It costs $19.00 to purchase 2 pounds of coffee and 3 pounds of tea. While it is $41.50 to purchase 5 pounds of coffee and 6 pounds and tea . how much per pound is the price of coffee?

Answer with explanation:

For any system of linear equations, we can use a method called substitution method for solving the equations.

We make one variable, from either of the equations, the subject of that equation and substitute it in the other equation.

This way, we get to find the value of the remaining variable and next we substitute this value in one of the equations to get the value of the variable left.

Final answer:

To solve linear equations using substitution, identify the unknowns, isolate a variable in one equation, substitute into the other to solve for one variable, then back-substitute to find the other variable and check the solutions for accuracy.

Explanation:

Solving Systems of Linear Equations Using Substitution

To solve a system of linear equations using the substitution method, one must follow a series of steps. Step one is to identify what needs to be determined, which in this case, is the values for the variables, known as the unknowns. In step two, find an equation in the system where one variable can be easily isolated. Next, in step three, express this isolated variable in terms of the other variable.

Once you have this expression, you move to step four, where you substitute this expression into the other equation in the system. This allows you to solve for the one remaining variable, eliminating the need for the original substituted variable. After finding this value, you proceed to step five and substitute it back into the expression from step three to find the value of the other variable.

Step six is an important verification step - checking the solutions. Substitute the values found for both variables back into the original equations to ensure that they satisfy both equations. If they do, you have found the solution to the system. If not, you need to review your steps to find any possible mistakes.

Final answer:

The expression x(x + 9) + 20x + 5 is equivalent to x² + 29x + 5.

Explanation:

To simplify the expression x(x + 9) + 20x + 5, we can distribute the x to both terms inside the parentheses:

x * x + x * 9 + 20x + 5

This simplifies to:

x² + 9x + 20x + 5

Combining like terms, we get:

x² + 29x + 5

Therefore, the expression x(x + 9) + 20x + 5 is equivalent to x² + 29x + 5.

Answer:

26.69 square meters

Step-by-step explanation:

A=r(3.14)

A= 8.5(3.14)

A=26.69 meters

Answer:

C

Step-by-step explanation:

Area (A) = length × width

A = 7 [tex]\frac{1}{2}[/tex] × 9 [tex]\frac{1}{8}[/tex]

Change both mixed numbers to improper fractions

7 [tex]\frac{1}{2}[/tex] = [tex]\frac{15}{2}[/tex]

9 [tex]\frac{1}{8}[/tex] = [tex]\frac{73}{8}[/tex]

Hence

[tex]\frac{15}{2}[/tex] × [tex]\frac{73}{8}[/tex]

= [tex]\frac{15(73)}{2(8)}[/tex]

= [tex]\frac{1095}{16}[/tex]

= 68 [tex]\frac{7}{16}[/tex]

Answer:

= 68 7/8

Step-by-step explanation:

I think it's correct

when it rises in popularity so they can raise the price and people will pay more for it (eg freddos /-/)

or sometimes the item price increases because it has cost the company more to make the product (eg shipping fares) so they need to charge more so they can still earn a profit (like fuel?)

When the Production of any good in a Particular year, is in decline, and if that good is very much essential for Human Being, then the Price of that Commodity increases.

Usually most of Natural good that is found on earth is very essential for Human being. So, when production of that good Decreases, then Price of that Commodity increases.

Answer:

B. 0.08

Explanation:

The general form of a linear equation is:

y = mx + c

where:

m is the slope or the rate of change (increase or decrease)

c is the y-intercept or the initial value

Therefore, in a linear equation, the slope simply gives us the rate of change of the function (increase/decrease)

Now, the given equation is:

y = 0.08x + 5

Comparing the given equation with the general form, we will find that:

m = 0.08

Therefore, the cost of water increase for every gallon (rate of change) is 0.08

Hope this helps :)

ANSWER

B. Function g has slope 3 which makes it steeper

EXPLANATION

The function f(x) has equation:

3x-y=6

We slope for y to get:

-y=-3x+6

y=3x-6

The slope of this function is 3.

The function g(x) passes through (-2,1) and (0,5).

The slope is

[tex]m = \frac{y_2-y_1}{x_2-x_1} [/tex]

[tex]m = \frac{5- 1}{0 - - 2} [/tex]

[tex]m = \frac{4}{2} = 2[/tex]

Function g has slope 3. Hence it is steeper.

The statement which correctly compares the slopes of two functions is:

If the slope of a function has a greater absolute value as compared to other then that function is steeper than the other.

Here we have a function f(x) as:

[tex]3x-y=6[/tex]

On changing to slope-intercept form of a line

i.e. y=mx+c

where m is the slope of the line and c is the y-intercept of the line we have:

[tex]f(x)=y=3x-6[/tex]

i.e. the  slope of function f(x) is: 3

The function g(x) is a graph that passes through (-2,1) and (-1,3)

The equation for y=g(x) is given by:

[tex]y-1=\dfrac{3-1}{-1-(-2)}\times (x-(-2))\\\\\\y-1=\dfrac{2}{-1+2}\times (x+2)\\\\\\i.e.\\\\\\y-1=\dfrac{2}{1}\times (x+2)\\\\\\i.e.\\\\\\y=2x+4+1\\\\\\i.e.\\\\\\y=2x+5[/tex]

( since we used a concept of a line passing through two-point (a,b) and (c,d) is given by the equation:

[tex]y-b=\dfrac{d-b}{c-a}\times (x-a)[/tex] )

Hence, the slope of function g(x) is: 2

The absolute value of slope of function f(x) is greater than function g(x)

( since 3>2 )

Hence, we get function f(x) is more steeper.

The answer to your question is 443.2 as the mean is the average

Answer:

55.68 square units

Step-by-step explanation:

To fond the area of a circle of diameter 8.42, we are using the area formula for a circle:

[tex]A=\frac{1}{4} \pi d^{2}[/tex]

where

[tex]A[/tex] is the area of the circle

[tex]d[/tex] is the diameter of the circle

We know from our problem that the diameter of our circle is 8.42, so [tex]d=8.42[/tex]. Replacing the values in our formula:

[tex]A=\frac{1}{4} \pi d^{2}[/tex]

[tex]A=\frac{1}{4} \pi (8.42)^{2}[/tex]

[tex]A=55.68[/tex] square units

We can conclude that the area of a circle of diameter of 8.42 units is 55.68 square units.

Answer:

[tex]A\ =55.65 \: square units[/tex]

step-by-step explanation :

Area of a circle with diameter 8.42

The area of a circle is given as

[tex]A\ =\pi ({ \frac{d}{2} })^{2} [/tex]

where d is the diameter.

Substituting into the formula :

[tex]d = 8.42 \: unts \: [/tex]

[tex]\pi = 3.14[/tex]

This implies that,

[tex]A\ =3.14 \times ({ \frac{8.42}{2} })^{2}[/tex]

We simplify to obtain :

[tex]A\ =55.65 \: square units[/tex]

Answer:

A. 9 ft

Step-by-step explanation:

Given that volume of the pyramid = 90 cu. ft.

Given that area of the base of the pyramid = 30 sq. ft.

Now we need to find about what is the height of the pyramid.

So plug the given values into formula of the volume of the pyramid

[tex]volume=\frac{1}{3}\left(Base\ Area\right)\left(Height\right)[/tex]

[tex]90=\frac{1}{3}\left(30\right)\left(Height\right)[/tex]

[tex]90=\left(10\right)\left(Height\right)[/tex]

[tex]\frac{90}{10}=Height[/tex]

[tex]9=Height[/tex]

Hence correct choice is A. 9 ft

Answer: =−x−7y

Step-by-step explanation:

First, Distribute the Negative Sign:

=3x −2y+ −1(4x+5y),

=3x+ − 2y + − 1(4x) + −1 (5y),

=3x+ −2y + −4x + −5y

Then, Combine Like Terms:

=3x+−2y+−4x+−5y

=(3x+−4x)+(−2y+−5y)

Finally you get the answer :

= −x + −7y

* Hopefully this helps:) Mark me the brainliest:)!!

∞ 234483279c20∞

Answer:

-x - 7y

Step-by-step explanation:

First, get rid of the parentheses by multiplying them out. Multiply them by one for them to go away.

Now, you have 1(3x - 2y) - 1(4x + 5y).

Now simplify, and it's 3x - 2y - 4x - 5y (Yes, -5y! It's beause -1 * 5y = -5y. The sign is supposed to change).

Ok. The next is easy: Identify your matching variables.

3x , -4x and -2y , -5y

So, we're going to assume x comes before y in the new equation, as that's how it is alphabetically, and that's it.

-x - 7y.

Hope this helps!

Answer:

Step-by-step explanation:

2x - 2 > -6             add 2 to both sides

2x - 2 + 2 > - 6 + 2

2x > -4        divide both sides by 2

2x/2 > -4/2

x > -2

or

-2x < -12              change the signs

2x > 12             divide both sides by 2

2x/2 > 12/2

x > 6

We have x > -2 or x > 6. Therefore x > -2.

Answer: Third option

The region shaded above a solid boundary line

Step-by-step explanation:

The limit for inequality [tex]y\geq\frac{1}{3}x[/tex] is the line [tex]y=\frac{1}{3}x[/tex].

Note that the inequality includes all values of y that are greater than or equal to the function [tex]f(x)=\frac{1}{3}x[/tex]. . This means that the region includes all values of y that are above the line [tex]f(x)=\frac{1}{3}x[/tex]. .

Remember that inequality includes values that are greater than or equal to the line [tex]f(x)=\frac{1}{3}x[/tex], therefore all values belonging to the limit line [tex]f(x)=\frac{1}{3}x[/tex], are also part of the region. This is represented by delimiting the region with a solid line

Finally the answer is the third option

Answer:

x = -2 or x = sqrt(13)/2 - 3/2 or x = -3/2 - sqrt(13)/2

Step-by-step explanation:

Solve for x:

x^3 + 5 x^2 + 5 x - 2 = 0

The left hand side factors into a product with two terms:

(x + 2) (x^2 + 3 x - 1) = 0

Split into two equations:

x + 2 = 0 or x^2 + 3 x - 1 = 0

Subtract 2 from both sides:

x = -2 or x^2 + 3 x - 1 = 0

Add 1 to both sides:

x = -2 or x^2 + 3 x = 1

Add 9/4 to both sides:

x = -2 or x^2 + 3 x + 9/4 = 13/4

Write the left hand side as a square:

x = -2 or (x + 3/2)^2 = 13/4

Take the square root of both sides:

x = -2 or x + 3/2 = sqrt(13)/2 or x + 3/2 = -sqrt(13)/2

Subtract 3/2 from both sides:

x = -2 or x = sqrt(13)/2 - 3/2 or x + 3/2 = -sqrt(13)/2

Subtract 3/2 from both sides:

Answer:  x = -2 or x = sqrt(13)/2 - 3/2 or x = -3/2 - sqrt(13)/2

The average cost of one box of candy is 2.35 per box

it’ll be $2.35 per box

How to find the answer:

14.10 divided by 6 = 2.35

Answer:

Tationia Rolon

Step-by-step explanation:

Here

Answer:

>6x=25<

Step-by-step explanation:

You will take the numbers (however many) multiply them and then use the two signs (greater than less than) to figure which it is. For additional help ask your teacher :)

Thank of it this way:

2 > 1 : this means that this little Pac-Man want to eat the bigger number so it would be the same if you have

1 < 2 : here 2 it's still greater then 1

1/2 = 0.5 : here we don't have a pacman but you know that 1/2 It's actually 0.5

So now if you have:

2n > -4 [divide by 2]

n > -2

And if you have a (image) Then this means that x is greater that -2 but it's less than 1, so x would be between -2 and 1

Hope this helps, ask any questions if you have.

a rectangle and a square

A rectangle & a square

The answer is probably 36

Answer:

The answer is 36 inches

Step-by-step explanation:

Since the rectangle is 9 inches long and the length is 4 inches wide and you need to find the area the formula is A=L*W so you would multiply 9 and 4 which gives you 36

Answer:

The cross section is just at the center of the rectangle. Sorry if I couldn't be of more help but good luck.

Step-by-step explanation:

Answer:

B. 8

Step-by-step explanation:

The sum of all exterior angles of pentagon is equal to 360°. There are such exterior angles: 62°, 66°, 77°, 59°, (12x)°. Thus, the sum

[tex]62^{\circ}+66^{\circ}+77^{\circ}+59^{\circ}+(12x)^{\circ}=360^{\circ},\\ \\264^{\circ}+(12x)^{\circ}=360^{\circ},\\ \\(12x)^{\circ}=360^{\circ}-264^{\circ},\\ \\(12x)^{\circ}=96^{\circ},\\ \\x^{\circ}=8^{\circ}.[/tex]

Answer:

ab

Step-by-step explanation:

Since the terms all have the variable ab then they are like terms.

Collect them by adding/subtracting the coefficients

ab(3 - 9 + 7)

= 1ab = ab ← the 1 is assumed

The expression 3ab - 9ab + 7ab simplifies to ab by combining like terms.

The student is asking to simplify the algebraic expression 3ab - 9ab + 7ab. This involves combining like terms. As all terms are multiples of ab, we can add and subtract them as coefficients:

3ab - 9ab + 7ab = (3 - 9 + 7)ab = 1ab = ab

The rules followed here are analogous to the rules of arithmetic addition and subtraction. This concept is fundamental as it provides a foundation for simplifying expressions and solving equations in algebra.

Answer:

You never gave any options, but the right answer is 3-(x+1)=1/2(3x+4)

Step-by-step explanation:

Answer:

3 - (n - 1) = (1/2)(3n - 4)

Step-by-step explanation:

Next time, please share the possible answer choices. Thank you.

"three minus the difference of a number and one"

can be represented algebraicallyl as   3 - (n - 1), where n is the number.

"one-half of the difference of three times the same number and four” can be represented by (1/2)(3n - 4).

The desired equation is thus:

3 - (n - 1) = (1/2)(3n - 4)

Answer:

y = x² - 10x + 41

Step-by-step explanation:

The standard form of a quadratic is ax² + bx + c : a ≠ 0

Given

y = (x - 5)² + 16 ← expand (x - 5)²

 = x² - 10x + 25 + 16

 = x² - 10x + 41 ← in standard form

Answer: [tex]y=x^2-10x+41[/tex]

Step-by-step explanation:

The standard form of a quadratic function is:

[tex]y=ax^2+bx+c[/tex]

You need to remember the square of a binomial:

[tex](a-b)^2=a^2-2ab+b^2[/tex]

Applying the above, you get:

[tex]y=(x-5)^2+16[/tex]

[tex]y=(x^2-2(x)(5)+5^2)+16[/tex]

Simplify the expression:

[tex]y=x^2-10x+25+16[/tex]

 Now you need to add the like terms.

THerefore, you get:

[tex]y=x^2-10x+41[/tex]

Answer:

(x, y) = (-2, 2)

Step-by-step explanation:

We are given the following two equations which we are to solve using the substitution method:

[tex]x - y = -4[/tex] --- (1)

[tex]x - 2y = -6[/tex] --- (2)

From equation (1):

[tex]x = y-4[/tex]

Substituting this value of x in (2) to get:

[tex]x = [tex]x - 2y = -6\\\\(y-4)-2y=-6\\\\-y=-6+4\\\\-y=-2[/tex][/tex]

y = 2

Substituting the value of y in (1) to get x:

[tex]x - y = -4[/tex]

[tex]x - 2 = -4[/tex]

[tex]x = -4 + 2[/tex]

x = -2

Therefore, (x, y) = (-2, 2).

Answer:

Step-by-step explanation:

Just by looking at y = 3x + 2, we can see that the slope of the line representing this function is 3 and the y-intercept is 2 (or (0, 2) ).

Plot (0, 2).  Starting from that point, move your pencil 1 unit to the right and 3 units up, plotting another dot there.

Draw a straight line thru your two dots.

A table and graph that represents the linear function y = 3x + 2 is shown in the image below.

In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical equation;

y = mx + b

Where:

Since the given linear equation y = 3x + 2 is in slope-intercept form, we would start by plotting its y-intercept on a graph;

y = 3(0) + 2

y = 2.

Lastly, we would use an online graphing calculator to plot the given linear equation for the values in its domain as shown in graph D attached above.

In conclusion, the slope of this linear equation y = 3x + 2 is equal to 3 and it does not represent a proportional relationship.

Read more on a graph here: brainly.com/question/4546414

#SPJ6

Answer:

[tex]ED=32\ units[/tex]

Step-by-step explanation:

we know that

Applying the Intersecting Secant Theorem

[tex]AC*BC=EC*DC[/tex]

substitute the values

[tex](16+5)*(5)=(ED+3)*(3)[/tex]

Solve for ED

[tex](21)*(5)=(ED+3)*(3)[/tex]

[tex]35=(ED+3)[/tex]

[tex]ED=35-3=32\ units[/tex]

Answer: 13.8%

Step-by-step explanation:

Percent error = approximate-exact/exact x 100

250-290/290 x 100 = |-13.8| = 13.8%

Answer:

The area of the triangle is 24 square feet.

Step-by-step explanation:

To find the area of the triangle you have to multiply the base and height, and then multiply the answer with 1/2.

First, multiply the base of the triangle, which is 8 feet, with the height of the triangle, which is 6 feet. Then your answer will be 48 and you can multiply that with 1/2, or divide it by two. The final answer will be 24 square feet.

Answer:

line graph and it is a function

Step-by-step explanation:

It shows a specific spot on the map

The mapping diagram is a function because each element in the domain is mapped to exactly one element in the range.

The mapping diagram that represents the given relation is:

(-3, -6)

(-1, -6)

(5, -6)

(8, -6)

This is because each element in the domain (the x-values) is mapped to exactly one element in the range (the y-values).

Is the relation a function :

Yes, the relation is a function. A function is a relation in which each element in the domain is mapped to exactly one element in the range.

In this case, each x-value is mapped to exactly one y-value.

Example:

(-3, -6) is a function because -3 is mapped to exactly one y-value, which is -6.

(5, -6) is a function because 5 is mapped to exactly one y-value, which is -6.

Conclusion:

The mapping diagram that represents the given relation is a function.

For similar question on mapping diagram.

https://brainly.com/question/7382340

#SPJ3

Complete question : 1. Identify the mapping diagram that represents the given relation and determine whether the relation is a function. {(–3, –6), (–1, –6), (5, –6), (8, –6)}