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3 years ago

Karen says the functions f(×)=×+3 and g(×)= -×+7 intersect at x=2 is she correct

Mathematics

2 answers:

Gemiola [76]3 years ago

8 0

Answer:

yes

Step-by-step explanation:

Given the 2 equations

y = x + 3 → (1)

y = - x + 7 → (2)

Substitute y = x + 3 into (2)

x + 3 = - x + 7 ( add x to both sides )

2x + 3 = 7 ( subtract 3 from both sides )

2x = 4 ( divide both sides by 2 )

x = 2

Thus the functions intersect at x = 2

frez [133]3 years ago

7 0

Answer:

Yes.

Step-by-step explanation:

To find the point of intersection we solve the system:

y = x + 3

y = -x + 7 Subtract:

0 = 2x - 4

2x = 4

x = 2.

She is correct.

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Caps hock Guess and Check (or use Algebra) to solve #3 & # 4 3. Plato has 36 coins in nickels, dimes, and quarters. The numb

Sedaia [141]

Answer:

Part 1:

Let the nickels be = n

Let the dimes be = d

Let the quarters be = q

Plato has 36 coins in nickels, dimes, and quarters. So, equation forms:

$n+d+q=36$ .....(1)

The number of nickels is three less than twice the number of dimes.

$n=2d-3$ ....(2)

The total value of the coins is $5.20.

$0.10d+0.05n+0.25q=5.20$ .... (3)

Substituting n=2d-3 in (1) and (3)

$2d-3+d+q=36$

=> $3d+q=39$ ....(4)

$0.10d+0.05(2d-3)+0.25q=5.20$

=> $0.10d+0.10d-0.15+0.25q=5.20$

=> $0.20d+0.25q=5.35$ ...(5)

Multiplying (4) by 0.25 and subtracting (5) from (4)

$0.75d+0.25q=9.75$ now subtracting (5) from this we get;

$0.55d=4.4$

=> d = 8

Substituting d = 8 in $3d+q=39$

$3(8)+q=39$

$24+q=39$

=> q = 15

Substituting values of d and q in $n+d+q=36$ , we get n

$n+8+15=36$

$n=36-23$

=> n = 13

Therefore Plato has 13 nickels, 15 quarters and 8 dimes.

-----------------------------------------------------------------------------------------

Part 2:

Let the original price of the ski hat be = x

Original price was marked down by 35% means value was lowered by 35%.

So, we can calculate as:

$x-\frac{35x}{100}=15.60$

=> $\frac{65x}{100}=15.60$

=> $65x=1560$

x = 24

Hence, the original price was $24 but after 35% marking down, it was available for $15.60.

5 0

3 years ago

Jodi bought a new sofa for $1,430, including finance charge. She made down payment of $130 and paid off the balance in 18 months

m_a_m_a [10]

The finance Charge would be $140. you would multiply 18 by 80 and then add the 130 and take that number and subtract the 1,430

6 0

3 years ago

Write a quadratic function in standard form with zeros 1 and -10

Licemer1 [7]

Answer:

f(x)=x^2+9x-10

Step-by-step explanation:

Standard Form of Quadratic Function

The standard form of a quadratic function is:

$f(x)=ax^2+bx+c$

where a,b, and c are constants.

The factored form of a quadratic equation is:

$f(x)=a(x-\alpha)(x-\beta)$

Where $\alpha$ and $\beta$ are the roots or zeros of f, and a is constant.

We know the zeros of the function are 1 and -10. The function is:

$f(x)=a(x-1)(x-(-10))$

$f(x)=a(x-1)(x+10)$

Operating:

$f(x)=a(x^2+10x-x-10)$

Joining like terms:

$f(x)=a(x^2+9x-10)$

Since we are not given any more restrictions, we can choose the value of a=1, thus. the required function is:

$\boxed{f(x)=x^2+9x-10}$

6 0

3 years ago

What is (5.03x -8.03) - (3.5x +6.2)?

Kryger [21]

Answer:

1.53x−14.23

Step-by-step explanation:

simplify:

5.03x−8.03−(3.5x+6.2)

Distribute the Negative Sign:

=5.03x−8.03−1(3.5x+6.2)

=5.03x−8.03−1(3.5x)+(−1)(6.2)

=5.03x−8.03−3.5x−6.2

Combine Like Terms:

=5.03x−8.03+−3.5x−6.2

=(5.03x−3.5x)+(−8.03−6.2)

=1.53x−14.23

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2 years ago

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AnnZ [28]

Answer:

36 And 59

Step-by-step explanation:

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3 years ago