How many pounds of coffee worth $9 a pound should be added to 10 pounds of coffee worth $3 a pound to get a mixture worth $7 a pound

x and y are whatever you want them to be.

It can be convenient for solving a problem like this to use x and y to represent what the problem is asking for: the number of cans of cola and the number of cans of root beer. It is also convenient (less confusing) to use those variable names in the same order that the nouns of the problem are named:

... x = # of cans of cola

... y = # of cans of root beer

Then the problem statement tells you ...

... x + y = 30 . . . . . . . 30 cans total were bought

... x = 2y . . . . . . . . . . the number of cans of cola is twice the number of cans of root beer

_____

This set of equations is nicely solved by substitution: use the second equation to substitute for x in the first.

... (2y) +y = 30 . . . . . put 2y where x was

... 3y = 30 . . . . . . . . collect terms

... y = 10 . . . . . . . . . divide by 3

... 2y = x = 20

You're not done yet. You need to answer the question the problem asks.

Jared bought 20 cans of cola and 10 cans of root beer.

_____

Comment on x and y

You customarily see x and y as the variables of a problem. Personally, I like to use variables that remind me what they stand for. In this problem, I might use "c" for cans of cola and "r" for cans of root beer. Then when I've found the solution, I know exactly how it relates to what the question is asking.

Always start by writing down what the variables stand for (as we did here). Sometimes, this is called writing a Let statement: Let x = number of colas; let y = number of root beers.

Comment on problems of this type

When a proportional relationship is given between the items in a sum (2 cola cans for every root beer can), it is often convenient to work the problem in terms of groups of items. Here, a group of 3 items can consist of 2 cola cans and 1 root beer can. Then 30 items will be 10 groups, so 10 root beers and 20 colas. The problem is solved even before you can name the variables.

Even when the relationship isn't exactly proportional, you can add or subtract the extras and still work the problem this way. Had we said colas numbered 3 more than twice as many root beers, we could have our groups of 3 total 27 (30 less the 3 extra), giving 9 root beers and 21 colas (3 + 2·9).

Answer:

The perimeter of [tex]\triangle DMN[/tex] will be 62.1939...

Step-by-step explanation:

In [tex]\triangle DMN[/tex], the length of side [tex]DM = 10\sqrt{3}[/tex] and the measures of [tex]\angle M[/tex] and [tex]\angle N[/tex] are 75° and 45° respectively.

As the sum of all angles in a triangle is always 180°, so the measure of [tex]\angle D[/tex] will be:  180°- (75°+45°) = 180°- 120° = 60°

Now using Sine rule, we will get......

[tex]\frac{MN}{Sin(D)}=\frac{DN}{Sin(M)}=\frac{DM}{Sin(N)}\\ \\ \frac{MN}{Sin(60)}=\frac{DN}{Sin(75)}=\frac{10\sqrt{3}}{Sin(45)}\\ \\ MN= \frac{10\sqrt{3}}{Sin(45)}*Sin(60)=21.2132...\\ \\ DN=\frac{10\sqrt{3}}{Sin(45)}*Sin(75)=23.6602...[/tex]

So, the perimeter of [tex]\triangle DMN[/tex] will be: [tex]DM+MN+DN = 10\sqrt{3}+21.2132...+23.6602... =62.1939...[/tex]

The example is 1 x (9 x 5) = 45

Using the associative property of multiplication, we basically rearrange the parenthesis to group the first two terms like so: (1 x 9) x 5

So this is why choice D (1 x 9) x 5 = 45 is the answer

This means that 1 x (9x 5) = (1 x 9) x 5 is a true equation

Use synthetic division to solve these problems

5 | 1    -4   -7    10

  |  v    5    5   -10

     1     1    -2    0

This leads to x^2+x-2          

Next we find what adds to 1 and multiplies to -2

The factors of f(x) are 2 and -1, written out as (x+2) and (x-1)

-1/2 | 2     3     -23    -12

      | v     -1       -1      12

        2      2    -24     0

This leads to 2x^2+2x-24

Next, multiply the 2 from the a value (since a is the value with x^2 and c is the value without any x) with -24, which is -48

Now find what adds to 2 and multiplies to -48

The values for this are 8 and -6, but keep in mind, when multiplying the value of a by c, you now have to add the values in place of what you tried adding it to, this time in the problem we found using synthetic division, in this case the 2 in the b value (the middle of the equation, or the value with only one x)

2x^2+8x-6x-24

When group factoring, you'd get 2x(x+4) -6 (x+4)

So, the factors of g(x) are (x+4) and (2x-6)

Answer: 546

Step-by-step explanation:

   14     ⇒    10 + 4    

x  39     ⇒   30 + 9      

   36 |   ←    9 x 4

   90 |   ←    9 x 10

  120 |   ←  30 x 4

 300 |   ←  30 x 10

 546

From the graph, we know the y-intercepts (look at the picture).

y = 2 → y = 3x + 2

y = 3 → y = -1/3x + 3

We have

y ≥ 3x + 2 (shadow up of a line)

y ≤ -1/3x + 3 (shadows down of a line)

the common region is D.

Answer:

Option (a) and (d) are correct.

region A and region D satisfies the given inequality y ≥ 3x + 2.

Step-by-step explanation:

Given :  The graph of the system of inequalities y ≥ 3x + 2.

We have to determine which region contains the solution to the system.

We will chose a test point in each region and  see which point satisfies the given inequality.

For region A)

(0,6) is in region A

Put x = 0 and y = 6 in given inequality

We get,

6 ≥ 3(0) + 2.

6 ≥  2 (True)

For region B)

(4,6) is in region B

Put x = 4 and y = 6 in given inequality

We get,

6 ≥ 3(4) + 2.

6 ≥  12 + 2 = 14 (False)

For region C)

(0,0) is in region C

Put x = 0 and y = 0 in given inequality

We get,

0 ≥ 3(0) + 2.

0 ≥  2 (False)

For region D)

(-2,2) is in region A

Put x = -2 and y = 2 in given inequality

We get,

2 ≥ -3(2) + 2.

2 ≥ -6+ 2 = -4  (True)

Thus, region A and region D satisfies the given inequality

Thus, Option (a) and (d) are correct.

667 pounds is the answer. There are 2000 pounds in a ton.  1/3 of a ton is 666.666667 pounds.  I think this question is a conversion from tons to pounds?

Given

A triangle.

with vertices at (−2, 1) , (2, 1) , and ​ (3, 4) ​

Find out  the area of a triangle.

To proof

Formula

[tex]Area\ of\ triangle = \frac{1}{2}[ x_{1} (y_{2} -y_{3} ) + x_{2} (y_{3} - y_{1})+x_{3}(y_{1}-y_{2})[/tex]

As given the vertices at (−2, 1) , (2, 1) , and ​ (3, 4)

put in the above equation

we get

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

solving

[tex]= \frac{1}{2} [6 + 6][/tex]

thus

[tex]=\frac{1}{2} [12][/tex]

area of the triangle is 6 units².

Hence proved

The area of a triangle with vertices at (−2, 1) , (2, 1) , and (3, 4) is; Area = 6 units²

The formula for the area of a triangle when given the 3 vertices is;

Area = ½[Ax(By - Cy) + Bx(Cy - Ay) + Cx(Ay - By)]

In this question, the vertices coordinates are; A(−2, 1), B(2, 1), and C(3, 4)

Thus;

Ax = -2

Bx = 2

Cx = 3

Ay = 1

By = 1

Cy = 4

Plugging in the relevant values into the area equation gives;

Area = ½[-2(1 - 4) + 2(4 - 1) + 3(1 - 1)]

Area = ½(6 + 6 + 0)

Area = ½ × 12

Area = 6 units²

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need more info in order to kinda see how many women there were

In step 2 multiply what is inside the parenthesis by 7 (distributive property):

7 * x = 7x

7 * 3 = 21

In step 3 subtract -7x on both sides of the equation.  (Property of subtraction of equality)

Then -7x + 4x = -3x

7x-7x + 21 = 21

In step 4, both sides of the equation are divided by -3.  (owned by the equality division)

So:

-3x / -3 = x

-21 / -3 = 7

Recall that the division of equal signs results in a positive number.

Answer:

de=11

Step-by-step explanation:

We are given that b is the midpoint of ac

ac=cd, ab=3x+4,ac=11x-17 and ce=49

We have to find the value of de

b is the midpoint of ac therefore we have

ab=bc

ac=ab+bc=ab+ab=2ab

[tex]11x-17=2(3x+4)[/tex]

[tex]11x-17=6x+8[/tex]

[tex]11x-6x=8+17=25[/tex]

[tex]5x=25[/tex]

[tex]x=\frac{25}{5}=5[/tex]

Then , substitute the value of x

[tex]ab=3(5)+4=19[/tex]

ac=[tex]11(5)-17=55-17=38=cd[/tex]

ce=cd+de

49=38+de

[tex]de=49-38[/tex]

de=11

The measure of segment DE is 11.

Given:

[tex]AB = 3x+4\\AC = 11x-17\\CE=49[/tex]

See image in the attachment below showing the information given in the question.

Since B is the midpoint of AC, therefore:

[tex]AB = AC[/tex]

[tex]2(AB) = AC[/tex]

Substitute

[tex]2(3x+4)=11x-17[/tex]

Solve for x

[tex]6x +8=11x-17\\17 + 8 = 11x-6x\\25 = 5x\\[/tex]

Divide both sides by 5

[tex]5 = x\\x=5[/tex]

Find DE:

[tex]DE = CE - CD[/tex] (Segment Addition Postulate)

[tex]AC = CD = 11x-17[/tex]

Plug in the value of x

[tex]CD = 11(5) -17 = 38[/tex]

[tex]CE = 49 (given)[/tex]

Substitute

[tex]DE = 49 - 38\\DE = 11[/tex]

Therefore the length of DE = 11.

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What is the value of the number 3 in the the number 12,532.628

Solution

Here we need to use the place chart. I have attached the place value chart.

According to the place chart 3 is in tens place.

Therefore, the value of the number 3 in the number 12,532.628 is   3 x 10 = 30.

The answer is 30.

In the number 12,532.628, the digit 3 is located in the hundreds place, which means its value is 300.

The value of the number 3 in the number 12,532.628 is located in the hundreds place. To determine the place value of this digit, we start from the rightmost digit after the decimal point and move towards the left before the decimal point, labeling each position as follows: tenths, hundredths, thousandths, then units, tens, hundreds, thousands, and so on.

In 12,532.628, there are 2 units, 5 tens, 3 hundreds, 2 thousands, and 1 ten-thousands. Hence, the value of the number 3 here is 300. The digit 3 represents three hundred because it is in the hundreds place value.

precise and accurate are two different things in measurements:

most precise means the most detailed. here Alice has 2 decimals so her measurements are the most precise.

but her measurements are very different so they are not accurate.

most accurate measurements are Ivan's as they are very close to each other.

Answer:

✔ Ivan

 took the most accurate measurements.

✔ Alice

took the most precise measurements.

Step-by-step explanation:

got it right:)

Answer:

5x^2+x+1

Step-by-step explanation:

the expression for f(x) - g(x) is 5x² - 9x - 1.

To find f(x) - g(x), we simply subtract the expression for function g(x) from the expression for f(x):

f(x) - g(x) = (5x² - 4x) - (5x + 1)

Now, let's simplify the expression by combining like terms:

f(x) - g(x) = 5x² - 4x - 5x - 1

Next, combine the x terms:

f(x) - g(x) = 5x² - (4x + 5x) - 1

Now, combine the x terms inside the parentheses:

f(x) - g(x) = 5x² - 9x - 1

So, the expression for f(x) - g(x) is 5x² - 9x - 1.

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Answer:

12.36

Step-by-step explanation:

Answer:

Its: 12.36

Step-by-step explanation:

Answer:

None of the above. (Ask your teacher to show you how to work this problem.)

Step-by-step explanation:

Since the results are identical, the matrix of the next three rolls will look exactly like this matrix. (A)

The matrix of all 6 rolls will look like a 6-row matrix with the bottom 3 rows identical to the top 3 rows.

Adding or multiplying A by a constant will not produce these results.

_____

You can replicate columns using matrix multiplication, so you can transpose A, multiply it by a suitable version of an identity matrix, then transpose the result:

((A^T)·[I | I ])^T will turn the 3-row matrix to a 6-row matrix where I is a 3x3 identity matrix. I've used [I | I] here to mean the 3x3 identity matrix is itself replicated horizontally to make a 6-column matrix. ^T indicates transpose.

To represent the results of repeating die rolls in a matrix, each entry in the initial results matrix A is multiplied by the scalar value of the experiment repetition. If matrix A reflects 6 die rolls, the matrix for repeating these results would be 2A.

The student's question pertains to outcomes from rolling a six-sided die and recording the results in a matrix. To find the matrix representation of repeating the same die rolls, we would need to multiply the matrix A by the scalar value that represents the number of times the experiment is repeated. For example, if we denote matrix A as the initial 6 results and they repeated the experiment for the same number of times, then we would just need to multiply each entry in matrix A by 2 (since the results were repeated once more).

If matrix A is represented as:

The area of a rectangle is the width times the length:

[tex] A = w\cdot l \iff 228 = w\cdot 12 \iff w = \dfrac{228}{12} = 19 [/tex]

The perimeter is twice the sum of the dimensions:

[tex] 2p = 2(12+19) = 2\cdot 31 = 62 [/tex]

The perimeter of the rectangle with dimensions 19 ft*12 ft comes to be 62 square feet.

Suppose the breadth of the rectangle is x.

The perimeter of a rectangle is the sum of all its sides i.e. the sum of two lengths and two breadths.

If length and breadth are a and b respectively then perimeter =2(l+b).

According to the question

Length =12 ft

Area=228 square ft

So, length * breadth = 228

[tex]12x =228[/tex]

[tex]x=\frac{228}{12}[/tex]

x=19

So, breadth of the rectangle =19 ft

So, perimeter = 2(12+19) = 62 square feet.

Hence, the perimeter of the rectangle with dimensions 19 ft*12 ft comes to be 62 square feet.

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why hello there

Your answer is C 8.02

If u can please mark me as brainliest i really want genius!

Answer:

The correct option is C.

Step-by-step explanation:

Given information: In circle O, AB=8.02, the distance of cord AB from the center is 8.31, the distance of cord CD from the center is 8.31.

According to the chords equidistant from the center theorem, if two cords are equidistant form the center, the length of both cords are equal.

Since the cords AB and CD are equidistant form the center O, therefore

[tex]AB=CD[/tex]

[tex]8.02=CD[/tex]

The length of cord CD is 8.02 units.

Therefore correct option is C.

Answer:

0.85 mile(rounded to nearest hundredth)

Step-by-step explanation:

We have to convert 1500 yards into miles.

To convert 1500 yards into miles, we first need to know the relation between yards and miles.

So we have,

[tex]1 \:\text{mile}=1760\:\text{yards}[/tex]

Now, to convert 1500 yards into miles, we need to know how many miles are there in 1 yard.

So, we have

               [tex]1\:\text{yard}=\frac{1}{1760} \:\text{miles}[/tex]

[tex]\implies1500 \:\text{yards}=\frac{1500}{1760} \:\text{mile}[/tex]

[tex]\implies1500 \:\text{yards}=\frac{150}{176} \:\text{mile}[/tex]

[tex]\implies1500 \:\text{yards}= \frac{75}{88}\:\text{mile}[/tex]

[tex]\implies1500 \:\text{yards}= 0.85\:\text{mile}[/tex]

Hence, 1500 yards is 0.85 mile, rounded to nearest hundredth.

Hello,

Please, see the attached graph.

Thanks.

Answer: :)

Step by Step: :)

Marc and Corlina will have the same amount of CD's after 8 months.

45 + 4(8) = 77

61 + 2(8) = 77

Answer:

[tex]f(x)=\left \{ {{x^2+4}\ \ \ \ \ x<2 \atop {-x+4}\ \ \ x\geq 2}\right[/tex]

C is correct

Step-by-step explanation:

In the given graph function break at point x=2.

Left side about point x=2 is parabolic and right side straight line.

So, it would be piece wise function.

For parabola:

vertex: (0,4) and passing point (2,8)

[tex]y=a(x-h)^2+k[/tex]

[tex]y=ax^2+4[/tex]

[tex]a=1[/tex]

[tex]y=x^2+4[/tex]    For x<2

For straight line:

Twp points (4,0) and (2,2)

[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]

[tex]y-2=\dfrac{0-2}{4-2}(x-2)[/tex]

[tex]y-2=-1(x-2)[/tex]

[tex]y=-x+4[/tex]     For x≥2

Hence, The piece wise function will be

[tex]f(x)=\left \{ {{x^2+4}\ \ \ \ \ x<2 \atop {-x+4}\ \ \ x\geq 2}\right[/tex]

x = [tex]\frac{51}{5}[/tex]

subtract [tex]\frac{4}{5}[/tex] from both sides of the equation

x = 11 - [tex]\frac{4}{5}[/tex] = [tex]\frac{55}{5}[/tex] - [tex]\frac{4}{5}[/tex] = [tex]\frac{51}{5}[/tex]

Answer:

10.92 or 10 23/25

Step-by-step explanation:

What you do is you try to get X by itself so put the fraction 4/5 on the other side so that is turns out to be 11-4/5. Now you can turn 4/5 into a decimal which would be .8 and subtract that by 11which gives you 10.92 or if you want to keep it as a fraction .92 as a fraction is 23/25 so you get 10 23/25

ANSWER

In 16 years time.

EXPLANATION.

If the number of subscribers is 324 million, then it means

[tex]f(t)=324[/tex]

But we were given that,

[tex]f(t)=18.997t+16.711[/tex]

This implies that,

[tex]324=18.997t+16.711[/tex]

We now solve for t,

[tex]324-16.711=18.997t[/tex]

[tex]307.289=18.997t[/tex]

[tex]\frac{307.289}{18.997}=t[/tex]

[tex]16.17566=t[/tex]

That will be approximately in the 16th year.

In order to calculate the year where the number of US cell phone subscribers matches a certain number using the given linear model equation, you solve for the time variable. With the specified 324 million subscribers, the corresponding year would be approximately 2011.

To use the provided linear model F(t) = 18.997t + 17.711 to predict the year where the number of subscribers will be 324 million, we need to solve the equation for t with C(t) set to 324:

324 = 18.997t + 17.711

To do so, subtract 17.711 from both sides to isolate the term with t:

324 - 17.711 = 18.997t

Then, divide both sides by 18.997 to solve for t:

(324 - 17.711) / 18.997 = t

After calculating, you will get approximately t = 16.123. Remember, t is the number of years after 1995, so you would add 16 (rounded from 16.123) to 1995. Thus, the model predicts that the number of US cell phone subscribers will reach 324 million in 2011.

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Using a number line to show what -4 + 3 equals:

Start at the -4.  Move three spaces to the right (+3).  You land on -1.

Using a number line to show what 3 + (-4) equals:

Start at the 3.  Move four spaces to the left (-4).  You land on -1.

The commutative property of addition states that a + b = b + a.

Carla

Amir

Carlo

Esther

From greatest to least!

Answer:

1. Carla

2. Amir

3. Carlo

4. Esther

The number 87.65487.65487, point, 654 can be placed on a place value chart as follows:

Tens Ones . Tenths Hundredths Thousandths

888 777 ..point 666 555 444  

Decimal place value

The first digit after the decimal represents the tenths place. The next digit after the decimal represents the hundredths place. The remaining digits continue to fill in the place values until there are no digits left.

Example: 0.810.810, point, 81

The number 0.\blueD8\greenD10.810, point, start color blueD, 8, end color blueD, start color greenD, 1, end color greenD is made up of \blueD88start color blueD, 8, end color blueD tenths and \greenD11start color greenD, 1, end color greenD hundredth.

We can also write this as:

0.\blueD8\greenD1=\blueD{0.8}+\greenD{0.01}0.81=0.8+0.010, point, start color blueD, 8, end color blueD, start color greenD, 1, end color greenD, equals, start color blueD, 0, point, 8, end color blueD, plus, start color greenD, 0, point, 01, end color greenD

or

0.\blueD8\greenD1=\blueD{\dfrac8{10}}+\greenD{\dfrac1{100}}0.81=  

10

8

​  +  

100

1

​  0, point, start color blueD, 8, end color blueD, start color greenD, 1, end color greenD, equals, start color blueD, start fraction, 8, divided by, 10, end fraction, end color blueD, plus, start color greenD, start fraction, 1, divided by, 100, end fraction, end color greenD

Or we can use a place value chart:

Ones . Tenths Hundredths

000 ..point \blueD88start color blueD, 8, end color blueD \greenD11start color greenD, 1, end color greenD

Want to learn more about decimal place value? Check out this video.

Want to review whole number place value? Check out this article.

Practice

If it is like in the picture, then:

Domain = [-3, 3] (we read from the x axis)

Range = [-3, 1] (we read from the y axis)

If there are no points at the ends of the segments, then:

Domain = all real numbers

Range = (-∞ , 1]