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3 years ago

15

Penny is counting the days until her grandma comes to visit. There are 98 days left. How many weeks are left until Penny's grand

ma comes to visit? (1 week = 7 days)

1 answer:

Lorico [155]3 years ago

3 0

Create a unit rate.
1 wk/ 7 days
x wk/ 98 days
Cross multiply.
98=7x
Solve the equation.
14=x
14 weeks until her grandmother visits

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Question 7 of 10

marin [14]

Answer:

<h2>Slope = 2</h2>

<u>Step-by-step explanation:</u>

co-ordinates = (2,2) and (-1,-4)

Slope = (y² - y¹) / (x² - x¹)

= (-4 - 2) / (-1 - 2)

= -6 / -3

= 6/3

= 2

4 0

2 years ago

One day a store sold 21 sweatshirts. white ones cost $9.95 and yellow ones cost $ 11.50. in all, $235.30 worth of sweatshirts

FromTheMoon [43]

For this problem you have yo set up two equations.

White shirts = w Yellow shirts = y

1st: w + y = 21
2nd: 9.95w + 11.50y = 235.30

Now we're going to do system of equations using substitution.

If w + y = 21, then y = 21 - w
If y = 21 - w, then you can substitute this in the second equation for y.

9.95w + 11.50(21 - w) = 235.30
9.95w + 241.5 - 11.50w = 235.30
-1.55w + 241.5 = 235.30
-1.55w = -6.2
w = 4, so 4 whites shirt were sold.

Now I'm finding out how many yellow shirts were sold using one of the two equations at the top.

w + y = 21
4 + y = 21
y = 17

So 17 yellow shirts were sold and 4 white shirts were sold.

5 0

2 years ago

Please give me some answers

Luda [366]

Answer:

4) 12 different calzones

5) 15 ways

6) 8 outfits

Step-by-step explanation:

When counting the total number of combinations like these situations, multiply the number of choices of each type together

For 4: 3 sizes, times 4 fillings, is 12 different calzones

For a small calzone, there are 4 diffferent fillings to choose from, making 4 calzones,

For a medium calzone, there are 4 differnt fillings, making 4 more for a total of 8,

For a large calzone, there are 4 different fillings, making 4 more for a total of 12

The same logic applies to the other problems

3 0

2 years ago

What is the nth term rule of the quadratic sequence below? 4,15,30,49,72,99,130,...

navik [9.2K]

Answer:

The nth term rule of the quadratic sequence is $2n^{2} +5n-3$ .

Step-by-step explanation:

We are given the following quadratic sequence below;

4, 15, 30, 49, 72, 99, 130,...

As we know that the formula for the nth term of the quadratic sequence is given by = $an^{2}+bn+c$

Firstly, we will find the difference between the term of the given sequence;

1st difference of the given sequence;

(2nd term - 1st term), (3rd term - 2nd term), (4th term - 3rd term), (5th term - 4th term), (6th term - 5th term), (7th term - 6th term)

= (15 - 4), (30 - 15), (49 - 30), (72 - 49), (99 - 72), (130 - 99),....

= (11, 15, 19, 23, 27, 31,.....)

Now, we will find the second difference of the given sequence, i.e;

= (15 - 11), (19 - 15), (23 - 19), (27 - 23), (31 - 27),....

= (4, 4, 4, 4, 4)

Since the differences are same now, so to find the value of a we have to divide the value of second difference by 2, i.e;

The value of a = $\dfrac{4}{2}$ = 2

SO, the first term of the nth term rule equation is $an^{2}$ = $2n^{2}$ .

Now, in the term $2n^{2}$ , put the value of n = 1, 2, 3, 4 and 5 and then form the sequence, i.e;

If n = 1, then $2n^{2}$ = $2 \times (1)^{2}$ = 2

If n = 2, then $2n^{2}$ = $2 \times (2)^{2}$ = 8

If n = 3, then $2n^{2}$ = $2 \times (3)^{2}$ = 18

If n = 4, then $2n^{2}$ = $2 \times (4)^{2}$ = 32

If n = 5, then $2n^{2}$ = $2 \times (5)^{2}$ = 50

SO, the sequence formed is (2, 8, 18, 32, 50).

Now, find the difference of this sequence and the original quadratic sequence, i.e;

= (4 - 2), (15 - 8), (30 - 18), (49 - 32), (72 - 50)

= (2, 7, 12, 17, 22)

Now, as we can see that the above sequence resembles the general form of (5n - 3) because:

If we put n = 1, then (5n - 3) = 5 - 3 = 2

If we put n = 2, then (5n - 3) = 10 - 3 = 7 and so on....

From this, we concluded that the value of b and c are 5 and (-3) respectively.

Hence, the nth term rule for the given quadratic sequence is $2n^{2} +5n-3$ .

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2 years ago

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vesna_86 [32]

In Quadrant I, sin(sin^-1(x)) = x.

The appropriate choice is
B. $\dfrac{\sqrt{3}}{2}$

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3 years ago