 10%

Then the remaining amount, $20,000, was invested at 8.5%.

___

If you would prefer an equation, you can let x represent the amount invested at the higher rate. (That is the most convenient assignment of variables, as it keeps all of the numbers positive.) Then (30,000 -x) is the amount invested at the lower rate. The total amount of interest is ...

  10%(x) +8.5%(30,000 -x) = 2700

  x(10% -8.5%) = 2700 -8.5%(30000) . . . . . subtract 8.5%(30,000)

  x = (2700 -8.5%(30,000))/(10% -8.5%) . . . . divide by the coefficient of x

We have purposely left the expression unevaluated so that you can compare it to the math we described above. If you factor out 30,000 from the numerator of this fraction, you see the ratio that we described in words:

  x=30000\left(\dfrac{\dfrac{2700}{30000}-8.5\%}{10\%-8.5\%}\right)\\\\x=10,000

This tells us $10,000 was invested at 10%, and $20,000 was invested at 8.5%.

8 0
3 years ago
Nick will move a storage bin from its current location to the new location shown on the coordinate plane. Describe how Nick coul
nlexa [21]

Answer:

Move downward by 7 units

Move leftward by 6 units

(x,y) \to (x -6,y-7)

Step-by-step explanation:

Given

See attachment for grid

Required

The transformation from the current location to the new location

To do this, we pick two corresponding points on the current location and the new location.

We have:

A = (3,2) -- Current location

A' = (-6,-5) -- New location

First, move A downwards by 7 units.

The rule to this is:

(x,y) \to (x,y-7)

So, we have:

(3,2) \to (3,2-7)

(3,2) \to (3,-5)

Next, move the above points leftward by 6 units.

The rule to this is:

(x,y) \to (x-6,y)

So, we have:

(3,-5) \to (3-6,-5)

(3,-5) \to (-3,-5)

6 0
2 years ago
Jamar and Peggy live on opposite sides of a park. Peggy counted how many steps it takes her to get from her house to Jamar's hou
creativ13 [48]

Answer:

A.96.25 steps.  B. Approximately 37 steps shorter

Step-by-step explanation:

From Pythagoras theory,

Hyp² = Adj² + Opp²

Hyp² = 52² + 81²

Hyp² = 2704 + 6561

Hyp² = 9265

Hyp = √9265

Hyp = 96.25 steps

= 81 + 52 = 133 - 96.25

= 36.75 or approximately 37 steps shorter

7 0
2 years ago
Help me please, you gonna be my hero
Lisa [10]

The rate of change of the relationship is 6/5

<h3>Rate of change of a line</h3>

The rate of change of a line is also known as the slope of the line. The formula for calculating the slope of a line is expressed as:

Slope =y2-y1/x2-x1

Given the coordinate points (-3,-2) and (2, 4). On substituting;

Slope = 4-(-2)/2-(-3)

Slope =4+2/2+3

Slope = 6/5

Hence the rate of change of the relationship is 6/5

Learn more on rate of change here: brainly.com/question/25184007

#SPJ1

8 0
2 years ago
Which is the Area of a circle with a diameter of 7 units?
saul85 [17]
Area of a circle = (3.14) * r^2
d = 7
r = 3.5

a = (3.14) * 3.5^2
a = (3.14) * 12.25
a = 38.47
7 0
3 years ago
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