1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Fed [463]
2 years ago
5

A scale model of a rectangular building lot measures 7feet by 5 feet. If the actual house will be built using a scale factor of

12 what is the area of the actual building lot
Mathematics
1 answer:
Tamiku [17]2 years ago
5 0
Actual area of the rectangular building = 5040 feet²
Step-by-step explanation:
Length of the rectangular building = 7 feet
Width of the rectangular building = 5 feet
Now, The building is made with a scale factor of 12
So, Actual length of the rectangular building = 84 feet
Actual width of the rectangular building = 60 feet
Now, Actual area of the rectangular building = Length × Width
⇒ Actual area of the rectangular building = 84 × 60
⇒ Actual area of the rectangular building = 5040 feet²
You might be interested in
3. The yearly profits of a company is $5,000. The profits have been decreasing by 6% per year.
natka813 [3]

Answer:

5000 X (0.96)^n

$3607

Step-by-step explanation:

Profit decreases at a rate of 6% per year = 100 - 6 = 96%

In year 1, profit would be = 5000 x 0.96 = 4800

In year 2 = 5000 x 0.96^2 =

5000 X (0.96)^n

5000 X (0.96)^8 = $3607

6 0
3 years ago
Graph each of the equations and then determine which one represents the rank catcher that is elevated
Tanya [424]
We have two functions that are Parabolas. A parabola is a type of quadratic function which is a special type of “U”-shaped curve called. So let's solve this problem for the first parabola and then for the second one.

1. Graph of the first equation

We have that:

y=x^2-2x+3

So if we graph this equation, the parabola that matches it is shown in Figure 1.

1.1 Direction of Parabola

In general, a parabola or quadratic function is given by the following way:

y=ax^2+bx+c \\ \\ where \ "a" \ is \ called \ the \ leading \ coefficient

Given that our leading coefficient is positive, then the direction of the parabola is upward, that is, it opens upward.

1.2 Location of vertex with respect to the x-axis

The vertex a parabola can be found as follows:

(-\frac{b}{2a},f(-\frac{b}{2a}))

But: \\ \\ a=1 \\ b=-2 \\ c=3 \\ \\ Accordingly: \\ \\ -\frac{b}{2a}=-\frac{(-2)}{2(1)}=1 \\ \\ f(1)=1^2-2(1)+3=2 \\ \\ So \ the \ vertex \ is: \\ \\ V(1,2)

So the vertex is located two units above the x-axis.

<span>1.3 Determine if the graph depicts the rain gauge
</span>
A rain gauge is an instrument used by meteorologists and hydrologists to gather and measure the amount of liquid precipitation<span> over a set period of time.
</span>
From Figure 4 we can affirm that this is the parabola that resembles a rain gauge elevated from the ground. 

1.4 Why or why not?

It basically the question asks for the parabola that has a vertex well above the x-axis. From Figure 4, you can see that the elevated parabola is in fact:

y=x^2-2x+3

2. Graph of the second equation

We have that:

y=x^2+4x+4

So if we graph this equation, the parabola that matches it is shown in Figure 2.

2.1 Direction of Parabola

As in the previous problem, given that our leading coefficient is positive, then the direction of the parabola is also upward, that is, it opens upward.

2.2 Location of vertex with respect to the x-axis

The vertex of a parabola can be found as follows:

(-\frac{b}{2a},f(-\frac{b}{2a}))

In \ this \ case: \\ \\ a=1 \\ b=4 \\ c=3 \\ \\ Accordingly: \\ \\ -\frac{b}{2a}=-\frac{4}{2(1)}=-2 \\ \\ f(-2)=(-2)^2+4(-2)+4=0 \\ \\ So \ the \ vertex \ is: \\ \\ V(-2,0)

So the vertex lies on the x-axis.

2.3 Determine if the graph depicts the rain gauge

This parabola does not resembles a rain gauge elevated from the ground.

2.4 Why or why not?

As you can see the parabola touches the x-axis. If the x-axis represents the ground, then the rain gauge is touching it, that is, it is not elevated.

3. Graph of the third equation

We have that:

y=3x^2+21x+30

So if we graph this equation, the parabola that matches it is shown in Figure 5.

3.1 Direction of Parabola

As in the previous parabolas, given that our leading coefficient is positive, then the direction of the parabola is also upward, that is, it opens upward.

3.2 Location of vertex with respect to the x-axis

In \ this \ case: \\ \\ a=3 \\ b=21 \\ c=30 \\ \\ Accordingly: \\ \\ -\frac{b}{2a}=-\frac{21}{2(3)}=-\frac{7}{2} \\ \\ f(-\frac{7}{2})=3(-\frac{7}{2})^2+21(-\frac{7}{2})+30=-\frac{27}{4} \\ \\ So \ the \ vertex \ is: \\ \\ V(-\frac{7}{2},-\frac{27}{4})

So the vertex is shifted \frac{27}{4} units downward the x-axis.

3.3 Determine if the graph depicts the rain gauge

This parabola does not resembles a rain gauge elevated from the ground.

3.4 Why or why not?

The vertex of this parabola lies on the negative y-axis. So it is not elevated from the ground.

5 0
3 years ago
What two numbers multiply to get 18 and add up to equal 7
LuckyWell [14K]
The 2 numbers you multiply to get 18 are 6 and 3.

6 0
3 years ago
The ratio of lollipops to pieces of bubble gum at the party is 2 to 3. There are 24 lollipops. ​ ​What is the total number of lo
disa [49]

Answer: 40

Step-by-step explanation: first make the ratio into a fraction, 2/3

then make 24 into a fraction with the numerator as a variable and the denominator as 24, x/24

then cross multiply 2 and 24.

2x24=48

then divide 48 by 3, 16.

last add the number of lollipops to 16 and the answer is 40.

5 0
3 years ago
Read 2 more answers
Simplify: − 7( 21 − 16) + 3(9) (24 − 18)
Mekhanik [1.2K]
The answer to the problem is 127
6 0
3 years ago
Read 2 more answers
Other questions:
  • A student decided to start saving money.On the first day he saved 1 cent, on the second day an additional 2 cents, on day 3 he s
    13·1 answer
  • Identify the prime factorization for the given number. 6 A. 2 × 2 × 3 B. 2 × 3 C. 1 × 6 D. 1 × 2 × 3 × 6
    5·1 answer
  • A cyclist rode 3.75 miles in 0.3 hours how fast was she going in Miles per hour
    6·1 answer
  • 05.01 MC)
    9·1 answer
  • 9. Only 12 students can be in the next school play.
    7·1 answer
  • Revel and Scooters are the best scooter experience in the Nation which is the best scooter rental service in the nation? Create
    9·1 answer
  • What’s (-3 , 1) reflected over the x-axis
    14·1 answer
  • Determine the value of y for y=x-6
    12·1 answer
  • Tell whether – 7 is a solution of y + 14 &gt; 2.
    7·1 answer
  • 83 + (25) : 5 &gt; 32 + 42
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!