In one day, Joe consumes 530 calories by drinking 1 serving of juice, 2 servings of milk, and 1 soda. Darius consumes 370 calories by drinking 2 servings of juice and 1 serving of milk. Marian consumes 510 calories by drinking 3 servings of milk and 1 soda. Using matrices to solve, how many calories are in 1 serving of milk?

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

Answer:

440x4=2200

Step-by-step explanation:

I'm guessing you meant 1/4, which is also known as 0.25, and if you know that 440 meters is equal to 1/4th of the whole race track you just have to multiply 440 by 4.

An expression for the total cost of the daycare for Lucy's dog this week is T = 3F + 2H and the total cost is equal to $114.

In this exercise, you're required to write an expression for the total cost of the daycare for Lucy's dog this week. Thus, we would assign a variable to the cost for full-day and half-day day care as follows:

Thus, the total cost of the daycare is given by:

T = 3F + 2H

Evaluating the expression, we have:

T = 3(28) + 2(15)

T = 84 + 30

T = $114.

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Answer:

1/3

Step-by-step explanation:

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:

1

Key:

Step-by-step explanation:

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

The value of x for the given equation is 5.

An equation can be defined as a mathematical statement consisting of an equal symbol between two algebraic expressions that have the same value. The most basic and common algebraic equations in math consist of one or more variables.

Here, as per the given Equation

[tex]2^x-1 = 31[/tex]

[tex]2^x = 31 + 1[/tex]

[tex]2^x = 32[/tex]

[tex]2^x = 2^5[/tex]

On comparing both sides, we get

x = 5

Thus, the value of x for the given equation is 5.

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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]

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.

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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Answer:

If the arcs are the same

4x+25=5x

x=25

So, QPR is 4(25)+25

QPR is 125

Answer:

-3 ,-2 ,-1, 0

Step-by-step explanation:

x is the smallest integer then, x+x+1+x+2+x+2=-6
4x+6= -6   4x=-12 x= -3 so the integers are..

Answer:

[tex]d = \sqrt{109}[/tex]

Step-by-step explanation:

Use the distance formula.

[tex]\text{The distance between two points } (x_1, y_1) \text{ and } (x_2, y_2) \text{ is given by the formula:}\\d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]

Your points are (-4, 11) and (6, 8).

[tex]d = \sqrt{(-4 - 6)^2 + (11 - 8)^2}\\\\d = \sqrt{(-10)^2 + (3)^2}\\\\d = \sqrt{100 + 9}\\\\d = \sqrt{109}[/tex]

Answer:

l

Step-by-step explanation:

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:

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:

143.8m^2

Step-by-step explanation:

surface area of a cylinder has the formular

2πr(r+h)

from the question,

radius= diameter/2 = 3.2/2 = 1.6m

height (h) = 12.7m

Area= 2× 3.142×1.6(1.6+12.7)

Area= 10.0544(14.3)

Area= 143.77

Area= 143.8m^2 to 1 decimal places

Answer: 174.3

Step-by-step explanation: diameter of cylindrical tank = 3.2m

so radius is half of 3.2m

length= 12.7m

T.S.A of tank = 2pie r ( r+h)

2 x 3.14 x 3.2/2 ( 3.2/2 + 12.7 )

= 174.29

rounding it off to one decimal the answer would be 174.3

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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Answer:

-3ab

Step-by-step explanation:

-27/9= 3

(a^2)/a=a

(b^2)/b=b

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]

--

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:

200m^3.

Step-by-step explanation:

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

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

The six values of 0 shown on the dot plot represent that 6 students out of the 30 sampled did not send any text messages daily.

With the sample being representative of the population, a dot plot for the entire population would have the same proportions as the sample but with a larger number of students.

The number of dots above a number indicates the number of students who send that number of text messages daily.

As there are 6 dots over 0, it means that 6 students do not send any text messages daily.

Seeing as the sample is representative of the entire population, a dot plot for the whole school would have a larger number of dots over each number but the proportions would be the same as the sample.

For instance, the proportion of total students who don't send any messages per day is:

= 6 / 30

= 20%

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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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Step-by-step explanation:

Given: x=5 and y=6

=>4x2+3y

=> 8+3(6)

=> 8+18

=> 26

Hope it helps

The value of this expression is 58

Algebraic expression is a mathematical sentence that involves all mathematical operations.

In an algebra - a real number is always accompanied by some letter, which can represent a variable or unknown.

— To solve this expression, just: change the letters for the numbers and multiply/add.

⚘ Resolution

[tex]\large \sf 4x2+3y[/tex]

[tex]\large \sf 4 \cdot 5 \cdot 2 +3 \cdot 6[/tex]

[tex]\large \sf 40 +18[/tex]

[tex]\red{\boxed{\boxed{\green{\large \sf \ 58 \ }}}}\\[/tex]

Therefore, the value of this expression will be 58