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3 years ago

There are 364 first-grade students in Park Elementary School. If there are 26 more girls than boys, how many girls are there?

Mathematics

1 answer:

wlad13 [49]3 years ago

5 0

Answer:

195

Step-by-step explanation:

If there are x boys, then there are x+26 girls. Hence, we write the equation,

x+(x+26)=364

Solve for x:

2x+26=364

2x-338

x=169

So there are 169+26 =195 girls

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A container holds 6 quarts of lemonade. How much is this in cups?

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3 years ago

Simplify the expression below. 3c - 2cd - 8c + 7d

jolli1 [7]

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3 years ago

Find the exponential function that passes through the points (2,80) and (5,5120)

juin [17]

Answer:

y = 5·4^x

Step-by-step explanation:

If you have two points, (x1, y1) and (x2, y2), whose relationship can be described by the exponential function ...

y = a·b^x

you can find the values of 'a' and 'b' as follows.

Substitute the given points:

y1 = a·b^(x1)

y2 = a·b^(x1)

Divide the second equation by the first:

y2/y1 = ((ab^(x2))/(ab^(x1)) = b^(x2 -x1)

Take the inverse power (root):

(y2/y1)^(1/(x2 -x1) = b

Use this value of 'b' to find 'a'. Here, we have solved the first equation for 'a'.

a = y1/(b^(x1))

In summary:

b = (y2/y1)^(1/(x2 -x1))
a = y1·b^(-x1)

For the problem at hand, (x1, y1) = (2, 80) and (x2, y2) = (5, 5120).

b = (5120/80)^(1/(5-2)) = ∛64 = 4

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The exponential function is ...

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3 0

3 years ago

What is the area of triangle pqr on the grid? a triangle pqr is shown on a grid. the vertex p is on ordered pair 7 and 6, vertex

horsena [70]

P(7,6), Q(1,6), R(4,2)

We have PQ parallel to the x axis. We'll call that the base,

b = 7 - 1 = 6

The altitude is then the y difference h = 6 - 2 = 4

The area is $\frac 1 2 bh = \frac 1 2 (6)(4) = 12$

Answer: 12 square units

In general we can use the shoelace formula for the area of any polygon given coordinates. We write the points like this:

(7,6), (1,6), (4,2)

(1,6), (4,2), (7,6)

The area is then half the absolute value of the sum of the cross products:

$A = \frac 1 2 | 7(6)-6(1) + 1(2)-6(4) + 4(6)-2(7) | = \frac 1 2 |24| = 12$

6 0

3 years ago

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