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3 years ago

Please help me so confused Solve. x^2 + 3x − 7 = 0 Enter your answers, as exact values, in the boxes. x = or x =

Mathematics

2 answers:

Rzqust [24]3 years ago

6 0

Answer:

x = -1/2 ( 3±sqrt(37))

Step-by-step explanation:

x^2 + 3x − 7 = 0

Add 7 to each side

x^2 + 3x =7

Using complete the square

Taking the coefficient of x

Divide by 2

3/2

Square it

(3/2)^2 = 9/4

Add this to each side

x^2 + 3x+ 9/4 = 7+9/4

( x+ 3/2) ^2 = 28/4 + 9/4

( x+ 3/2) ^2 = 37/4

Take the square root of each side

x+3/2 = ±sqrt(37/4)

x+3/2 = ±sqrt(37) / sqrt(4)

x+ 3/2 = ±sqrt(37) / 2

Subtract 3/2 from each side

x = -3/2 ±sqrt(37) / 2

x = -1/2 ( 3±sqrt(37))

igomit [66]3 years ago

5 0

Answer:

-1.5 -√9.25 or -1.5 +√9.25

Step-by-step explanation:

x^2 + 3x - 7 = 0

This will not factor so we can use completing the square:

x^2 + 3x = 7

(x + 1.5)^2 - 2.25 = 7

(x + 1.5)^2 = 9.25

x + 1.5 = ±√9.25

x = -1.5 ±√9.25

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HELP ME PLEASE ASAP ASAP

WITCHER [35]

The answer to this question is £155

8 0

2 years ago

What conclusions can be made about the amount of money in each account if f represents Molly's account and g represents her brot

Nat2105 [25]

Answer:

(b) is true

Step-by-step explanation:

Given

Molly

$a = 500$ --- starting balance

$m = 10$ --- monthly rate

Her brother

$a = 100$ ---- starting balance

$r = 10\%$ --- annual rate

Required

Determine which option is true

First, we calculate her brother's function.

The function is an exponential function calculated as:

$y = ab^x$

Where $b = 1 + r$

So, we have:

$y = ab^x$

$y = 100 *(1 + 10\%) ^x$

$y = 100 *(1 + 0.10) ^x$

$y = 100 *(1.10) ^x$

Hence:

$g(x) = 100 *(1.10) ^x$

Next, we calculate Molly's function (a linear function)

The monthly function is:

$y = mx + a$

So, we have:

$y = 10x + 500$

Annually, the function will be:

$y = 10x*12 + 500$

$y = 120x + 500$

So, we have:

$f(x) = 120x + 500$

At this point, we have:

$f(x) = 120x + 500$ ---- Molly

$g(x) = 100 *(1.10) ^x$ ---- Her brother

<u>Next, we test each option</u>

(a): Molly's account will have a faster rate of change over [32,40]

We calculated Molly's function to be:

$y = 120x + 500$

The slope of a linear function with the form: $y = mx + b$ is m

By comparison:

$m = 120$

Since Molly's account is a linear function, the rate of change over any interval will always be the same; i.e.

$m = 120$

For his brother:

Rate of change is calculated using:

$m = \frac{g(b) - g(a)}{b - a}$

$m = \frac{g(40) - g(32)}{40 - 32}$

$m = \frac{g(40) - g(32)}{8}$

Calculate g(40) and g(32)

$g(x) = 100 *(1.10) ^x$

$g(40) = 100 * 1.10^{40} =4526$

$g(32) = 100 * 1.10^{32} = 2111$

So, we have:

$m = \frac{4526 - 2111}{8}$

$m = \frac{2415}{8}$

$m = 302$

By comparison: $302 > 120$

Hence, her brother's account has a faster rate over [32,40]

(a) is false

(b): Molly's account will have a slower rate of change over [24,30]

$m = 120$ --- Molly's rate of change

For his brother:

$m = \frac{g(b) - g(a)}{b - a}$

$m = \frac{g(30) - g(24)}{30 - 24}$

$m = \frac{g(30) - g(24)}{6}$

Calculate g(30) and g(24)

$g(x) = 100 *(1.10) ^x$

$g(40) = 100 * 1.10^{30} =1745$

$g(32) = 100 * 1.10^{24} = 985$

So, we have:

$m = \frac{g(30) - g(24)}{6}$

$m = \frac{1745 - 985}{6}$

$m = \frac{760}{6}$

$m = 127$

By comparison: $127 > 120$

Hence, Molly's account has a slower rate over [24,30]

(b) is false

(c): Molly's account will have a slower rate of change over [0,4]

$m = 120$ --- Molly's rate of change

For his brother:

$m = \frac{g(b) - g(a)}{b - a}$

$m = \frac{g(4) - g(0)}{4 - 0}$

$m = \frac{g(4) - g(0)}{4}$

Calculate g(4) and g(0)

$g(x) = 100 *(1.10) ^x$

$g(4) = 100 * 1.10^4 =146$

$g(0) = 100 * 1.10^{0} = 100$

So, we have:

$m = \frac{g(4) - g(0)}{4}$

$m = \frac{146 - 100}{4}$

$m = \frac{46}{4}$

$m = 11.5$

By comparison: $120>11.5$

Hence, Molly's account has a faster rate over [0,4]

(c) is false

4 0

3 years ago

The units of the subway map below are in miles. Suppose the routes between

levacccp [35]

Distance between Station E and Station G is 8.48 miles (Approx.)

<u>Given:</u>

Distance 3 miles east

Distance 5 miles south

Distance between Station E and Station G

<u>Computation:</u>

Co-ordinate of Point E = (-3 , 1)

Co-ordinate of Point G is 3 mile east and 5 mile south

So,

Co-ordinate of Point G = (3 , -5)

Distance between two point = √(x2 - x1)² + (y2 - y1)²

So,

Distance between Station E and Station G = √(3 + 3)² + (-5 - 1)²

Distance between Station E and Station G = √(6)² + (-6)²

Distance between Station E and Station G = √36 + 36

Distance between Station E and Station G = √72

Distance between Station E and Station G = 8.48 miles (Approx.)

Learn more:

brainly.com/question/12052812?referrer=searchResults

4 0

2 years ago

Please help with answers I need them as soon as possible!

Tcecarenko [31]

5 because 5/6 is equal to 15/18

8 0

3 years ago

What is the approximate measure of angle T in the triangle below 79° 84° 96° 101°

Anestetic [448]

The approximate measure of angle T in the given diagram is 79°. The correct option is the first option 79°

<h3>Law of Cosines</h3>

From the question, we are to determine the approximate measure of angle T

From the law of cosines, we can write that

cosT = (s² + u² - t²)/2su

From the diagram,

s = 3.9 cm

u = 2.7 cm

t = 4.3 cm

Thus,

cosT = (3.9² + 2.7² - 4.3²)/2(3.9)(2.7)

cosT = (15.21 + 7.29 - 18.49)/21.06

cosT = 4.01/21.06

cosT = 0.1904

T = cos⁻¹(0.1904)

T = 79.02°

T ≈ 79°

Hence, the approximate measure of angle T in the given diagram is 79°. The correct option is the first option 79°

Learn more on Law of Cosines here: brainly.com/question/28081595

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4 0

1 year ago