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3 years ago

The following table shows a proportional relationship between m and n

Mathematics

2 answers:

slavikrds [6]3 years ago

7 0

Answer:

m = 7 n ( the '=' is meant to be the proportional sign)

Step-by-step explanation:

21 ÷ 3 = 7

35 ÷ 5 = 7

56 ÷ 8 = 7

11111nata11111 [884]3 years ago

4 0

Answer:

$y=7x$

Step-by-step explanation:

Notice that if you divide each n-value by its correspoding m-value, you always have 7 as a result, that means it's the constant ratio of change,

21/3 = 7

35/5 = 7

56/8 = 7

Now, this is a linear relatioship by definition, where its constant ratio is 7, but geometrically, that ratio is the slope of a linear equation.

So, we need to use the slope 7, one pair from the table and the point-slope formula

$y-y_{1} =m(x-x_{1} )\\y-21=7(x-3)\\y=7x-21+21\\y=7x$

<h3>Therefore, an equation that models the given table is</h3>

$y=7x$

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Holly drove 100 miles in 4 hours, and Yemi drove 100 miles in 5 hours. How can you compare the speeds of Holly and Yemi? Explain

Lelu [443]

The first thing that yo do is divide 100 by 5 for Yemi and that's how fast she drove which is 20 miles per hour. And then you do the same thing for Holly 100 divided by 4 which is 25 mph. So Holly is driving faster than Yemi. So you can compare them by dividing the miles by hours for both of them.

3 0

3 years ago

Let $P$ and $Q$ be constants. The graphs of the lines $x + 5y = 7$ and $15x + Py = Q$ are perpendicular and intersect at the poi

Marta_Voda [28]

Answer:

Step-by-step explanation:

Given

Two lines:

$x + 5y = 7$

$15x + Py = Q$

are perpendicular to each other and intersect at point (-8,3).

To find: (P, Q)

Solution:

The two lines intersect at (-8,3).

It means, the equation of line will be satisfied when we put value of x = -8 and y = 3

Putting in the second equation, we will get an equation in P and Q:

$15\times (-8) + P \times 3 = Q\\\Rightarrow 3P = Q +120 ..... (1)$

Given that two lines are perpendicular.

It means the product of their slopes will be equal to -1.

i.e. $m_1\times m_2=-1$

Slope of a line of the form $ax+by+c=0$ is given as:

$m=-\dfrac{a}{b}$

So, slopes of given lines are:

$m_1=-\dfrac{1}{5}\\m_2=-\dfrac{15}{P}$

Using the condition:

$-\dfrac{1}{5}\times \dfrac{-15}{P}=-1\\\Rightarrow P = -3$

Putting the value of P in equation (1):

$\Rightarrow 3\times (-3) = Q +120 \\\Rightarrow Q = -9-120 = -129$

So, answer is <em>(-3, -129)</em>

7 0

3 years ago

In the square below, the two semi-circles are congruent. Find the area of the shaded region. If necessary, round your answer to

Jobisdone [24]

Let's start with the area of the square
$area \: square = s \times s = 8 \times 8 = 64$
now let's subtract the are of the two half circles.
two half circles are the same as one circle, and we know that the diameter of the circle is 8 (same as the side of a square) so it's radius is 8/2= 4 inches

$area \: circle = \pi {r}^{2} = \pi \times {4}^{2} = 16\pi$
now we just subtract and our answer is

$64 - 16\pi = 64 - 16 \times (3.14) = 13.73$

3 0

3 years ago

What is the interest rate if the principal is $25,000, the interest is $10,875, and the time is 15 years?

mel-nik [20]

Answer:

interest rate = 2.9%

Step-by-step explanation:

the principal is $25,000, the interest is $10,875

Number of years = 15

We use simple interest formula

I = P*r*t

Where I is the interest amount=10,875

P is the principal amount= 25000

r is the interest rate = r

t is the number of years = 15

Plug in all the value in the formula

I = P*r*t

10875 = 25000 * r * 15

10875 = 375000 * r

Divide both sides by 375000

r=0.029

We always write rate of interest in percentage so we multiply by 100

0.029 * 100= 2.9%

So interest rate = 2.9%

8 0

3 years ago

With a short time remaining in the day, a delivery driver has time to make deliveries at 4 locations among the 7 locations rema

omeli [17]

Answer:

35 different routes

Step-by-step explanation:

The problem of how many different routes are possible if a driver wants to make deliveries at 4 locations among 7 locations is a combination problem.

Combination problems are usually selection problems, of all or part of a set of options, without considering the order in which options are selected.

The number of combinations of n objects taken r at a time is: ⁿCᵣ

So, the number of ways the driver can make deliveries at 4 locations out of 7 locations of given by

⁷C₄ = 35 different ways.

Hence, 35 different routes are possible to make deliveries at 4 locations out of 7 locations.

Hope this Helps!!!

3 0

3 years ago