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3 years ago

I need a step by step explanation how to solve for the solutions of this (Not by graphing)

Mathematics

1 answer:

tester [92]3 years ago

5 0

Answer:

(0, 15) and (11, 48)

Step-by-step explanation:

Given the 2 equations

y = x² - 8x + 15 → (1)

y = 3x + 15 → (2)

Substitute y = x² - 8x + 15 into (2)

x² - 8x + 15 = 3x + 15 ( subtract 3x + 15 from both sides )

x² - 11x = 0 ← in standard form

x(x - 11) = 0 ← in factored form

Equate each factor to zero and solve for x

x = 0

x - 11 = 0 ⇒ x = 11

Substitute these values into (2) for corresponding values of y

x = 0 : y = 0 + 15 = 15 ⇒ (0, 15)

x = 11 : y = 33 + 15 = 48 ⇒ (11, 48)

Solutions are (0, 15), (11, 48)

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Alexxandr [17]

The first thing you would do is add all the numbers to get the total budget : $1500

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2 years ago

A set of twins, Andrea and Courtney, are initially 10 years old. While Courtney remains on Earth, Andrea rides on a spaceship th

SVETLANKA909090 [29]

The initial age of 10 years and the spaceship speed of 0.60•c, gives the Andrea's age at the end of the trip as 18 years.

<h3>How can Andrea's new age be calculated?</h3>

The time dilation using the Lorentz transformation formula is presented as follows;

$t' = \frac{t}{ \sqrt{1 - \frac{ {v}^{2} }{ {c}^{2} } } }$

From the question, we have;

The spaceship's speed, <em>v</em> = 0.6•c

∆t = Rest frame, Courtney's time, change = 10 years

Therefore;

$\delta t' =\delta t \times \sqrt{1 - \frac{ {(0.6 \cdot c)}^{2} }{ {c}^{2} } } = 8$

The time that elapses as measured by Andrea = 8 years

Andrea's age, <em>A</em>, at the end of the trip is therefore;

A = 10 years + 8 years = 18 years

Learn more about the Lorentz transformation formula here:

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2 years ago

• Packaging of a product can cost a lot of money. Can you design

podryga [215]

The best arrangement can be

3 rows and 4balls each row

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Width=1.8(3)=5.4cm
Height=1.8(2)=3.6cm

TSA

2(LB+BH+LH)
2(5.4(7.2)+(7.2)(3.6)+3.6(5.4))
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2 years ago

Eugene walked all the way to school at 3 mph then realized she forgot her math book (how could she?!), so she ran back at 7 mph.

Fynjy0 [20]

$\text{Answer: }1\frac{23}{40}\ miles\text{ far she live from school.}$

Explanation:

Since we have given that

Speed at which Eugene walked all the way to school = 3 mph

After realizing that she forgot her math book, she ran back

Speed at which Eugene walked back to her house = 7 mph

Let the distance between her house and her school be x

According to question,

$\frac{x}{3}+\frac{x}{7}=\frac{45}{60}\\\\\frac{7x+3x}{21}=\frac{3}{4}\\\\\frac{10x}{21}=\frac{3}{4}\\\\x=\frac{3\times 63}{4\times 10}=\frac{63}{40}=1\frac{23}{40}\ miles.$

Hence,

$1\frac{23}{40}\ miles\text{ far she live from school.}$

8 0

2 years ago

F(x)=8_-4x-x^3. g(x)=x^2+7x-9. Find f(x)+g(x)

11111nata11111 [884]

$(8 - 4x - {x}^{3} ) + ( {x}^{2} + 7x - 9) \\ = - {x}^{3} + {x}^{2} - 4x + 7x + 8 - 9 \\ = - {x}^{3} + {x}^{2} + 3x - 1$
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The answer is either B, and you forgot to put in the ^2 in the answer choice, or C, and you forgot to put an x where there is a _ in the question.

Check the actual question (the one you recieved, not the one posted here) and see where the mistakes are. If f(x) = 8x - 4x - x^3, then your answer is C. However, if B is actually -x^3 + x^2 + 3x - 1, then the answer is B.

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3 years ago