Luis is helping to make tacos for a school fundraiser. He needs to buy tortillas. Happy Grocery sells small packs of 20 tortillas for $4.40 and large packs of 45 tortillas for $8.55. Luis has been given $48 to spend on tortillas. Fill in the blanks to complete the statements. Tortillas The unit price for the small pack is $ A per tortilla. The unit price for the large pack is $ B per tortilla.

Answer: (a) 3270 (b) 6270

Step-by-step explanation:

Formula for compound interest: P (1 + r/100 ) ^n,

where P = principal, r = interest rate,  n = number of years

------------------------------------------------------------------------------------------------------------

In question (a),

P = $3000

r = 9%

n = 1

3000 ( 1 + 9/100) ^1 = $3270

------------------------------------------------------------------------------------------------------------

In question (b),

P = $3000

r = 9%

n = 2

3000 ( 1 + 9/100) ^2 = $6270

Midpoint formula : -

Midpoint calculation

The midpoint formula is a method used to locate the midway point between two coordinates on a graph. The midpoint of a line segment with endpoints A and B is the point that is precisely between A and B, that is, it is placed at the same distance from A and B, as shown in the illustration below.

The midpoint formula can be utilized when two points on a graph in the coordinate plane are known. The midpoint M of two points (x1, y1) and (x2, y2) is:

Notice that the midpoint formula includes calculating an average of the x- and y-values of two coordinates. The midway formula may be simpler to recall as a result. The sum of two number is equal to multiplying a number by 2. In a coordinate system, a line segment's midpoint is defined as the point midway between two points in the vertical and horizontal directions. This value is equivalent to the line segment's average x- and y-coordinates. It should be rather simple to recall the midway formula if you keep this in mind.

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Answer:

(-1, -4)

Step-by-step explanation:

y = -x is the 45° diagonal through the origin from top left to bottom right.

a reflection across that line brings anything that is in quadrant 1 (x and y are positive) to quadrant 3 (x and y are negative) like this point. and vice versa.

points in quadrant 2 stay in quadrant 2, points in quadrant 4 stay in quadrant 4.

but in every case x and y are exchanged and both signs are flipped like (-1, 2) turns into (-2, 1).

or for our point : (4, 1) turns into (-1, -4)

The light's coverage area is given mathematically as i.e. Area=[tex]\pi d^{2}[/tex]

Given that a lighthouse casts a revolving beam of light as far as they peir and asked the area is covered.

The revolving beam of light covers the whole space i.e entirely 360°

I.e. it forms a circle-like region

Area of circle = [tex]\pi r^{2}[/tex]{ where r is the radius of circle}

Let's assume the distance traveled by light as "d"

as it forms a circular region, it forms a circle of radius "d"

Mathematical connection i.e. area of the region

⇒area of circular region=[tex]\pi d^{2}[/tex] {where d is the radius of region}

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Answer:

3x+4x-1+x+2=73

8x+1=73

8x=73-1

8x=72

8x/8=72/8

x=9

Perimeter (p) of a triangle:

[tex]p = a + b + c[/tex]

P = 73 units

To find the value of x

[tex]73 = 3x + 4x - 1 + x + 2[/tex]

→[tex]73 = 8x + 1 \\ 73 - 1 = 8x[/tex]

→[tex]8x = 72[/tex]

→[tex] \frac{8x}{8} = \frac{72}{8} [/tex]

[tex]x = 9[/tex]

Answer: i=-1.75

Step-by-step explanation:

3i - 6 = 7i + 1

3i-3i-6=7i-3i+1

-6=4i+1

-6-1=4i+1-1

4i=-7

i=-7/4

i=-1.75

Answer: 26

Step-by-step explanation:

17 + 2 × 9 ÷ 3 + 4 × 6 ÷ 8=

17 + (2 × 9 ÷ 3) + (4 × 6 ÷ 8)=    ==> multiplication and division come before addition

17 + (18 ÷ 3) + (24 ÷ 8)=

17 + 6 + 3=

23+3=26

Answer:

Hello,

Step-by-step explanation:

[tex]1 < x\leq 5 \ \\\Longrightarrow\ 4 < 4x \leq 20 \ \\\Longrightarrow\ -1 < 4x-5 \leq 15 \\\Longrightarrow\ -1 < f(x) \leq 15 \\\\range=]-1; 15][/tex]

The range of the function f(x) = 4x - 5 will range from -1 to 15.

The expression that established the relationship between the dependent variable and independent variable is referred to as a function. In the function as the value of the independent variable varies the value of the dependent variable also varies.

A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.

Given that the function f(x) = 4x – 5 and the interval is  1 < x ≤ 5. The range will be calculated as,

1 < x ≤ 5

4 < 4x ≤ 20

4-5<4x - 5< 20-5

-1 < 4x - 5 < 15

Therefore, the range of the function f(x) = 4x - 5 will range from -1 to 15.

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Answer:

Answer is (-10,7) and inequality form: -10<c<7

Step-by-step explanation:

First factor the equation.

(c+7)(c-10)

Then find out which intervals make (c+7)(c-10)<0.

Answer:

this question is wrong .................

Answer:

39÷(5+(4×5÷2) )

39÷(5+(20÷2) )

39÷(5+10)

39÷15

2.6

Answer:

-x^2-2xy-3x

Step-by-step explanation:

The perimeter of the given rectangle is a 3.31 meter.

According to the statement

We have to find that the perimeter of rectangle.

So, For this purpose, we know that the

Perimeter is the distance around the edge of a shape.

From the given information:

The length of the tabletop is 1.83 meters and the width is 0.74 meter.

Then the formula to find the perimeter is a

P =l +2w

Here substitute the values then

P =l +2w

P = 1.83 +2*0.74

Now add the terms to get a perimeter of the rectangle.

Then

P = 1.83 +1.48

P = 3.31.

So, The perimeter of the given rectangle is a 3.31 meter.

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Answer: 70

Step-by-step explanation:

7 days a week x 2 lawns = 14

14 lawns x 5 weeks = 70 lawns

Answer:

70 lawns

Step-by-step explanation:

If Bob mows lawns every day for 5 weeks this is how the equation would work:

2 * 7 = 14

14 * 5 = 70

I got the 7 because there's seven days per week.

The total number of hours taken by farmer's son to plow the farm is 19 hours.

Time refers to the duration of any task or activity that occurs or continues.

Work is a process or set of tasks designed to achieve a specific result.

For, the given question;

Let F be the number of hours taken by farmer to finish the work.

Let S be the number of hours taken by farmer' son to finish the work.

The amount of work finished in 1 hour by farmer is 1/F = 1/11.

The amount of work finished in 1 hour by farmer's son is 1/S.

The amount of work finished by both in 1 hours is;

1/F + 1/S = 1/7

1/S = 1/7 - 1/F

1/S = 1/7 - 1/11

Simplifying the given term;

1/S = 4/77

or, S = 77/4 = 19.25 hours.

S = 19 hours (fraction reduced to lowest terms)

Thus, the time taken by the farmer's son to complete the plow of field is 19 hours.

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Answer: C=550+121m

Step-by-step explanation:

In the above question the |x| represents the absolute value. |x - 1| < 5  is equivalent to -5 < x - 1 < 5.

Algebra usually requires us to be careful about not just size of a value but also its sign. -10 is different than the 10. 3+7  yields a different result than the 3+(-7) . But there are circumstances in which sign doesn’t matter, in mathematics and in real life. Have you ever stumbled stepping on or off the moving walkway? It doesn’t really matter if you’re moving faster or slower than ground surface—it’s the magnitude of difference that makes you lose your balance. Or think of taking long hike—your feet will get just as the sore whether you go to north or south. Direction doesn’t matter, only the distance.

In mathematics, there’s a concept for dealing with the situations where size matters more than sign. It’s called the absolute value. Absolute value of a number is it's value regardless of its sign.

Given,

|x - 1| < 5

|x| this represents absolute value. It is the distance of x from 0, so value of x can be both positive and negative.

⇒ |x - 1| < 5 can be (x - 1) < 5 and -(x - 1) < 5

⇒ -(x - 1) < 5

⇒ (x - 1) < -5

So equivalent of |x - 1| < 5 is -5 < x - 1 < 5

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Answer:

Its C

which is –5 < x – 1 < 5

The new ratio of ownership once the business was owned by only Andrea and Lindsay is 8 : 7

The ratio is given as:

Andrea : Dina : Lindsay = 7 : 9 : 14

The partnership worth is given as

Worth = $1,800,000

The amount received by Dina is:

Dina = Dina Ratio/Total Ratio * Worth

So, we have

Dina = 9/(7 + 9 + 14) * 1800000

Evaluate

Dina = 540000

Hence, Andrea pays Dina $540,000 for her share of the partnership

Initially, we have:

Andrea : Dina : Lindsay = 7 : 9 : 14

So, the new ratio is

Andrea : Lindsay = (7 + 9) : 14

Evaluate

Andrea : Lindsay = 16 : 14

As a percentage, we have

Andrea = 16/(16 + 14) * 100%

This gives

Andrea = 53.33%

Hence, Andrea owns 53.33% of the business after she bought out Dina

In (b), we have:

Andrea : Lindsay = 16 : 14

Simplify

Andrea : Lindsay = 8 : 7

Hence, the new ratio of ownership once the business was owned by only Andrea and Lindsay is 8 : 7

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We get that the birds and the dancers will clock out again in 30 minutes.

We are given that:

a cuckoo clock has birds that pop out of their nests every 6 minutes.

And the dancers that pop out every 15 minutes.

Now, they have popped out the same time. For this to happen again, we will find the LCM of 6 and 15.

6 = 2 × 3

15 = 3 × 5

LCM = 2 × 3 × 5

LCM = 3 × 10

LCM = 30

So, they will pop out again after 30 minutes.

Therefore, we get that the birds and the dancers will clock out again in 30 minutes.

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The inequality that correctly compares the numbers is 0.47 < 125% < three and two fifths

The numbers are given as:

125%, 0.47, and three and two fifths

Rewrite properly as:

125%, 0.47, and 3.4

Express the percentage as decimal

1.25, 0.47, and 3.4

Reorder the numbers in ascending order

0.47, 1.25 and 3.4

Rewrite as

0.47, 125% and three and two fifths

Include the less than inequality symbol

0.47 < 125% < three and two fifths

Hence, the inequality that correctly compares the numbers is 0.47 < 125% < three and two fifths

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Answer:

Number of 12$ Shares? 25

Number of 14$ Shares? 57

Step-by-step explanation:

Let x = number of $12 shares.

Let y = number of $14 shares.

"Ivan has $1098 worth of $12 and $14 stock shares."
12x + 14y = 1098

The number of $14 shares is seven more than twice the number of $12 shares.

y = 2x + 7

We have a system of equations.

12x + 14y = 1098

y = 2x + 7

We can use the substitution method since the second equation is already solved for y. Substitute 2x + 7 for y in the first equation.

12x + 14(2x + 7) = 1098

12x + 28x + 98 = 1098

40x = 1000

x = 25

There are 25 $12 shares.

y = 2x + 7 = 2(25) + 7 = 57

There are 57 $14 shares.

Check:

25 × $12 + 57 × $1`4 = $300 + $798 = $1098

The total value is correct, so the answer is correct.

The value of x is 4 , 12 , - 1 resp. in eq 1 , 2 and 3 .

Finding values of unknown variable x .

Following are linear equations in one variable .

On solving them we get ,

1 )          2 ( 3 x - 5 ) = - 4 x + 30

             6 x - 10 = - 4 x + 30

              10 x =40

                 x = 4

2 )          5 x - 6 - 3 x = 18

              2 x = 18 + 6

              2 x = 24

               x = 12

3 )         - 11 - 5 x = 6 ( 5 x + 4 )

               - 11 - 5 x = 30 x + 24

                 - 35 x = 35

                x = - 1

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Step-by-step explanation:

9y - 5 + 9y - 1 = 9y + 9y - 5 - 1

= (9 + 9)y - 6

= 18y - 6

Figure in option A is the figure that represents a rotation of 90° clockwise of the trapezoid

The term rotation refers to the circular movement of an object or something about a point. The point mentioned is also called axis. The movement is circular because it involves turning round.

Rotation may be clockwise or anticlockwise. clockwise is the reverse of anticlockwise, and clockwise involves moving in same direction as the clock is turning,

As regards the trapezium, rotating it clockwise will result to the image depicted by option A

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The probability that voter also plans to vote “yes” on issue Q is found to be 0.4.

The following equation is used to determine the probability of an event.

Probability(Event) = Favorable Outcomes/Total Outcomes

Probability(Event) = x/n

Eight voters intend to vote "yes" on both issues.

So, the favourable outcome becomes = 8.

Twenty voters intend to vote "yes" on issue P.

Thus, the total outcome = 20.

This is denoted by 8 /20 = 0.4.

Therefore, the likelihood that a voter will vote "yes" on issue Q is found to be 0.4.

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The probability that all of them are rose bouquets is 0.143.

It should be noted that this question is about probability without replacement.

The probability of picking a rise bouquet is 5/7. It should be noted that each value decreases since Ariel is selecting 4 bouquets.

The probability that all of them are rose bouquets will be:

= 5/7 × 4/6 × 3/5 × 2/4

= 5/7 × 2/3 × 3/5 × 1/2

= 30/210

= 1/7

= 0.143

The probability is 0.143.

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Answer:

i think is 7/12

because if 4/7 chose pasta,1/5 chose pizza then we add 7+5=12 then we sudstract 12-4-1 = 7.

hope that helps

Answer:

21

Step-by-step explanation:

the price of the lower priced docs for that week would be 3x because the store sold 3 times as many low priced than the higher priced.

> so 90(3x) = 270x

170x + 270x = 440x

3080/440 = 7

7 high priced speakers were sold

to find out the cost of the lower ones you'd do

3x7 and get 21

Answer:

Step-by-step explanation:

Given function:

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

The domain is the set of all possible input values (x-values).

As the square root of a negative number cannot be taken, the domain of the given function is restricted.

[tex]x-2\geq 0 \implies x\geq 2[/tex]

Therefore, the domain of the given function is [2, ∞).

The range is the set of all possible output values (y-values).

As the square root of a negative number cannot be taken, the range of the given function is restricted.  

Therefore, the range of the given function is [0, ∞).

A function f(x) is continuous when, for every value [tex]c[/tex] in its domain:

[tex]\text{$f(c)$ is de\:\!fined \quad and \quad $\displaystyle \lim_{x \to c} f(x) = f(c)$}[/tex]

Therefore, the function is continuous on its domain [2, ∞).

Stationary points occur when the gradient of a graph is zero.

Therefore, to find the x-coordinate(s) of the stationary points of a function, differentiate the function, set it to zero and solve for x.

[tex]\begin{aligned}y & = \sqrt{x-2}\\& = (x-2)^{\frac{1}{2}\\\implies \dfrac{\text{d}y}{\text{d}x} & = \dfrac{1}{2}(x-2)^{-\frac{1}{2}}\\ & = \dfrac{1}{2\sqrt{x-2}}\\\\\dfrac{\text{d}y}{\text{d}x} & = 0\\\implies \dfrac{1}{2\sqrt{x-2}} &= 0\\\dfrac{1}{2} &\neq 0\end{aligned}[/tex]

Therefore, there are no stationary points.

As the domain is restricted and f(x) ≥ 0, the minimum point of the function is at point (2, 0).

[tex]\textsf{A function is \textbf{increasing} when the \underline{gradient is positive}} \implies \dfrac{\text{d}y}{\text{d}x} > 0[/tex]

[tex]\textsf{A function is \textbf{decreasing} when the \underline{gradient is negative}} \implies \dfrac{\text{d}y}{\text{d}x} < 0[/tex]

Increasing

[tex]\begin{aligned}\dfrac{\text{d}y}{\text{d}x} & > 0 \\ \implies \dfrac{1}{2\sqrt{x-2}} & > 0 \\ \dfrac{1}{\sqrt{x-2}} & > 0\\ \textsf{If $\frac{1}{a} > 0$ then $a > 0$}: \\ \implies \sqrt{x-2} & > 0\\ x-2 & > 0\\ x & > 2\end{aligned}[/tex]

Decreasing

[tex]\begin{aligned}\dfrac{\text{d}y}{\text{d}x} & < 0 \\ \implies \dfrac{1}{2\sqrt{x-2}} & < 0 \\ \dfrac{1}{\sqrt{x-2}} & < 0\\ \textsf{If $\frac{1}{a} < 0$ then $a < 0$}: \\ \implies \sqrt{x-2} & < 0\\ \textsf{As $\sqrt{x}\geq 0$, no solution.}\end{aligned}[/tex]

Therefore:

[tex]\textsf{A function is \underline{even} when $f(x) = f(-x)$ for all $x$.}[/tex]

[tex]\textsf{A function is \underline{odd} when $-f(x) = f(-x)$ for all $x$.}[/tex]

As there is no symmetry about the y-axis (even symmetry) and no origin symmetry (odd symmetry), the symmetry of the function is neither.

Answer:

Domain: [2, ∞)

Range: [0, ∞)

Continuity: Function is continuous on its domain [2, ∞).

Minimum point at (2, 0).

Increasing function: (2, ∞)

Symmetry: Neither as there is no symmetry about the y-axis and no origin symmetry.

The value of x that makes ∠U and ∠V to be supplementary angles are; x = 15°

When we are talking about angle theorem and congruency in mathematics, it is well know that supplementary angles are defined as angles whose sum is equal to 180 degrees.

Now, we are given;

∠U = 3x°

∠V = 3(∠U)

Thus;

∠V = 3(3x°) = 9x°

From definition of supplementary angles, we can say that;

3x° + 9x° = 180°

12x = 180°

x = 180/12

x = 15°

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