The first graph represent a=450-20t, which describes the relationship between gallons of water in tank and time in minutes. a. Where on the graph can we see 450? Where can we see the -20? b. What do these numbers mean in this situation?
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Answer:

x = -8

y = 0

Step-by-step explanation:

The two shown equations can be added together:

   x + 4y = -8

+ ( x - 4y = -8 )

The two x's would combine to make two x, the 4y and -4y cancel out to zero, and -8 added to -8 is -16:

2x = -16

Therefore, x = -8. We can plug this into the first equation to get:

-8 + 4y = -8

Subtracting 8 on both sides yields:

4y = 0

Now divide by 4 on both sides to get

y = 0

We can check these values by plugging them into the second equation:

(-8) - 4(0) = -8

-8 - 0 = -8

-8 = -8

Since -8 always equals -8, the answer is correct.

Answer:

-3ab

Step-by-step explanation:

-27/9= 3

(a^2)/a=a

(b^2)/b=b

The height in feet of the missile after 5 seconds in the air is; 875 ft

We are given the  quadratic function of the height in terms of time, x, in seconds as; h(x) = - 17x² + 260x

where;

h(x) is height after x seconds

x seconds is time of missile in air when thrown.

Thus, after five seconds, we have;

h(5) = - 17(5)² + 260(5)

h(5) = -425 + 1300

h(5) = 875 feet

Complete question is;

A missile is launched from the ground. Its height, h(x), can be represented by a quadratic function in terms of time, x, in seconds.

After 1 second, the missile is 243 feet in the air; after 2 seconds, it is 452 feet in the air.

The height of the can be represented by this function:

h(x) = - 17x² + 260x

Find the height, in feet, of the missile after 5 seconds in the air.

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It will take 764664.6875 days to empty the water

The given parameters are:

The time is calculated as:

Time = Volume/Rate

So, we have:

Time = 1 cubic mile ÷ 1000 gallons per minute

Convert gallons to cubic mile

Time = 1 cubic mile ÷ (9.0817e-13 * 1000) cubic mile per minute

Divide

Time = 1.10111715 × 10^9 minute

Convert to days

Time = 764664.6875 days

Hence, it will take 764664.6875 days to empty the water

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A. The number of hours of training that you can purchase with a $3,000 training budget at $40 per employee per hour and a one-time $200 fee is 70-employee-training-hours.

B. Each employee will get 7 hours of training, assuming your organization has 10 employees.

The training cost of employees varies from one organization to another.

The training cost also depends on the training provider and the number of hours of training being offered.

Training budget = $3,000

One-time fee = $200

Remainder after the one-time fee = $2,800 ($3,000 - $200)

Training costs per employer per hour = $40

Hours of training to purchase = 70 ($2,800/$40)

Thus, an organization with 10 employees can obtain 70 hours of training with the training budget.

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Answer:

  12

Step-by-step explanation:

The problem statement tells us the definition of 3f(x). In order to find the value of 3f(2), we substitute 2 for x and do the arithmetic.

__

  3f(x) = 3x² . . . . given

  3f(2) = 3·2² = 3·4 = 12 . . . . . substitute 2 for x

The value of 3f(2) is 12.

There are 4.15E12 ways to select the members of the committee to have the same number of Reds as Blues

The given parameters are:

Reds = 44

Blues = 56

Committee member = 10

To have the same number of Reds as Blues, the committee must have 5 reds and 5 blues.

So, the number of ways is;

Ways = 44C5 * 56C5

Evaluate the combination expressions:

Ways =  1.086008 E+6 *  3.819816 E+6

Evaluate the product

Ways =  4.15E12

Hence, there are 4.15E12 ways to select the members of the committee

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Answer:

100

Step-by-step explanation:

In this sequence, we can observe that the consistent change between each number in the series is divided by half.

From 400, we divide by 2 to get 200.

400 / 2 = 200

From 50, we divide by 2 to get 25.

50 / 2 = 25

So, to fill in the number after 200, we should logically divide by 2:

200 / 2 = 100

100 also fits into the following numbers, because 100 / 2 is 5.

Answer:

The missing number would be 100

Step-by-step explanation:

You're essentially cutting the numbers in half. For example:

half of 400 would be 200

half of 200 is 100

half of 100 is 50

half of 50 is 25

Answer:

(7x-3)/-1

Step-by-step explanation:

swap the x and y and then move the y by itself

x=(3-y)/7

7x=3-y

7x-3=-y

(7x-3)/-1=y

well, from 2005 to 2009 is 4 years, so, in 4 years that account went from 360 to 420 at a rate "r", let's find that rate.

[tex]\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$420\\ P=\textit{initial amount}\dotfill &360\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\dotfill &4\\ \end{cases} \\\\\\ 420=360(1 + \frac{r}{100})^{4} \implies \cfrac{420}{360}=(1 + \frac{r}{100})^{4}\implies \cfrac{7}{6}=\left( \cfrac{100+r}{100} \right)^4 \\\\\\ \sqrt[4]{\cfrac{7}{6}}=\cfrac{100+r}{100}\implies 100\sqrt[4]{\cfrac{7}{6}}=100+r[/tex]

[tex]100\sqrt[4]{\cfrac{7}{6}}-100=r\implies 3.92899\approx r \\\\[-0.35em] ~\dotfill\\\\ \underset{2015~~ - ~~2005}{\stackrel{\textit{in the year 2015}}{t=10}}\hspace{5em}A=360\left(1 + \frac{3.92899}{100} \right)^{10}\implies A\approx 529.26[/tex]

Answer:

1/3

Step-by-step explanation:

Answer:

l

Step-by-step explanation:

Answer:

Below

Step-by-step explanation:

Lines that are parallel have the same slope, so all lines parallel to the one given have the same slope as it does. That slope value is most easily seen by transforming the given equation to slope-intercept form

(y = mx + b).

This line would be y = 2x -7, so the slope of any line parallel to it must have a slope value of 2.

Hi there.

[tex]= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =[/tex]

First of all, we can't find the equation of the line that is parallel to the line we are provided with in this problem, which is [tex]\bf{2x-y=7}[/tex], until we convert this equation into another form.

.

.

This form has a name, and it's called "[tex]\bf{Slope-Intercept\:Form}[/tex].

.

.

So first, what we need to do is subtract 2x from both sides:

.

[tex]\bf{-y=7-2x}[/tex]

.

It's not mandatory, but we can re-arrange the terms "7" and "-2x":

.

[tex]\bf{-y=-2x+7}[/tex]

.

Last step: Divide both sides of the equation by -1:

.

[tex]\bf{y=2x-7}[/tex]

.

"-2x" turned into "2x" because a negative number multiplied or divided by a negative number equals a positive number.

.

"7" turned into "-7" because a positive number multiplied or divided by a negative number equals a negative number.

.

Now, our equation is in "Slope-Intercept Form".

.

Remember that "Slope-Intercept Form" looks like this:

.

[tex]\bf{y=mx+b}[/tex].

.

Now what we need to find is the equation of the line.

.

Let's skim through the provided information to see whether or not there's some information that can help us find the equation.

.

We're also provided with the fact that these lines, or equations, are parallel.

.

What that means is if two lines are parallel, their slopes are the same.

.

The slope of the line whose equation we just found is -2 (it's the number next to "x").

.

I hope that this helped clear your doubts; if any are left, please ask.

.

I wish you a nice rest of your day.

.

[tex]\bf{W}\sf{r}\bf{i}\sf{t}\bf{i}\sf{n}\bf{g}\:\sf{A}\:\bf{L}\sf{e}\bf{t}\sf{t}\bf{e}\sf{r}.[/tex]

--

Answer:

1

Key:

Step-by-step explanation:

[tex]2^0=1[/tex]

Answer: C

Step-by-step explanation:

We know that [tex]\angle AHB=90^{\circ}[/tex], and thus by the exterior angle theorem,

[tex]90^{\circ}+\alpha=4\alpha\\\\90=3\alpha\\\\\alpha=30^{\circ}[/tex]

Thus, [tex]\angle CAB=2\theta=\boxed{60^{\circ}}[/tex]

u₁₂ represents the amount of loan remaining after 12 years

The function is given as:

u₀ = 8000

[tex]u_n = u_{n-1}(1 + 0.054) - 500[/tex]

Given that the subscript n in [tex]u_n[/tex] represents number of years and [tex]u_n[/tex] represents the amount left to be paid after n years.

We can conclude that:

u₁₂ represents the amount of loan remaining after 12 years

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Rhiannna needs 1024 inches longer bedspread if Rhiannna gets a new bedspread that is 33 in length.

It is defined as the two-dimensional geometry in which the angle between the adjacent sides are 90 degrees. It is a type of quadrilateral.

The question is incomplete.

The complete question is:

Rhiannna has a rectangular bedspread that measures 234 in. By 245 in. She wants to sew a fringe around the edge of the bedspread. What length of fringe does Rhiannna need to purchase. Rhiannna gets a new bedspread that is 33 in length. What length of the fringe does Rhiannna need for the longer bedspread?

We know perimeter of the rectangle = 2(length + width)

= 2(234 + 245 )

= 958 inches

Rihannon gets a new bedspread that is 33 in length:

New perimeter = 2(33) + 958 = 1024 inches

Thus,  Rhiannna needs 1024 inches longer bedspread if Rhiannna gets a new bedspread that is 33 in length.

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Answer:

[tex]15[/tex]

Step-by-step explanation:

if [tex]f(x) = x^2 -2x[/tex], then that means that [tex]f(5) = (5)^2 - 2(5)[/tex] which equals [tex]15[/tex].

Step-by-step explanation:

A function f is defined by f (x) = 2x - 5. Write down the values of In mathematics, a function means a correspondence from one value x of the first set to another value y of the second set. NCERT Solutions Class 11 Math's Chapter 2 Exercise 2.3 Question 3 A function f is defined by f (x) = 2x - 5.

3 hearts

4 triangle

H:T

3:4

So, ratio of hearts to triangles in simplest form is 3:4

(we can't simplify any further - HCF of 3 & 4 is 1)

Hope this helps!

Answer:

[tex]x=\boxed{6.6}[/tex]

[tex]\overline{\sf DE}=\boxed{13.2}\:\:\sf units[/tex]

Step-by-step explanation:

Geometric Mean Theorem - Altitude Rule

The altitude drawn from the vertex of the right angle perpendicular to the hypotenuse separates the hypotenuse into two segments.  The ratio of one segment to the altitude is equal to the ratio of the altitude to the other segment:

[tex]\sf \dfrac{segment\:1}{altitude}=\dfrac{altitude}{segment\:2}[/tex]

From inspection of the given diagram:

[tex]\begin{aligned}\sf \dfrac{segment\:1}{altitude} & = \sf \dfrac{altitude}{segment\:2}\\\\\implies \dfrac{5}{9} & = \dfrac{9}{2x+3}\\\\5(2x+3) & = 81\\\\10x+15 & = 81\\\\10x & = 66\\\\ \implies x & = 6.6\end{aligned}[/tex]

Substitute the found value of x into the expression for DE:

[tex]\begin{aligned}\sf \overline{DE} & = 2x+3\\\implies \sf \overline{DE} & = 2(6.6)+3\\& = 13.2+3\\& =16.2\:\: \sf units\end{aligned}[/tex]

Answer:

$60

Step-by-step explanation:

cost = $50 + $0.25x

Since x = 40

$(50 + 10) = $60

Answer:

$60/month

Step-by-step explanation:

So the equation would be 50 + (0.25 * 40), solve parenthesis 50 + 10, so answer would be $60.

Answer:

200m^3.

Step-by-step explanation:

Volume of a rectangular prism = lenght x width x height.

(5m)(10m)(4m) = 200m^3.

Using proportions, considering the total number of students, it is found that 216 boys to linking their school lunch.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

In this problem, 400 - 152 = 248 boys were surveyed. 32 said they liked the school lunch and 248 - 32 = 216 said no liking their school lunch.

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