Jim wants to buy strawberries and raspberries for the company party. Strawberries cost $1.80 per pound and raspberries cost $1.95 per pound. If he only has $15 to spend on berries, which inequality represents the situation where he buys x pounds of strawberries and y pounds of raspberries?

A) 1.80x + 1.95y ≤ 15
B) 1.80x + 1.95y ≥ 15
C) 1.95x + 1.80y ≤ 15
D) 1.95x + 1.80y ≥ 15

Answer: The second equation (2y=4x+6) can be divided by 2 to get y=2x+3. Since this is the same equation as the first one, there are infinite solutions.

Answer: C

Step-by-step explanation:

 x² + 25

= x² - (-25)

This can now be factored using the sum & difference formula:

√x² = x

√-25 = 5i

So, x² - (-25) = (x - 5i)(x + 5i)

Answer:

Well some places are more expensive. This will effect the prices of utilities because some places have a higher expense of living because of the lack of certain materials or because of the desirable location. For example, although living in Hawaii was beautiful, it was extremely expensive for everyday items because most things needed to be shipped and because of constant tourism.

The factor for dependency of Utility Cost shown below.

The cost of using utilities like power, water, waste disposal, heating, and sewage is known as a utilities expense. During the reporting period, the costs are incurred, computed, and accumulated for, or a payment is made.

Given:

Due to climate and fluctuating utility prices, location might affect your utility expenditures. The expense of heating would be higher in an extremely cold climate than in a warmer one.

Certain locations are more pricey. The cost of utilities will be impacted because some regions have a greater cost of living due to a shortage of specific materials or a desirable location.

For instance, even though Hawaii was a wonderful place to live, the cost of basic necessities was very high due to the frequent tourism and the fact that the majority of goods had to be shipped.

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Answer:

8 minutes

Step-by-step explanation:

time = distance/speed

A decrease of 15 mph from 45 mph means the speed on the second segment is 30 mph. Filling in the given values in the above equation, we have ...

... time = (4 mi)/(30 mi/h) = 4/30 h = 8/60 h × (60 min/h) = 8 min

Answer:

Part 1. [tex]\dfrac{x+1}{2x}=\dfrac{x^2-7x+10}{4x}.[/tex]

Part 2. Solutions: [tex]x_1=1,\ x_2=8.[/tex]

Extraneous solution: [tex]x=0.[/tex]

Step-by-step explanation:

Part 1. You are given the equation

[tex]\dfrac{1}{2}+\dfrac{1}{2x}=\dfrac{x^2-7x+10}{4x}.[/tex]

Note that

[tex]\dfrac{1}{2}+\dfrac{1}{2x}=\dfrac{x+1}{2x},[/tex]

then the equation  rewritten as proportion is

[tex]\dfrac{x+1}{2x}=\dfrac{x^2-7x+10}{4x}.[/tex]

Part 2. Solve this equation using the main property of proportion:

[tex]4x\cdot (x+1)=2x\cdot (x^2-7x+10),\\ \\2x(2x+2-x^2+7x-10)=0,\\ \\2x(-x^2+9x-8)=0.[/tex]

x cannot be equal 0 (it is placed in the denominator of the initial equation and denominator cannot be 0), so [tex]x=0[/tex] is  extraneous solution to the equation.

Thus,

[tex]-x^2+9x-8=0,\\ \\x^2-9x+8=0,\\ \\x_{1,2}=\dfrac{9\pm\sqrt{(-9)^2-4\cdot 8}}{2}=\dfrac{9\pm7}{2}=1,\ 8.[/tex]

Part A: i forgot the question but i know its the third option (c)

Part B:

Solve the original equation by solving the proportion.

The solutions are: (1,6)

Part c:

Name the extraneous solution(s) to the equation

answer: Neither

These are for edu2020

If

[tex]ax^2+bx+c=(Ax+B)(Cx+D)[/tex]

then

[tex]ax^2+bx+c=ACx^2+(AD+BC)x+BD[/tex]

[tex]\implies a=AC[/tex]

If [tex]a[/tex] is known and Jimmy wants to find [tex]A[/tex], then he has to know the value of [tex]C[/tex].

Answer:

possible value of A are 1, 2, 4

Step-by-step explanation:

Jimmy is trying to factor the quadratic equation ax^2 + bx + c = 0.

He assumes that it will factor in the form ax^2 + bx + c = (Ax + B)(C x + D)

Given a=4

We need to find the value of A

When we do factoring we use the factors of the numbers

(Ax+B)(Cx+D) is ACx^2 + ADx + BCx + BD

[tex]ax^2 + bx + c =ACx^2 + ADx + BCx + BD[/tex]

When a=4  then AC is also 4

A* C = 4

1 * 4= 4

2 * 2= 4

4 * 1 = 4

So possible value of A are 1, 2, 4

The required quadratic equation is [tex]2x^{2} -20x+48[/tex].

Given roots of quadratic equation are 4 and 6.

Also given here leading coefficient is 2.

We know that, the formulae for forming quadratic equation when its roots are given is as follows: [tex]x^{2} -(\alpha +\beta )x+\alpha \beta[/tex]

Here [tex]\alpha and \beta[/tex] are the roots of the quadratic equation.

Let [tex]\alpha =4 and \beta = 6[/tex]

Putting the value of [tex]\alpha and\beta[/tex] in the above formulae we get,

[tex]x^{2} -(4+6)x+4\times6[/tex]

[tex]x^{2} -10x+24[/tex]

But remember here 2 is the leading coefficient of the quadratic equation with roots 4 and 6 (given in question),so we have to multiply the equation by 2 to get the final answer.

So, [tex]2(x^{2} -10x+24)[/tex]

[tex]2x^{2} -20x+48[/tex].

Hence the required quadratic equation is [tex]2x^{2} -20x+48[/tex].

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Answer: y = {5, 4, 8}

Step-by-step explanation:

f(x) = 4 + x²

f(-1) = 4 + (-1)²

      = 4 + 1

      = 5

f(0) = 4 + (0)²

      = 4 + 0

      = 4

f(1) = 4 + (1)²

      = 4 + 1

      = 5

f(2) = 4 + (2)²

      = 4 + 4

      = 8

Put the values from domain to the equation of the function.

f(x) = 4 + x²

f(-1) = 4 + (-1)² = 4 + 1 = 5

f(0) = 4 + 0² = 4 + 0 = 4

f(1) = 4 + 1² = 4 + 1 = 5

f(2) = 4 + 2² = 4 + 4 = 8

Answer: Geometric , convergent

Step-by-step explanation:

Given sequence is    {  12 + ( -8 )  + 16/3 + ( - 32/9 ) + 64/27 + . . .  . . . . }

To check whether the sequence is arithmetic , we first find difference of first two terms then find difference of third and second term .

If we get both the difference same , then it is arithmetic .

d₁   =   - 8 - ( 12 ) =  - 20

           16                              40

d₂  =   ------     - ( - 8 )  =    ------------

             3                                3

Common difference is not same , thus it is not arithmetic .

To check whether sequence is geometric , we divide second by first term and then third by second term . If we get the same ratio , then it is geometric .

             -8              - 2

r₁   =   ----------- =   ----------

             12                3

            16/3           16                     -2

r₂   =   ---------- =    ----------    =    -----------

            - 8              3 * ( -8)              3

Thus common ratio is same , so it is geometric .

Now we need to check whether it is convergent or divergent .

We have an infinite geometric series .

It is convergent if | r | < 1 , that is common ratio is less than 1 .

We have | r |  = | - 2/3 |  = | - 0.66 |  = 0.66 < 1 .

Thus the  geometric series converges .

Thus given series is geometric , convergent .

Third is the correct option .

Answer:

Convergent and Divergent Sequences and Series Practice.

1. The sequence diverges; the series diverges.
2. geometric, divergent
3. 3/5 and -1/6

Convergent and Divergent Sequences and

Series
1. 1/5 and 2/3

2.geometric, convergent

3. arithmetic, divergent

Step-by-step explanation:

You’re welcome

x = 3

"Standard form" is the form ...

... ax + by = c

where a, b, c are mutually prime integers. The coefficients a and b cannot both be zero. The leading coefficient must be positive. If "a" is zero, then the leading coefficient is "b".

So ...

... x = 3

is in standard form already. (a=1, b=0, c=3)

_____

Further comments on Standard Form

Of course, if the line has irrational slope or intercept, the coefficients cannot all be integers.

The order of the variables may be swapped, in which case the coefficient of y is the leading coefficient and must be positive.

This is the only way a vertical line can be written, as slope-intercept form is undefined for a vertical line.

Answer:

Option d is correct.

no , because y does not vary directly with x.

Step-by-step explanation:

Direct variation states that a relationship between any two variables in which one is a constant multiple of the other.

in other way, when one of the  variable changes then the other changes in proportion to the first.

If y is directly proportional to x i.e,  [tex]y \propto x[/tex]

then the equation is of the form;

[tex]y = kx[/tex] where k is the constant of Variation.

From the table:

Consider any values of x and y:

Let x = 4 and y = 28

then by definition of direct variation solve for k;

28 = 4k

Divide both sides by 4 we get;

k = 7

Then the equation become: y = 7x           .....[1]

Check whether the other data follows this equation or not,

x = 6 and y = 48

Substitute in equation [1];

48 = 7(6)

48 = 42 False

Also, for;

x = 8 and  y= 72

72 = 7(8)

72 = 56  False

⇒ y= 7x does not follows the data of the given table.

Therefore, y does not vary directly with x.

Answer:

1 cubic foot

Step-by-step explanation:

Volume = length * width * height

= 1*1*1 = 1 ft^3

The volume of the given box shaped like a cube is 1 cubic foot.

We have given that,

The box has a length of 1 foot, a width of 1 foot, and a height of 1 foot.

Volume = length * width * height

Volume= 1*1*1

Volume= 1 ft^3

Therefore the volume of the given box shaped like a cube is 1 cubic foot.

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Answer:

$1.02

Step-by-step explanation:

We are told that Clark buys 2 gallons of paint for $ 16.39.

To find the cost per pint of paint let us convert amount of paint in gallons.

1 gallon = 8 pints.          

2 gallons= 8*2 pints= 16 pints.

Now let us find cost per pint of paint by dividing the total cost of paint by number of pints in 2 gallons.

[tex]\text{The cost per pint of paint}=\frac{16.39}{16}[/tex]

[tex]\text{The cost per pint of paint}=1.024375[/tex]

Upon rounding our answer to nearest cent we will get,

[tex]\text{The cost per pint of paint}=1.02[/tex]

Therefore, the cost per pint of paint is $1.02.

If a, b and c are the lengths of the sides of a triangle then

if a ≤ b ≤ c, then a + b > c.

5, 7, 11

5 + 7 = 12 > 11   CORRECT

7, 10, 11

7 + 10 = 17 > 11   CORRECT

7, 11, 12

7 + 11 = 18 > 12   CORRECT

7, 11, 19

7 + 11 = 18 < 19   INCORRECT

Using the Triangle Inequality Theorem, the third side of the triangle must be less than the sum of other two sides and more than the absolute difference of the two sides. With the sides 7 and 11 given, the third side must be more than 4 but less than 18. Therefore, 19 cannot be the length of the third side.

In mathematics, particularly in geometry, the length of the third side of a triangle when the lengths of two sides are known, can be determined by using the Triangle Inequality Theorem. This theorem states that the length of any side of a triangle must be less than the sum of the lengths of the other two sides. In this case, the lengths of the two sides are given as 7 and 11. The sum of these two lengths is 18.

So the possible length of the third side must be less than 18 but more than the absolute difference of 7 and 11 (which is 4). Hence, the third side can be more than 4 and less than 18. Therefore out of the options provided, the value 19 could not be the length of the third side of the triangle.

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We are given that revenue of Tacos is given by the mathematical expression [tex]-7x^{2}+32x+240[/tex].

(A) The constant term in this revenue function is 240 and it represents the revenue when price per Taco is $4. That is, 240 dollars is the revenue without making any incremental increase in the price.

(B) Let us factor the given revenue expression.

[tex]-7x^{2}+32x+240=-7x^{2}+60x-28x+240\\-7x^{2}+32x+240=x(-7x+60)+4(-7x+60)\\-7x^{2}+32x+240=(-7x+60)(x+4)\\[/tex]

Therefore, correct option for part (B) is the third option.

(C) The factor (-7x+60) represents the number of Tacos sold per day after increasing the price x times. Factor (4+x) represents the new price after making x increments of 1 dollar.

(D) Writing the polynomial in factored form gives us the expression for new price as well as the expression for number of Tacos sold per day after making x increments of 1 dollar to the price.

(E) The table is attached.

Since revenue is maximum when price is 6 dollars. Therefore, optimal price is 6 dollars.

Answer:

Associative property.

Step-by-step explanation:

Associative property implies that, for instance; no matter how the numbers are grouped in the sum involving (-5, x and 4), the result is the same.

There are 750 spectators in the stadium. 420 of these spectators are women and the rest are men. What percent of the spectators are men.

The fraction [tex]\frac{420}{750}[/tex] represents the number of women in the stadium out of all the 750 people in the stadium. We can subtract 420 from 750 and we will get a difference of 330. Now we know that there are 330 men in the stadium.

The fraction [tex]\frac{330}{750}[/tex] represents the number of men at the stadium out of everyone. To find the percent of men at the stadium, we need to turn [tex]\frac{330}{750}[/tex] into a percent. [tex]\frac{330}{750}[/tex] reduced is [tex]\frac{11}{25}[/tex] because we are dividing both the numerator and denominator by the Greatest Common Factor of 330 and 750 using 30.

11 ÷ 25 = 0.44

0.44 × 100 = 44%

Therefore, 44% of the spectators in the stadium are men.

The perimeter of a rectangle is found by multiplying the length by 2 and then adding that to the width multiplied by 2.

The length is 7, multiplied by 2 = 7x2 = 14.

Subtract that from the total perimeter:

42 - 14 = 28

The length of the 2 widths is equal to 28, to find the length of 1 width, divide that by 2:

Width = 28 / 2 = 14

The width is 14 feet.

Answer:

8 adults

Step-by-step explanation:

The proper equation to find the number of adults is as follows...

(1 x 5) +(10x) = 85

Since there is only one child will will have 1 ticket for a child. hint ( 1 x 5)

Since we need to find the total number of adults at the movie group we will put (10x)

Since the total cost is 85 we will have it equal to $85

Now time to solve

5 + 10x = 85

first subtract 5 from both sides ( 5 - 5 ) and ( 85 - 5 )

10x=80

Now divide both sides by 10 ( 10x/10 ) and 80/10

x=8

So there are 8 adults.

Answer:

The daily rental rate is 75 dollars

The cost per mile is .14

The cost for the mileage is .14m

The total cost per day  is .14m+75

Step-by-step explanation:

cost = 75 + 0.14m

Let's rewrite this in the form  

y= mx+b

 where m is the slope and b is the y intercept

cost = .14m +75

The daily rental rate is 75 dollars

The cost per mile is .14

The cost for the mileage is .14m

The total cost per day  is .14m+75

Part A:

The range is the difference between the highest and lowest values:

Highest value = 78

Lowest value = 40

Range = 78-40 = 38

Part B:

The interquartile range is the difference between Q1 and Q3.

Q1 is the middle value of the lower half and Q3 is the middle value of the upper half.

There are 11 total numbers,  40 , 64, 66, 67,67,68,69,70, 71, 72, 78

The median would be the middle value, 68, so the lower half would be the 5 numbers below 68:  40 , 64, 66, 67,67.

The middle value of those numbers would be 66

The upper half are the 5 numbers above 68: 69,70, 71, 72, 78.

The middle value of those numbers is 71

The interquartile range would be 71 - 66 = 5

Part C:

The interquartile range is the better measure.

Answer:

correct choice is 1st option

Step-by-step explanation:

Two given triangles have two pairs of congruent sides: one pair of length 7 units and second pair of length 8 units. The third side is common, i.e the lengths of third sides are equal too.

Use SSS theorem that states that if three sides of one triangle are congruent to three sides of another triangle, then these two triangles are congruent.

Thus, given triangles are congruent by SSS theorem.

Answer:

5x

Step-by-step explanation:

Answer:

( -1,-5 )

Step-by-step explanation:

We have the co-ordinates A( -3,3 ), B( -1,7 ) and C( 3,3 ).

We will find the orthocenter using below steps:

1. First, we find the equations of AB and BC.

The general form of a line is y=mx+b where m is the slope and b is the y-intercept.

Using the formula of slope given by [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1} }[/tex], we will find the slope of AB and BC.

Now, slope of AB is [tex]m=\frac{7-3}{-1+3}[/tex] i.e. [tex]m=\frac{4}{2}[/tex] i.e.  [tex]m=2[/tex].

Putting this 'm' in the general form and using the point B( -1,1 ), we get the y-intercept as,

y = mx + b i.e. 1 = 2 × (-1) + b i.e. b = 3.

So, the equation of AB is y = 2x + 3.

Also, slope of BC is [tex]m=\frac{3-7}{3+1}[/tex] i.e. [tex]m=\frac{-4}{4}[/tex] i.e. [tex]m=-1[/tex].

Putting this 'm' in the general form and using the point B( -1,1 ), we get the y-intercept as,

y = mx + b i.e. 1 = (-1) × (-1) + b i.e. b = 0.

So, the equation of BC is y = -x.

2. We will find the slope of line perpendicular to AB and BC.

When two lines are perpendicular, then the product of their slopes is -1.

So, slope of line perpendicular to AB is [tex]m \times 2 = -1[/tex] i.e. [tex]m=\frac{-1}{2}[/tex]

So, slope of line perpendicular to BC is [tex]m \times (-1) = -1[/tex] i.e. m = 1.

3. We will now find the equations of line perpendicular to AB and BC.

Using the slope of line perpendicular to AB i.e. [tex]m=\frac{-1}{2}[/tex] and the point opposite to AB i.e. C( 3,3 ), we get,

y = mx+b i.e. [tex]3=\frac{-1}{2} \times 3 + b[/tex]  i.e. [tex]b=\frac{9}{2}[/tex]

So, the equation of line perpendicular to AB is [tex]y=\frac{-x}{2} +\frac{9}{2}[/tex]

Again, using the slope of line perpendicular to BC i.e. m = 1 and the point opposite to BC i.e. A( -3,3 ), we get,

y = mx + b i.e. 3 = 1 × -3 + b i.e. b = 6.

So, the equation of line perpendicular to BC is y = x+6

4. Finally, we will solve the obtained equations to find the value of ( x,y ).

As, we have y = x+6 and  [tex]y=\frac{-x}{2}+\frac{9}{2}[/tex]

This gives,  [tex]y=\frac{-x}{2}+\frac{9}{2}[/tex] → [tex]x+6=\frac{-x}{2} +\frac{9}{2}[/tex] → 2x+12 = -x+9 → 3x = -3 → x = -1.

So, y = x+6 → y = -1+6 → y=5.

Hence, the orthocenter of the ΔABC is ( -1,5 ).

The correct Answer is option (A).10,800 [tex]cm^3[/tex] oil can the small container carry.

To determine how much oil the small container can carry, given the scale factor and the capacity of the large container, follow these steps:

1. Identify the given values:

  - Capacity of the large container: [tex]\( 144,000 \, \text{cm}^3 \)[/tex]

  - Scale factor from large to small container: [tex]\( 0.075 \)[/tex]

2. Calculate the capacity of the small container:

  - Use the formula: [tex]\[ \text{Capacity of small container} = \text{Capacity of large container} \times \text{Scale factor} \][/tex]

  - Substitute the given values: [tex]\[ \text{Capacity of small container} = 144,000 \, \text{cm}^3 \times 0.075 \][/tex]

3. Perform the multiplication:

[tex]\[ 144,000 \times 0.075 = 10,800 \, \text{cm}^3 \][/tex]

Therefore, the capacity of the small container is:

[tex]\[ \boxed{10,800 \, \text{cm}^3} \][/tex]

Answer:

The total inventory is 200 + 300 + 400 + 100 = 1000.

Step-by-step explanation:

If 300 units remained, the we calculate the cost of the 700 sold via LIFO. These 700 units include the 100 units at $12.00, the 400 units at $11.00, and 200 units at $10.00 (out of the 300 purchased). This is a total cost of 100*12 + 400*11 + 200*10 = 1200 + 4400 + 2000 = $7600.

Answer:

2 hours

Step-by-step explanation:

using the relationship

distance = speed × time, then

time = [tex]\frac{distance}{speed}[/tex] = [tex]\frac{30}{15}[/tex] = 2 hours

It will take 2 hours to cover 30 miles so option (C) is correct.

The ratio is the division of the two numbers.

For example, a/b, where a will be the numerator and b will be the denominator.

Proportion is the relation of a variable with another. It could be direct or inverse.

Given that,

A cyclist rode at an average speed of 15 mph for 30 miles.

So,

15 miles ⇒ hour

Multiply by 2

2 hours ⇒ 30 miles.

Hence "It will take 2 hours to cover 30 miles".

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Answer:

50+2p=C

Step-by-step explanation:

Answer: Our required equation to find the total cost of his monthly membership to the gym  would be [tex]C=50+2p[/tex]

Step-by-step explanation:

Let C be the total cost for your monthly membership.

Let p be the number of times you used the pool in one month.

Cost of every time he want to use the pool = $2

Monthly fee = $50

According to question, it becomes,

[tex]C=50+2p[/tex]

Hence, our required equation to find the total cost of his monthly membership to the gym  would be [tex]C=50+2p[/tex]