Match the numerical expressions to their simplified forms

Answer:

Step-by-step explanation:

Line LP = Line ON

Line MP =  Line MN

Line ML = Line MO

__       __

LP  =   ON

Answer:

5/9 of a foot

Step-by-step explanation:

given:

first length = 8/9 feet

second length = 1/3 feet

difference in length,

= 8/9 - 1/3

= 8/9 - 3/9

= (8-3) / 9

= 5/9 of a foot

Final answer:

The first piece of lumber is 5/9 of a foot longer than the second piece, after converting both lengths to a common denominator and performing the subtraction.

Explanation:

The question asks how much longer the first piece of lumber is than the second piece, given that one piece is 8/9 of a foot long and the other is 1/3 of a foot long. To find the difference in length between the two pieces, we subtract the length of the shorter piece from the length of the longer piece:

8/9 foot - 1/3 foot

To subtract these fractions, we need a common denominator, which is 9 in this case. Rewriting 1/3 with a denominator of 9 gives us:

8/9 - 3/9 = 5/9 foot

Therefore, the first piece of lumber is 5/9 of a foot longer than the second piece. This is a mathematics question typically suited for middle school students, who are learning about fractions and how to compute with them.

Answer:

x = 7

Step-by-step explanation:

Since the segment is an angle bisector, the sides are in the ratio

[tex]\frac{14}{21}[/tex] = [tex]\frac{6}{3x-12}[/tex] ( cross- multiply )

14(3x - 12) = 126 ( divide both sides by 14 )

3x - 12 = 9 ( add 12 to both sides )

3x = 21 ( divide both sides by 3 )

x = 7

Answer:thousandths

Step-by-step explanation:i dk

Answer:

Since the independent variable x is not the exponent, [tex]y = - 7 x^{8}[/tex] does not represent an exponential function.

Step-by-step explanation:

The general expression of an exponential function is [tex]f(x) = a^{x}[/tex], where a > 0 and a ≠ 1

Now the given function is [tex]y = - 7 x^{8}[/tex] ..... (1)

So, we can say that the function f(x) = y is not an exponential function as x is not in power of any constant.

Therefore, since the independent variable x is not the exponent, [tex]y = - 7 x^{8}[/tex] does not represent an exponential function. (Answer)

We need to find the least common denominator of the given numbers.

[tex]36[/tex] will be the lowest common denominator.

The given numbers are  [tex]\dfrac{5}{12}[/tex] and [tex]\dfrac{1}{9}[/tex]

Keep multiplying each number with a greater number starting from one.

Notice when the products are same.

The product which is common will be the lowest common denominator.

[tex]12: 12\times1=12,12\times2=24,12\times3=36[/tex]

[tex]9: 9\times1=9,9\times 2=18,9\times 3=27,9\times 4=36[/tex]

So, here [tex]36[/tex] will be the lowest common denominator.

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Using the area of a triangle formula, and given the area as 36 square centimeters and the height as 18 centimeters, it was calculated that the base of the triangle is 4 centimeters.

To find the base of a triangle when the area and height are known, we use the formula for the area of a triangle, which is Area = 1/2 × base × height. Given that the area is 36 square centimeters and the height is 18 centimeters, we can set up the equation as follows:

36 = 1/2 × base × 18

By rearranging the equation to solve for the base, we get:

base = (36 × 2) / 18

base = 72 / 18

base = 4 centimeters

Therefore, the base of the triangle is 4 centimeters.

Answer:

$0.89/1        the cost is $0.89.

Step-by-step explanation:

cost over lb

13.35/15

unit rate means for 1 so divide 15 by 15 to get  1  

what ever u do to the denominator do to the numerator so divide 13.35 by 15

13.35/15 divided by 15/15= 0.89/1

$0.89 for 1 lb

The unit rate is $0.89 per pound when 15 pounds cost $13.35. The cost for any other quantity can be found by multiplying the unit rate by the desired number of pounds.

To find the unit rate, which is the cost per pound in this case, you would divide the total cost by the number of pounds. The question states that 15 pounds of an item cost $13.35. Therefore, the unit rate is calculated as $13.35 divided by 15 lb, which equals $0.89 per pound.

The cost is already given as $13.35 for the 15-pound quantity. If you need to find the cost for a different quantity, you can multiply the unit rate by that quantity. For example, if you need to know the cost of 1 pound, it would be $0.89, while the cost for 5 pounds would be 5 multiplied by $0.89, which equals $4.45.

Answer:

You have a total of 2.25 cups of liquid each time you add 2 cups of water with .25 cups of concentrate.

You want to know how many times 2.25 cup "units" there are in 18 cups.

(18)/(2.25) = 8, so you have 8 "units" of water and concentrate

In each of those 8 "units" you have .25 cups concentrate, so (8)(.25) = 2 cups of concentrate.

In each of the "units" you have 2 cups of water, so (8)(2) = 16 cups water.

Please let me know if you have any questions.

Step-by-step explanation:

To make 18 cups of juice, you'll need approximately 2 cups of concentrate and 16 cups of water given the ratio of the recipe.

To answer your question, we need to solve a proportion problem.

The recipe's ratio is 0.25 cups of juice concentrate to 2 cups of water. This means for every 0.25 cups of concentrate, you add 2 cups of water to get 2.25 cups of juice.

Since you want to make 18 cups of juice, you can set up a proportion:

Therefore, to make 18 cups of juice, you'll need approximately 2 cups of concentrate and 16 cups of water.

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Answer:

The expressions that are equivalent are A, D, and E.

Step-by-step explanation:

Given:

-7z+ ( - 6.5) + 3.5z + 6y - 1.5.

On solving the equation:

[tex]-7z+ ( - 6.5) + 3.5z + 6y - 1.5[/tex]

[tex]-7z - 6.5+ 3.5z + 6y - 1.5[/tex]

[tex]-7z  + 3.5z + 6y - 1.5-6.5[/tex]

[tex]-3.5z+6y-8[/tex]

So, on solving the equation we get the expression:

[tex]-3.5z+6y-8[/tex]

According to question:

We see that expressions:

A. [tex]-8+6y+(-3.5z)[/tex]

   [tex]=-8+6y-3.5z = 3.5z+6y-8[/tex]

So, this expression is equivalent.

D. [tex]6y-8-3.5z[/tex]

   [tex]=3.5z+6y-8[/tex]

So, this expression is also equivalent.

E. [tex]-3.5z+6y-8[/tex]

So, this expression is also equivalent.  

Therefore, the expressions that are equivalent are A, D, and E.

Answer:

1/2

Step-by-step explanation:

p(-2) = 2 | -1/2(-2) |

= 2 | -1/-4|

= 2 |1/4|

= 1/2

Answer:

40 single tickets were sold.

Step-by-step explanation:

12x+8y=1580

2x+y=250

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

y=250-2x

12x+8(250-2x)=1580

12x+2000-16x=1580

-4x+2000=1580

-4x=1580-2000

-4x=-420

4x=420

x=420/4=105

y=250-2(105)=250-210=40

The requried number of singles tickets sold is 40. Option B is correct.

Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.

Here,
As mentioned in the quesiton, Tickets are $12 for couples and $8 for singles. Let x be the number of couples and y be the number of singles. This system of equations represents the situation in which ticket sales totaled $1,580 and a total of 250 students attended the dance.

12x + 8y = 1,580 - - - - -(1)

2x + y = 250 - - - - - -(2)

From equation 2
y = 250 - 2x - - - - -(3)

Put y from 3 in equation 1
12x + 8(250 - 2x) = 1580
12x + 2000 - 16x = 1580
-4x = 1580 - 2000
x = -420/-4
x = 105

Now,
y = 250 - 2(105)
y = 250 - 210
y = 40

Thus, the requried number of singles tickets sold is 40. Option B is correct.

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Answer:

R = √2

α = π/4 or 45°

Step-by-step explanation:

R cos(2n + α)

Use angle sum formula:

R [cos(2n) cos α − sin(2n) sin α]

R cos(2n) cos α − R sin(2n) sin α

Match the coefficients:

R cos α = 1

R sin α = 1

Divide:

tan α = 1

α = π/4 or 45°

Solve for R:

R cos(π/4) = 1

R / √2 = 1

R = √2

Answer:

Step-by-step explanation:

In each triangle, the longest side is opposite the largest angle, and the shortest side is opposite the smallest angle.

Calculate a measure of an angle A.

We know: The sum of the angle measures in a triangle is 180°.

Therefore:

m∠A = 180° - (46° + 62°) = 180° - 108° = 72°

m∠B = 62°

LB is opposite ∠A, LA is opposite ∠B.

m∠A > m∠B → LB > LA.

Therefore Ship B is further away.

Answer:

The solutions are 3 and -8

Step-by-step explanation:

2x² + 10x - 48 = 0

Divide both sides by 2:

x² + 5x - 24 = 0

Factor using AM method (What two numbers add to 5 and multiply to -24?):

(x - 3)(x + 8) = 0

Set both expressions equal to 0:

x - 3 = 0   x + 8 = 0

Solve both equations for x:

x = 3   x = -8

The solutions to the quadratic equation 2x² + 10x - 48 = 0 are x = 3 and x = -8.

To find the solutions to the quadratic equation 2x2 + 10x - 48 = 0, we can use the quadratic formula: x = (-b ± √(b2 - 4ac)) / (2a), where a, b, and c are the coefficients from the equation. In this case, a = 2, b = 10, and c = -48. Plugging these values into the formula, we have: x = (-10 ± √(102 - 4(2)(-48))) / (2(2)). Simplifying further, x = (-10 ± √(100 + 384)) / 4. Continuing to simplify, x = (-10 ± √484) / 4, which becomes x = (-10 ± 22) / 4. Finally, we have x = (-10 + 22) / 4 and x = (-10 - 22) / 4, giving us x = 3 and x = -8 as the two solutions to the quadratic equation.

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Multiply √2 by √72. The product is a rational number because √144 can be simplified to an integer.

Step-by-step explanation:

As Landon has to prove that two product of two rational numbers, he has to choose two rational numbers from the list and then multiply and show that the product is also a rational number.

Let us define the rational numbers first

A number that can be written in the form of p/q where p,q are integers and q is not equal to zero, is called a rational number.

From the give =n list of rational numbers

Taking

√2 and √72

[tex]\sqrt{2} * \sqrt{72}\\=\sqrt{2*72}\\=\sqrt{144}\\=12\\=\frac{12}{1}[/tex]

As we can see that the product of √2 and √72 is 12 which is also a rational number.

So,

Multiply √2 by √72. The product is a rational number because √144 can be simplified to an integer.

Keywords: Rational numbers, Product

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Answer: 1/3

Step-by-step explanation: Probability is the likelihood that an event will happen.

In this problem, we want to find the probability of rolling an odd number on a standard 6-sided die.

To find the probability of rolling an odd number on a 6-sided die, we first have to think about what numbers are on a standard die.

On a standard die, we have 3 odd numbers 1, 3, and 5 and 3 even numbers 2, 4, and 6.

Since there are an equal amount of even numbers and odd numbers on a standard die, we say the probability of rolling an odd number is 3 out of 6 or 3/6 since there are 3 odd numbers and 6 total outcomes we could get. The 6 total outcomes would be all the numbers on the die.

However, we have no 3/6 on the list so we can reduce this fraction by dividing the numerator and the denominator by 3 to get the equivalent fraction 1/3. Remember, always reduce when possible when finding probability.

Therefore, the probability of rolling an odd number on a standard 6-sided die is 1/3.

Answer:

12.5%

Step-by-step explanation:

Step1. Determine the points Matthew had during playoff by subtracting points made during regular season from total points in season.

   168 points this season

-   147 points regular season

    21 points scored in playoff

Step 2. Get the percentage, by dividing playoff points over total points in season

21 ÷ 168 = 0.125

Step 3. Multiply it by 100 to get the percentage equivalent from decimal.

0.125 x 100% = 12.5%

Answer:

45 cm

Step-by-step explanation:

Find LCM(15,9). First factor both numbers:

[tex]15=3\cdot 5\\ \\9=3\cdot 3[/tex]

So,

[tex]LCM(15,9)=3\cdot 5\cdot 3=45[/tex]

This means that the length of the side of the smallest square area that can be covered by these tiles is 45 cm.

Practically, you can put 3 tiles in a row (to make 3 lenghts of 15 cm each that add up to 45 cm) and put such 5 rows (to make 5 lengths of 9 cm that add up to 45 cm).

Answer:

5x-y +5 =0

Step-by-step explanation:

y – 5x = 5

5x-y +5 =0

The standard form of y - 5x = 5 is 5x – y = -5

Given equation is y - 5x = 5

We have to express in standard form

The standard form of a line is in the form Ax + By = C where A is a positive integer, and B, and C are integers.

The standard form of a line is just another way of writing the equation of a line.

So, to write the given equation in standard form we need to rearrange the terms.

Hence the equation becomes:

y - 5x = 5

On rearranging the terms, we get

-5x + y = 5

We need the x-term to be positive, so multiply the equation by -1 to get our answer

5x - y = -5

Hence the standard form is found out

Answer:

[tex]\large\boxed{6\dfrac{3}{4}\ meters=675\ centimeters}[/tex]

Step-by-step explanation:

[tex]PREFIXES\\\\mega\ (M)=10^6\\\\kilo\ (k)=10^3\\\\hecto\ (h)=10^2\\\\deko\ (da)=10\\\\decy\ (d)=10^{-1}=0.01\\\\centi\ (c)=10^{-2}=0.01\\\\mili\ (m)=10^{-3}=0.001\\\\mikro\ (\mu)=10^{-6}=0.000001[/tex]

[tex]1\ m=100\ cm\qquad(1\ meter=100\ centimeters)\\\\\text{Therefore}\\\\6\dfrac{3}{4}\ m=\dfrac{6\cdot4+3}{4}\ m=\dfrac{27}{4}\ m=\dfrac{27}{4}\cdot100\ cm=\dfrac{2700}{4}\ cm=675\ cm[/tex]

Answer:

sum: 7.3 difference:2.7

Step-by-step explanation:

Answer:

7.3 is the sum and the difference is 2.7.

Answer:

Hint just simplfy and apply bodmas

You get:30+17x

Answer:

30+17x

Step-by-step explanation:

Answer:

31

Step-by-step explanation:

50 x .62= 31

(games played) x the percentage won.

You could muliply 50 by 62% if your calculator has the % symbol if not you have to turn it into a decimal. To go from percent to decimal just take your percentage and move the decimal to the left twice. 62% = .62

Final answer:

To find the 8th term of the geometric sequence with a first term of 7 and a common ratio of 1/3, we apply the geometric sequence formula to get ≈ 0.0032.

Explanation:

To find the 8th term of a geometric sequence, you can use the formula for the nth term of a geometric sequence, which is an = a1 × [tex]r^{(n-1)}[/tex], where a1 is the first term, r is the common ratio, and n is the term number. In this case, the first term a1 is 7 and the common ratio r is 1/3. Applying the formula gives us the 8th term as a8 = 7 × [tex](\frac{1}{3} )^{7}[/tex].

First, we need to calculate the power of the common ratio: [tex](\frac{1}{3} )^{7}[/tex]

The 8th term of the sequence can be simplified to a8 = 7 × 1/2187, which calculates to approximately 0.0032.

The 8th term of the geometric sequence with a first term of 7 and a common ratio of 1/3 is approximately 0.0032.

We will use the formula for the nth term of a geometric sequence, which is given by:

[tex]a_n = a(r)^{(n-1)[/tex]

For this sequence:

Plugging in the values, the 8th term is found as follows:

a₈ = 7(1/3)⁽⁸⁻¹⁾

= 7(1/3)⁷

Calculating the powered fraction:

(1/3)⁷ = 1/(3⁷) = 1/2187

So:

a₈ = 7 × 1/2187

= 7/2187

≈ 0.0032

Answer: OPTION A.

Step-by-step explanation:

Let be "x" the amount of cups of mayonnaise that he will need to make 1 cup of tuna fish salad and "y" the amount of cups of mayonnaise that he will need to make 9 times the recipe.

Knowing that it takes [tex]\frac{1}{4}\ cups[/tex] of mayonnaise to make [tex]\frac{3}{4}\ cups[/tex] of tuna fish salad, we can set up the following proportion:

[tex]\frac{\frac{1}{4}}{\frac{3}{4}}=\frac{x}{1}[/tex]

Solving for "x", you get:

[tex]\frac{\frac{1}{4}}{\frac{3}{4}}=\frac{x}{1}\\\\\frac{1}{3}=\frac{x}{1}\\\\x=\frac{1}{3}[/tex]

So "y" will be:

[tex]y=9x[/tex]

Substituting the value of "x" into the equation, we get:

[tex]y=9(\frac{1}{3})\\\\y=3[/tex]

Final answer:

Cory will need 3 cups of mayonnaise to make 9 times the recipe for 1 cup of tuna fish salad.

Therefore, the correct answer is 3 cups of mayonnaise (Option A).

Explanation:

To find out how much mayonnaise Cory will need to make 9 times the recipe for 1 cup of tuna fish salad, we need to calculate the proportional amount of mayonnaise.

It takes 1/4 cups of mayonnaise to make 3/4 cups of tuna fish salad.

So, the ratio is 1/4 : 3/4.

To find the amount of mayonnaise needed for 1 cup of tuna fish salad, we scale the ratio by multiplying both sides by 4/3: 1/4 * 4/3 = 1/3 cup of mayonnaise.

Therefore, for 9 times the recipe, Cory will need 9 * 1/3 = 3 cups of mayonnaise.

Answer:

The lcm of 5 and 7 is 35.

Step-by-step explanation:

   35 / 5 = 7.

   35 / 7 = 5.

Answer:

35

Step-by-step explanation:

i did the testttt

Final answer:

According to the recipe, 3.5 cups of flour will be needed when using 4 and 2/3 cups of milk.

Explanation:

To determine the quantity of flour needed according to the recipe, we can set up a proportion using the given ratios. The recipe states that 1 and 1/3 cups of milk is needed for 1 cup of flour. So, we can set up the proportion:

Next, process is to cross-multiply and find x:

Therefore, according to the recipe, 3.5 cups of flour will be needed when using 4 and 2/3 cups of milk.

Answer:

Step-by-step explanation:

Solve for the quantity of flour using a proportion.

let x be the missing quantity of flour

Recipe ratio is        1  1/3   to  1

Needed ratio is      4 2/3  to x

Write each milk to flour ratio as a fraction. Equate them, and they become a proportion:

[tex]\dfrac{1\dfrac{1}{3} }{1} = \dfrac{4 \dfrac{2}{3} }{x}[/tex]

Find the scale factor for the increase of milk by dividing the needed quantity by the recipe quantity .

Divide 4 2/3 by 1  1/3:

[tex]4\dfrac{2}{3} \div 1\dfrac{1}{3}[/tex]

[tex]=\dfrac{14}{3} \div \dfrac{4}{3} = \dfrac{14}{3} * \dfrac{3}{4}[/tex]

[tex]= \dfrac{42}{12} = \dfrac{7}{2} = 3.5[/tex]

The scale factor is 3.5.

The scale factor for increasing milk is the same for flour. Multiply the recipe quantity of flour by the scale factor to get the needed quantity of flour.

Multiply  1  by 3.5:

1 * 3.5 = 3.5

We will write this in word form, just as it is in the question.

Therefore, we need three and a half cups of flour when there are four and two-thirds cup of milk.

Final answer:

To meet the minimum sales requirement of $4800, with 18 chairs already sold, the online furniture store must sell a minimum of 6 tables.

Explanation:

The online furniture store sells chairs for $150 each and tables for $350 each. With the sale of 18 chairs, the store has already made $2700 ($150 × 18). To meet the minimum sales requirement of $4800, we must determine how many tables need to be sold.

First, subtract the total sales from chairs from the minimum sales requirement:
$4800 - $2700 = $2100.

This is the amount that must be made from the sale of tables. Since each table is sold for $350, divide $2100 by $350 to find the number of tables needed:
$2100 / $350 = 6 tables.

Therefore, the store must sell a minimum of 6 tables to meet the $4800 sales requirement, assuming 18 chairs are sold and they don't exceed the shipping limit of 20 pieces of furniture.

To meet the daily sales requirement of $4800, the store needs to sell at least 6 tables along with 18 chairs. However, given the shipping capacity of 20 pieces per day, it is not possible to meet both requirements simultaneously.

Determining the Minimum Number of Tables

We need to determine the minimum number of tables the store must sell. Given that each chair is sold for $150, the revenue from selling 18 chairs is:

Revenue from chairs = 18 chairs * $150/chair = $2700

To meet the daily sales target of $4800, the remaining required revenue from tables is:

Required revenue from tables = $4800 - $2700 = $2100

Since each table sells for $350, the minimum number of tables required can be calculated as:

Number of tables = $2100 / $350 per table = 6 tables

Therefore, to meet the daily sales requirement of $4800, the store must sell at least 6 tables.

Additionally, the store can ship a maximum of 20 pieces of furniture per day. Having sold 18 chairs, the store can ship:

Remaining pieces = 20 - 18 = 2 pieces

Since we need at least 6 tables to meet the revenue requirement, and the shipping capacity allows only 2 more pieces, **it is not possible** to meet both constraints simultaneously.