Ask question

Ask question

All categories

aleksklad [387]

3 years ago

7

Leonard and Liam each own a collection of vintage cars. Leonard has 7 cars more than Liam has. Three times the number of cars Le

onard has and two times the number of cars Liam has add up to 96. The system of linear equations that relates the number of cars Leonard has (x) and the number of cars Liam has (y) is . The solution of this system is .

2 answers:

gladu [14]3 years ago

7 0

In order to find the solution of the system we need to solve:
x = y+7
3x+2y=96

where x = number of cars that Leonard has
and y = number of Liam's cars

3(y+7)+27=96
3y+21+27=96
3y+48=96
3y=48
y=16
x=16+7=23

dimulka [17.4K]3 years ago

5 0

Answer: The answer is (22, 15).

Step-by-step explanation: Given that 'x' represents the number of cars Leonard has and 'y' represents the number of cars Liam has.

Then, according to the given information, we have

$x-y=7,\\\\3x+2y=96.$

Multiplying the first equation by 2 and adding to the second equation, we have

$2x+3x=14+96\\\\\Rightarrow 5x=110\\\\\Rightarrow x=22.$

So,

$y=x-7=22-7=15.$

Therefore, Leonard has 22 cars and Liam has 15 cars.

Thus, (22, 15) is the solution to the given system.

You might be interested in

What is an equivalent fraction for 4/12

const2013 [10]

Answer:1/3

its 1/3 because 4 dived by 4 = 1 and 12 dived by 4 =3 so answer is 1/3

8 0

3 years ago

Read 2 more answers

Which of the following are types of insurance?

garik1379 [7]

Answer:

life insurance is a type n other are together called as non-life insurance.

4 0

3 years ago

Read 2 more answers

The exponential function f(x) = 3(5)x grows by a factor of 25 between x = 1 and x = 3. What factor does it grow by between x = 5

notsponge [240]

<h2> Question # 1</h2>

Answer:

25 is the factor which grows by between x = 5 and x = 7.

Step-by-step explanation:

Considering the exponential function

$f\left(x\right)\:=\:3\left(5\right)^x$

The growth factor between $x=1$ and $x=3$ is given by:

$\left[3\left(5\right)^3\right]\div \left[3\left(5\right)^1\right]$

$\mathrm{Calculate\:within\:parentheses}\:\left[3\left(5\right)^3\right]\::\quad 375$

$\mathrm{Calculate\:within\:parentheses}\:\left[3\left(5\right)^1\right]\::\quad 15$

So,

= $375\div \:15$

= $25$

Similarly, growth factor between $x=5$ and $x=7$ is given by:

$\left[3\left(5\right)^7\right]\div \left[3\left(5\right)^5\right]$

= $\frac{3\cdot \:5^7}{3\cdot \:5^5}$

$\mathrm{Divide\:the\:numbers:}\:\frac{3}{3}=1$

= $\frac{5^7}{5^5}$

$\mathrm{Apply\:exponent\:rule}:\quad \frac{x^a}{x^b}=x^{a-b}$

$\frac{5^7}{5^5}=5^{7-5}$

= $5^{7-5}$

= $5^2$

= $25$

Therefore, 25 is the factor which grows by between x = 5 and x = 7.

<h2> Question # 2</h2>

Answer:

The population be in 24 years will be 27000.

Also, the population growth modeled by an exponential function as $y=A\cdot \left(b\right)^t$ is an exponential function.

The graph for $y=A\cdot \left(b\right)^t$ is also shown in attached figure.

Step-by-step explanation:

If a city that currently has a population of 1000 triples in size every 8 years.
what will the population be in 24 years?
Is the population growth modeled by a linear function or an exponential function?

As the city that currently has a population of 1000 triples in size every 8 years.

So, for this case

$y=A\cdot \left(b\right)^t$

where

$A$ = Initial population amount

$b$ = growth rate

$t$ = time

Substituting the values in the function

$y=A\cdot \left(b\right)^t$

$y=1000\cdot \:\:3^{\frac{1}{8}t}$

So, the population be in 24 years

$y=1000\cdot \:\:3^{\frac{1}{8}24}$

As

$3^{\frac{1}{8}\cdot \:24}=3^3$

So

$\:y=3^3\cdot 1000$

$y=1000\cdot \:\:27$

$y=27000$

Therefore, the population be in 24 years will be 27000.

Also, the population growth modeled by an exponential function as $y=A\cdot \left(b\right)^t$ is an exponential function.

<h2 /><h2> Question # 3</h2>

Answer:

the graph of the function will translate horizontally 3/5 units right.

Step-by-step explanation:

We have to find the effect on the graph of the function $f(x)=2x$ when it is replaced by f(x- 3/5).

We already have an idea that rule for horizontal translation:

Given a function $f(x)$ , and a constant c > 0, the function $g(x) = f(x - a)$ represents a horizontal shift c units to the right from f(x). The function $h(x) = f(x + a)$ represents a horizontal shift c units to the left.

As 3/5 > 0, so the graph of the function will translate horizontally 3/5 units right.

Therefore, the graph of the function will translate horizontally 3/5 units right.

Keywords: exponential function, translation function, growth factor

Learn more about exponential function and growth factor form brainly.com/question/10147339

#learnwithBrainly

6 0

3 years ago

2g + h =2<br>g -h= -5<br><br>find g and h step by step explanation

wel

Answer:

Step-by-step explanation:

2g + h = 2 --------------(I)

g - h = -5------------(II)

g = -5 + h

Plugin g = -5 + h in equation (I)

2(-5 + h) + h = 2 {Distributive property:a(b+c) = a*b +a*c}

(-5)*2 + h *2 + h= 2

-10 + 2h + h = 2

3h = 2 + 10

3h = 12

h = 12/3

h = 4

Substitute h= 6 in equation (I)

2g + 4 = 2

2g = 2 - 4

2g = -2

g = -2/2

g = -1

6 0

2 years ago

For the equation below, determine its order. Name the independent variable, the dependent variable, and any parameters in the eq

PIT_PIT [208]

Answer:

The equation is an differential equation of second order.

The dependent variable is x, while t is the independent variable.

Step-by-step explanation:

The order of the equation depends on the greatest grade of the derivative, in this case it's the second derivative (x'')

Since x is a function of t, we would have that t is the independent variable while x is the dependent variable.

3 0

3 years ago