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Function that models the situation is  f(x) = 1/2(x-6)²+2.

A parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped.

Given parabola is of concave upward type.

So, the parabola will be of form f(x)=p(x-q)²+r....(1)

As vertices of parabola are (6,2)

So, we can put q=6 and r =2 in (1)

So, (1) becomes f(x) = p(x-6)²+2.....(2)

The y-intercept of the parabola is 20

This means, (2) becomes 20 = p(0-6)²+2

i.e. p = 1/2

So, function will be f(x) = 1/2(x-6)²+2

Therefore, function that models the situation is  f(x) = 1/2(x-6)²+2.

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Answer:

Step-by-step explanation:

answer: owen can afford to keep and drive the car for 4 days.

The total owing on the car rental is R(d) = ($77.25/day)d + ($0.12/mile)m ≤ $330.  Substitute 1 for d (that is, the rental is for 1 day) and 175 for m:

R(d) = ($77.25/day)(d days) + ($0.12/mile)(175 miles) ≤ $330

    =   $77.25d                   + $21     ≤ $330

This simplifies to   $77.25d + $21 ≤ $330, or

                                $77.25d ≤ $309

Solving this by dividing both sides of the above equation by $77.25, we get                          

d = ($309)/($77.25) = 4

Answer: D: x/2 = 45; x = 90

Step-by-step explanation:

half of a number is 45:

x/2 = 45

.: x = 90

Your answer is D

Answer:

D

Step-by-step explanation:

Answer:

-3

Step-by-step explanation:

10+2X-4= 0

2X= -10 + 4

2X = -6

X = -3

Answer:

1.5 inches

Step-by-step explanation:

18 divided by 12 = 1.5

Answer:

4.2 team members per day

Step-by-step explanation:

5 + 4 + 2 + 7 + 3 = 21

21/5 = 4.2

An average is the arithmetic mean of a set of observations. The average number of team members who reached their goal per day is 4.2.

An average is the arithmetic mean of a set of observations. it is given by the formula,

[tex]\rm Average=\dfrac{\text{Sum of All the workers of reached their goal}}{\text{Number of working days}}[/tex]

As it is given that the Number of team members that reach their goal on the weekdays Monday, Tuesday, Wednesday, Thursday, and Friday are 5, 4, 2, 7, and 3 respectively. Therefore, the average number of team members who reached their goal per day can be written as,

[tex]\rm Average=\dfrac{\text{Sum of All the workers of reached their goal}}{\text{Number of working days}}\\\\\\Average = \dfrac{5+4+2+7+3}{5} = \dfrac{21}{5}=4.2[/tex]

Thus, the average number of team members who reached their goal per day is 4.2.

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First of all, to find the area of a triangle you multiply the base * height and divide the result by two (2).

Let's use a triangle which sides are all 2 inches. To find the area, you do 2*2/2  which equals 2.

Now, double each side and each side of the triangle is now 4.

We do 4*4/2 which now equals 8.

The percentage increase from 2 --> 8 is 600%.

The percentage of the old area to the new area is 800%

ANSWER: 600%

? Pick one graph

Step-by-step explanation:

There's no graph visible

f(x) is the same as y

Hope this helps!

to get the equation of any straight line we only need two points off of it, hmmm let's use P and Q here and then let's set the equation in standard form, that is

standard form for a linear equation means

• all coefficients must be integers, no fractions

• only the constant on the right-hand-side

• all variables on the left-hand-side, sorted

• "x" must not have a negative coefficient

[tex](\stackrel{x_1}{6}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{2}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{2}-\stackrel{y1}{0}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{6}}}\implies \cfrac{2}{-3}\implies -\cfrac{2}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{0}=\stackrel{m}{-\cfrac{2}{3}}(x-\stackrel{x_1}{6})[/tex]

[tex]\stackrel{\textit{multiplying both sides by }\stackrel{LCD}{3}}{3(y-0)~~ = ~~3\left( -\cfrac{2}{3}(x-6) \right)}\implies 3y=-2(x-6) \\\\\\ 3y=-2x+12 \implies \stackrel{a}{2} x+\stackrel{b}{3} y=12[/tex]

Answer:

Integers and decimals

Step-by-step explanation:

Soorry im too lazy to read all this

Answer:

Arnie is mixing red and yellow paints to make two different shades of orange. To make 1 cup of dark orange​ paint, he needs 7 ounces of red paint and 1 ounce of yellow paint. To make 2 cups of light orange​ paint, he needs 13 ounces of yellow paint and 3 ounces of red paint. Answer parts a and b.

a. Arnie buys a​ 32-oz can of red paint. Does he have enough red paint to make 3 cups of dark orange paint and 3 cups of light orange​ paint? Explain.

▼  

Yes.

No.

The 3 cups of dark orange paint require  

nothing ​ounce(s) of red​ paint, and the 3 cups of light orange paint require  

nothing ​ounce(s) of red paint. Arnie needs  

nothing ​ounce(s) of red paint in​ total, so the​ 32-oz can is  

▼  

enough.

not enough.

Step-by-step explanation:

Answer:

The constant of proportionality is 5 minutes per bracelet

Step-by-step explanation:

If x and y are proportion, then y = k x, where

Let us solve our question

∵ Olivia is making bead bracelets for her friends

∵ She can make 3 bracelets in 15 minutes

We need to find the constant of proportionality in terms of minutes per bracelet, which means y represents the minutes and x represents the bracelet

∴ y = the time in minutes

∴ x = the number of bracelets

∵ y proportion with x

∴ k = [tex]\frac{y}{x}[/tex]

∵ y = 15 and x = 3

∴ k = [tex]\frac{15}{3}[/tex]

∴ k = 5

∴ The constant of proportionality is 5 minutes per bracelet

Answer:

1

Step-by-step explanation:

x is the number

x+2 is divided by 3

x+2 ÷ 3 =1

Multiple 3 on both sides

x=1

Answer:

B

Step-by-step explanation:

The slope is -1, which equals m= -1.

The answer is B.

Answer:

2.837%

Step-by-step explanation:

1/2 ×567.375/100

therefore= 2.837%

Answer:

630

Step-by-step explanation:

Answer:

630

Step-by-step explanation:

1 minute = 60 words multiply everything by 10.5

10.5 minutes = 10.5(60) = 630 words

Answer:

C. As the children's weight increased, their height decreased

Step-by-step explanation:

This is your answer becuse you can see here that the height is increasing as the weight is increasing

Thanks!

Mark me brainliest!

Answer:

In standard from, the value will be 8.234 * 10^17

Step-by-step explanation:

The answer shown on the screen of the calculator after multiplying is;

8,234 E14

This is same as;

8,234 * 10^14

In the stands from, this will be;

8.234 * 10^3 * 10^14 = 8.234 * 10^17

Answer:

Yes

Step-by-step explanation:

1/2 + 6/6

= (1*3)/(2*3) + 6/6

= 3/6 + 6/6

= 9/6

= 3/2

So the fraction 1/2 make the equation true.

Let's check

[tex]\\ \rm\Rrightarrow 6/6+1/2[/tex]

[tex]\\ \rm\Rrightarrow 1+1/2[/tex]

[tex]\\ \rm\Rrightarrow 2+1/2[/tex]

[tex]\\ \rm\Rrightarrow 3/2[/tex]

Yes true

Answer:

Step-by-step explanation:

2x-8+3x+2=4x+10+3x-6

5x-6=7x+4

minus 7x from both sides, add 6 to both dies

-2x=10

divide by -2

x=-5

Answer:

20705.875

Step-by-step explanation:

Area of a pentagon is 1/2 * P * A  p being the perimeter of the pentagon and a being the apothem.  1/2 * 548.5 * 75.5 equals 20705.875.  I'm almost positive this is correct.  So sorry if it's not.  Have a good day/night!

Answer:

X=[tex]\frac{-16-Z}{Y}[/tex]

Step-by-step explanation:

XY+Z=-16

Subtract both sides by Z

XY=-16-Z

Divide both sides by Y

X=[tex]\frac{-16-Z}{Y}[/tex]

Answer:

b=119, and c=119

Step-by-step explanation:

this is because b+61 equal 180 degrees and b and c are congruent angles

Answer:

C. All numbers are rational numbers

Step-by-step explanation:

In mathematics, any number that can be stated in fraction form or ratios is said to be a rational number. This simply means that some numbers cannot be written in fraction form and so all numbers are not rational numbers.

Examples of rational numbers include terminating decimals, integers, repeating decimals and the fractions.  

The other non-rational numbers are called irrational numbers, as they cannot be written in fraction form.

We know that:

This means that:

Step-by step calculations:

Subtract 3x both sides.

Subtract 4 both sides.

Divide 6 both sides.

*Note that:-

Using this equation we will solve for x and then find each angle...

[tex]\red{ \rule{35pt}{2pt}} \orange{ \rule{35pt}{2pt}} \color{yellow}{ \rule{35pt} {2pt}} \green{ \rule{35pt} {2pt}} \blue{ \rule{35pt} {2pt}} \purple{ \rule{35pt} {2pt}}[/tex]

[tex]9x + 4 = 3x + 16 \\ 9x + 4 - 3x = 16 \\ 9x - 3x = 16 - 4 \\ 6x = 12 \\ x = 2[/tex]

[tex]\large{|\underline{\mathsf{\red{1}\blue{ ^{s} }\orange{^{t} }\pink{ \: }\blue{a}\purple{n}\green{g}\red{l}\blue{e}\orange{ \: }\green{↯}\red{}\purple{}\pink{}}}}[/tex]

[tex] \pmb{9x + 4} \\ \pmb{9 \times 2 + 4} \\ \pmb{18 + 4} \\ \boxed{ \tt \: ∠1 = 22 \degree }[/tex]

[tex]\large{|\underline{\mathsf{\red{2}\blue{ ^{n} }\orange{^{d} }\pink{ \: }\blue{a}\purple{n}\green{g}\red{l}\blue{e}\orange{ \: }\green{↯}\red{}\purple{}\pink{}}}}[/tex]

[tex] \pmb{3x + 16} \\ \pmb{3 \times 2 + 16} \\ \pmb{6 + 16} \\ \boxed{ \tt \: ∠2 = 22 \degree }[/tex]

Answer:

3 1/9

Step-by-step explanation:

divide 4 2/3 and 1 1/2 together to find width

Answer: 9 over 10

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

Given,

[tex]6+log\frac{3}{2} (\frac{1}{3\sqrt{2} } \sqrt{4-\frac{1}{3\sqrt{2} }\sqrt{4-\frac{1}{3\sqrt{2} } ...} }[/tex]

Let,

[tex]x= \sqrt{4-\frac{1}{3\sqrt{2} }\sqrt{4-\frac{1}{3\sqrt{2} }\\[/tex]

By this we get

[tex]x=\sqrt{4-\frac{1}{3\sqrt{2} }(x) } }[/tex]

On squaring both sides,

[tex]x^{2} =4-\frac{1}{3\sqrt{2} }(x) } }\\\\x^{2} -4+\frac{x}{3\sqrt{2} } =0\\\\3\sqrt{2} x^{2} -12\sqrt{2} +x=0\\\\x=\frac{-1+\sqrt{1-(-12\sqrt{2})*(3\sqrt{2})*4 } }{2*3\sqrt{2} } \\\\x=\frac{-1+\sqrt{289} }{6\sqrt{2} } \\\\x=\frac{-1+17}{6\sqrt{2} } \\\\x=\frac{8}{3\sqrt{2} }[/tex]

Now,

[tex]6+log\frac{3}{2} [\frac{1}{3\sqrt{2} } *\frac{8}{3\sqrt{2} } ]+log\frac{3}{2} *[\frac{8}{9*2} ]\\\\6+log\frac{3}{2}(\frac{4}{9} )\\\\6-log\frac{3}{2}(\frac{9}{4} )\\\\6-log\frac{3}{2} (\frac{3}{2})^2 \\\\6-2=4[/tex]

[tex]\sqrt{4 - \dfrac1{3\sqrt2} \sqrt{4 - \dfrac1{3\sqrt2} \sqrt{4 - \dfrac1{3\sqrt2} \sqrt{\cdots}}}}[/tex]

Starting from the identity

[tex](x - y)^2 = x^2 - 2xy + y^2[/tex]

take the positive square root on both sides.

[tex]x - y = \sqrt{x^2 - 2xy + y^2}[/tex]

Note that we must have [tex]x\ge y[/tex]. Rewrite the radicand and substitute [tex]x-y[/tex].

[tex]x - y = \sqrt{x^2 - xy - y (x - y)} \\\\ ~~~~ = \sqrt{x^2 - xy - y \sqrt{x^2 - xy - y (x - y)}} \\\\ ~~~~ = \sqrt{x^2 - xy - y \sqrt{x^2 - xy - y \sqrt{x^2 - xy - y (x - y)}}} \\\\ ~~~~ \vdots \\\\ ~~~~ = \sqrt{x^2 - xy - y \sqrt{x^2 - xy - y \sqrt{x^2 - xy - y \sqrt{\cdots}}}}[/tex]

Let [tex]y=\frac1{3\sqrt2}[/tex]. Solve for [tex]x[/tex].

[tex]x^2 - \dfrac x{3\sqrt2} = 4 \\\\ x^2 - \dfrac x{3\sqrt2} + \dfrac1{72} = \dfrac{289}{72} \\\\ \left(x - \dfrac1{6\sqrt2}\right)^2 = \dfrac{289}{72} \\\\ x - \dfrac1{6\sqrt2} = \pm \dfrac{17}{6\sqrt2} \\\\ x = \dfrac{18}{6\sqrt2} \text{ or } x = -\dfrac{16}{6\sqrt2} \\\\ x = \dfrac3{\sqrt2} \text{ or } x = -\dfrac8{3\sqrt2}[/tex]

Take the positive solution to ensure [tex]x>y[/tex]. Then the infinitely nested root expression in the logarithm converges to

[tex]x - y = \dfrac3{\sqrt2} - \dfrac1{3\sqrt2} = \dfrac{4\sqrt2}3[/tex]

and the overall expression has a value of

[tex]6 + \log_{\frac32} \left(\dfrac1{3\sqrt2} \times \dfrac{4\sqrt2}3\right) = 6 + \log_{\frac32} \left(\dfrac49\right) \\\\ ~~~~ = 6 + \log_{\frac32} \left(\dfrac23\right)^2 \\\\ ~~~~ = 6 - 2 \log_{\frac32} \left(\dfrac32\right) \\\\ ~~~~ = 6 - 2 = \boxed{4}[/tex]