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ludmilkaskok [199]
2 years ago
9

A school administrator bought 6 desk sets. Each set consists of one table and one chair. He paid $48.50 for each chair. If he pa

id a total of $663 for the 6 sets, the cost of each table is
$
Mathematics
1 answer:
zloy xaker [14]2 years ago
5 0

Answer: The cost of each table was $62

Step-by-step explanation:

$48.50 x 6

= $291 this is the total cost of the chairs

$663 - $291

= $372 this is the overall cost of the tables

$372 ÷ 6

= $62 this is the cost of each table

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Write the slope-intercept form of the equation of each line given the slope and y-intercept.
saul85 [17]

Answer:

4b. −6x + y = −4

4a. 7x + 4y = −12

3b. y = ½x + 3

3a. y = −6x + 5

2b. y + 2 = −⅔(x + 3)

2a. y - 3 = ⅘(x - 5)

1b. y = -x + 5

1a. y = 5x - 3

Step-by-step explanation:

4.

Plug the coordinates into the Slope-Intercept Formula first, then convert to Standard Form [Ax + By = C]:

b.

2 = 6[1] + b

6

−4 = b

y = 6x - 4

-6x - 6x

_________

−6x + y = −4 >> Standard Equation

a.

4 = −7⁄4[-4] + b

7

−3 = b

y = −7⁄4x - 3

+7⁄4x +7⁄4x

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7⁄4x + y = −3 [We do not want fractions in our Standard Equation, so multiply by the denominator to get rid of it.]

4[7⁄4x + y = −3]

7x + 4y = −12 >> Standard Equation

__________________________________________________________

3.

Plug both coordinates into the Slope-Intercept Formula:

b.

5 = ½[4] + b

2

3 = b

y = ½x + 3 >> EXACT SAME EQUATION

a.

−1 = −6[1] + b

−6

5 = b

y = −6x + 5

* Parallel lines have SIMILAR <em>RATE OF CHANGES</em> [<em>SLOPES</em>].

__________________________________________________________

2.

b. y + 2 = −⅔(x + 3)

a. y - 3 = ⅘(x - 5)

According to the <em>Point-Slope Formula</em>, <em>y - y₁ = m(x - x₁)</em>, all the negative symbols give the OPPOSITE TERMS OF WHAT THEY REALLY ARE, so be EXTREMELY CAREFUL inserting the coordinates into the formula with their CORRECT SIGNS.

__________________________________________________________

1.

b. y = -x + 5

a. y = 5x - 3

Just write out the Slope-Intercept Formula as it is given to you.

I am joyous to assist you anytime.

3 0
3 years ago
On a hot summer day, Leo and Stefano decided to buy some refreshments at the Fruit and Smoothies store. Fruit kabobs cost $1.75
Lera25 [3.4K]

Answer:

$6.00

Step-by-step explanation:

2(1.75)+2.50=6

8 0
3 years ago
Write an exponential function y = abx for a graph that includes (–3, 16) and (–1, 4) f(x) = 2(0.5)x f(x) = 0.5(2)x f(x) = 4(0.3)
Arisa [49]

Answer: f(x)=2(0.5)^x

Step-by-step explanation:

Given, the exponential function y = ab^x for a graph that includes (–3, 16) and (–1, 4).

On putting these points, we will have

f(-3)=16=ab^{-3}\\\\ f(-1)=4=ab^{-1}

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\dfrac{f(-3)}{f(-1)}=\dfrac{16}{4}=\dfrac{ab^{-3}}{ab^{-1}}\\\\\Rightarrow\ \dfrac{4}{1}=\dfrac{b^{-3}}{b^{-1}}\\\\\Rightarrow\ \dfrac{4}{1}=\dfrac{b}{b^3}=\dfrac{1}{b^2}\\\\\Rightarrow\ b^2=\dfrac{1}{4}\\\\\Rightarrow\ b=\pm\dfrac{1}{2}=\pm0.5

since the multiplicative factor cannot be negative, so b= 0.5.

At b= 0.5

4=a(0.5)^{-1}\\\\\Rightarrow\ 4=a(\dfrac{1}{2})^{-1}\\\\\Rightarrow\ 4=a(2)\\\\\Rightarrow \ a=2

So, the required function is f(x)=2(0.5)^x.

3 0
4 years ago
Which shows the following expression after the negative exponents have been eliminated?
gregori [183]

<u>Answer:</u>

The correct answer option is \frac {a ^ 3 b^4 } {a b^2}.

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

We are given the following expression and we are to figure out which of the given answer options show the expression after the negative exponents have been eliminated:

\frac {a^3 b^{-2}} {a b^{-4}}

When negative exponent changes sign, then it moves from numerator to denominator or from denominator to numerator.

\frac {a^3 b^4} {ab^2}

7 0
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Step-by-step explanation:

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