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2 years ago

This chart shows Dan’s budget:

Mathematics

2 answers:

kotykmax [81]2 years ago

5 0

The correct answer is D. No, Dan should reduce his discretionary spending.

Hope this helps

Drupady [299]2 years ago

4 0

The correct answer is D No, Dan should reduce his discretionary spending

Explanation:

For Dan to stay on the budget he needs to spend the amount budgeted for each expense or less than the amount budgeted. This occurred in the case of the Internet, food, and rent; for example, the amount budgeted for the internet was $35 and Dan spent this money, also, the amount budgeted for food was $100 and Dan spent $95, which means he stood in the budget. However, this did not occur with discretionary spending, which refers to other non-necessary expenses, because in this case, Dan spent $140 even when the budget limit was $100. Also, this exceeds the total income considering 35 + 95 + 500+ 140 = $770, which is above the income ($750). Thus, Dan did not stay in the budget because he spent more money than expected in discretionary spending and should reduce this.

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Suppose that y = k * (x - 1/3) ^ 2 is a parabola in the xy -plane that passes through the point (2/3, 1) :Find k and the length

Dennis_Churaev [7]

Answer:

k = 9

length of chord = 2/3

Step-by-step explanation:

Equation of parabola: $y=k (x-\frac13)^2$

Part 1

If the curve passes through point $(\frac23 ,1)$ , this means that when $x=\dfrac23$ , $y = 1$

Substitute these values into the equation and solve for $k$ :

$\implies 1=k \left(\dfrac23-\dfrac13\right)^2$

$\implies 1=k \left(\dfrac13 \right)^2$

Apply the exponent rule $\left(\dfrac{a}{b} \right)^c=\dfrac{a^c}{b^c}$ :

$\implies 1=k \left(\dfrac{1^2}{3^2} \right)$

$\implies 1=\dfrac{1}{9}k$

$\implies k=9$

Part 2

The chord of a parabola is a line segment whose endpoints are points on the parabola.

We are told that one end of the chord is at $(\frac23 ,1)$ and that the chord is horizontal. Therefore, the y-coordinate of the other end of the chord will also be 1. Substitute y = 1 into the equation for the parabola and solve for x:

$\implies 1=9 \left(x-\dfrac13 \right)^2$

$\implies \dfrac19 = \left(x-\dfrac13 \right)^2$

$\implies \sqrt{\dfrac19} = x-\dfrac13$

$\implies \pm \dfrac13 = x-\dfrac13$

$\implies x=\dfrac23, x=0$

Therefore, the endpoints of the horizontal chord are: (0, 1) and (2/3, 1)

To calculate the length of the chord, find the difference between the x-coordinates:

$\implies \dfrac23-0=\dfrac23$

**Please see attached diagram for drawn graph. Chord is in red**

6 0

1 year ago

At the city museum, child admission is $5.30 and adult admission is $9.20 . On Monday, 166 tickets were sold for a total sales o

Sonbull [250]

C+a=166
a=166-c
5.3c+9.2a=1254.2
5.3c+9.2(166-c)=1254.2
5.3c+1527.2-9.2c=1254.2
5.3c-9.2c=1254.2-1527.2
-3.9c=-273
c=-273/-3.9
c=70
Hope this helps!

3 0

2 years ago

Evaluate the function below for f(3) f (x) = 3x2 - 5 what’s the answer

Novay_Z [31]

The answer is 13 because you would plug in 3(3) which is 9 then you multiply (9)(2) which is 18 they you subtract 18-5 which equals 13

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2 years ago

Given m || n, which pair of angles are not vertical angles?

vodomira [7]

Answer:

Step-by-step explanation:

its right

8 0

2 years ago

Read 2 more answers

Graph f(x) = 2x^4+3 let x = 0, 1, and 2. please show your work

mestny [16]

Sub those points for x
f(x) is the y

(x,y)

so for x=0
f(0)=2(0)^4+3
f(0)=0+3
f(0)=3
(0,3) is a opint

for x=1
f(1)=2(1)^4+3
f(1)=2(1)+3
f(1)=2+3
f(1)=5
(1,5) is another point

for x=2
f(2)=2(2^4)+3
f(2)=2(16)+3
f(2)=32+3
f(2)=35
(2,35) is another point

points are
(0,3)
(1,5)
(2,35)

3 0

2 years ago