HELP FOR 20 pointsss!!!

A baker buys 19 apples of two different varieties to make pies. The total cost of the apples is $5.10. Granny Smith apples cost

Natasha2012 [34]

The baker bought 7 gala apples, and 12 granny smiths apples

Solution:

Let "x" be the number of gala apples bought

Let "y" be the number of granny smith apples bought

Cost of 1 gala apple = $ 0.30

Cost of 1 granny smith apple = $ 0.25

A baker buys 19 apples of two different varieties to make pies

Therefore,

number of gala apples bought + number of granny smith apples bought = 19

x + y = 19 --------- eqn 1

The total cost of the apples is $5.10

Therefore, we can frame a equation as:

number of gala apples bought x Cost of 1 gala apple + number of granny smith apples bought x Cost of 1 granny smith apple = 5.10

$x \times 0.30 + y \times 0.25 = 5.10$

0.3x + 0.25y = 5.1 -------- eqn 2

Let us solve eqn 1 and eqn 2

From eqn 1,

x = 19 - y ---------- eqn 3

Substitute eqn 3 in eqn 2

0.3(19 - y) + 0.25y = 5.1

5.7 - 0.3y + 0.25y = 5.1

5.7 - 0.05y = 5.1

0.05y = 5.7 - 5.1

0.05y = 0.6

y = 12

Substitute y = 12 in eqn 3

x = 19 - 12

x = 7

Thus the baker bought 7 gala apples, and 12 granny smiths apples

6 0

3 years ago

Mrs. Ramiriz is making pies to sell at the local farmer’s market. It costs her $5 to make each pie, plus a one-time cost of $30

gregori [183]

The answer is 5x + 30 = 12x

x - the number of pies

It costs her $5 to make each pie, plus a one-time cost of $30 for baking supplies:
COST: f(c) = 5x + 30

She plans to sell the pies for $12 each:
PROFIT: f(p) = 12x

To find the number of pies she needs to sell to break even:
f(c) = f(p)
5x + 30 = 12x

5 0

3 years ago

Ren can eat a pizza in 3 minutes and Isaac can eat a pizza in four minutes. How long will it take them to eat the pizza together

Ronch [10]

Ren and Isaac will eat the pizza in a 7 minutes

8 0

3 years ago

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Rationalize the denominator and simplify 6/√2-√3

ss7ja [257]

Answer:

=3√6−3√5

Explanation:

3√5+√6

We rationalise the denominator by multiplying the expression by the conjugate of the denominator. √5−√6

3⋅(√5−√6)(√5+√6)⋅(√5−√6)

=3⋅(√5)+3⋅(−√6)(√5+√6)⋅(√5−√6)

=3√5−3√6(√5+√6)⋅(√5−√6)

Applying identity
(a+b)(a−b)=a2−b2 to the denominator.

=3√5−3√6(√5)2−(√6)2

=3√5−3√65−6

=3√5−3√6−1

=−3√5+3√6

=3√6−3√5

5 0

3 years ago

F(x) is a quadratic function with x-intercepts at (−1, 0) and (−3, 0). If the range of f(x) is [−4, ∞) and g(x) = 2x2 + 8x + 6,

svetlana [45]

Answer:

B) Both functions have the same domain.

C) Both functions have the same x-intercepts.

D) Both functions are decreasing on the interval (−∞, −2).

Step-by-step explanation:

step 1

Find the vertex of f(x)

we know that

The x-coordinate of the vertex is the midpoint of the roots

we have

x=-1 and x=-3

so

the midpoint is

(-1-3)/2=-2

The y-coordinate of the vertex is -4 (because the range is [−4, ∞))

therefore

The vertex of f(x) is the point (-2,-4)

Is a vertical parabola open upward

The vertex is a minimum

The domain is all real numbers

step 2

we have

$g(x)=2x^2+8x+6$

Find the vertex

Factor the leading coefficient

$g(x)=2(x^2+4x)+6$

Complete the square

$g(x)=2(x^2+4x+4)+6-8$

$g(x)=2(x^2+4x+4)-2$

Rewrite as perfect squares

$g(x)=2(x+2)^2-2$

Is a vertical parabola open upward

The vertex is the point (-2,-2)

The domain is all real numbers

The range is the interval [−2, ∞)

Find the x-intercepts

For g(x)=0

$0=2(x+2)^2-2$

$2(x+2)^2=2$

$(x+2)^2=1\\x+2=\pm1\\x=-2\pm1$

so

The roots or x-intercepts are

x=-1 and x=-3

Verify each statement

A) Both functions have the same vertex

The statement is false

The vertex of f(x) is (-2,-4) and the vertex of g(x) is (-2,-2)

B) Both functions have the same domain.

The statement is true

The domain is all real numbers

C) Both functions have the same x-intercepts

The statement is true (see the explanation)

D) Both functions are decreasing on the interval (−∞, −2)

The statement is true

Because the x-coordinate of the vertex is the same in both functions, and both functions open upward

7 0

3 years ago

Read 2 more answers