10x - 26y=-38
6x + 13y=28

Answer:

8<74 square root<9

Step-by-step explanation:

The first thing we have to do is to find the lowest number that can be squared to 74. 1,4,9,16,25,36,49,64,81,100.

As we see, 64 is the lowest closest number to 74 and the square root of 64 is 8. So right now, is 8<square root of 74<___.

Now, we have to find the highest number closest to 74. As we look back at our square roots, 81 is the closest number to 74 in the square roots and the square root is 9 and voila. 8<sqrt74<9

The inequality is -

8 < √74  < 9.

We have the following inequality -

_____<√74 <____.

We have to fill in the blanks with two consecutive integers to complete the above inequality.

In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions.

According to the question -

Let A = √74

Then -   A² = 74

The nearest integers, square of between which A² lies is between 8 and 9. So -

8² < A² < 9²

Therefore, the two consecutive integers will be - 8 and 9.

Hence, the inequality is -

8 < √74  < 9

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Answer:

When the denominator is an irrational number in order to make the denominator a rational number we rationalize the denominator.

Step-by-step explanation:

For example,

[tex]\frac{1}{1+\sqrt{2} }[/tex] (here the denominator is an irrational number)

Multiply the numerator and denominator by [tex]1-\sqrt{2}[/tex]

We get [tex]\frac{1-\sqrt{2} }{(1+\sqrt{2})(1-\sqrt{2}) }[/tex]

Here (1+\sqrt{2})(1-\sqrt{2}) = -1

Thus we get [tex]\sqrt{2} -1[/tex]

Here the denominator has become a rational number.

When we are isolating a variable we are only taking the required variables to one side thus it doesn't require rationalization.

[tex]a = \frac{x}{1+\sqrt{2} }[/tex]

Then we can say,

[tex]x = a(1+\sqrt{2})[/tex]

No rationalisation required

Answer:

a

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

EDGE 2021

Answer:

4 is the greatest

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

7-3 pretty much

Answer: x=-10

Step-by-step explanation:

let x be that number

so, 7+x=-3

subtract 7 on both sides and...

x=-10

Answer:

The answer is 384.

Step-by-step explanation:

It starts at 3 going up by three to 6 then from there it adds 6 equaling 12 then so forth so it would be 3, 6, 12, 24, 48, 96, 192, 384

Answer:

aₙ = a₁ . 5⁽ⁿ⁻¹⁾

Step-by-step explanation:

The first term in the sequence is a₁ = 6.

a₂ = 30. a₃ = 150.

We see that each consecutive term is multiplies by 5 to arrive at the next term.

That is: a₂ = 30 = a₁ . [tex]$ 5^{2 - 1}  = 5 $[/tex] = 6.5 = 30.

Similarly, a₃ = 150 = 6 [tex]$ \times $[/tex] [tex]$ 5^{3 - 1} = 5^2 = 25 $[/tex]

Generalizing this, we have:

aₙ = a₁ . [tex]$ 5^{n - 1} $[/tex]

This is called the recursive formula of the sequence.

Answer:

Step-by-step explanation:

       Meghan is soon going to have to spend $78.99 on a dress, $32.50 on shoes, $25 for the ticket and $50 for dinner.

       Meghan already has $52 from her savings to spend. She earns money from babysitting at $12 each hour.

       Let the number of hours Meghan babysits be denoted by [tex]x[/tex].

From [tex]x[/tex] hours of babysitting, Meghan earns $([tex]x\times12[/tex]).

So, her total earnings sum up to [tex]12x+52[/tex]. This should be greater than total spendings.

       [tex]12x+52\geq 78.99+32.50+25+50\\12x\geq 134.49\\x\geq 11.208[/tex]

So, Meghan must work for 12 hours so she has something left after spendings.

∴ Meghan must babysit for 12 hours.

 Answer:

Number of Adult's tickets sold on Saturday = 3,356

Number of Children's tickets sold on Saturday = 2, 928

Total number of tickets sold over these two days is 8,938.

Step-by-step explanation:

Here, the number of tickets sold on FRIDAY:

Adult Ticket sold = 1,678

Children's Tickets sold = 976

So, the total number of tickets sold on Friday  

= Sum of ( Adult + Children's ) tickets  = 1,678  + 976 = 2,654 ....  (1)

The number of tickets sold on SATURDAY:

Adult Ticket sold =   2 times  the number of adult tickets sold on Friday  

                             =  1,678 x 2  = 3,356

Children's Tickets sold = 3 x the number of children's tickets sold on Friday.

                                      =  976  x 3 = 2, 928

So, the total number of tickets sold on Saturday  

= Sum of ( Adult + Children's ) tickets  = 3,356 + 2,928 = 6, 284 ....  (2)

Now, the total number of tickets booked in these two days :

Sum of tickets booked on (Friday + Saturday)

= 2,654 +  6, 284  =   8,938

Hence, total number of tickets sold over these two days is 8,938

The new copier can create 2000 copies in 20 minutes.

Step-by-step explanation:

Given,

It takes 60 minutes to make 2000 copies by old printer and 15 minutes to made x number of copies, therefore, using proportion

[tex]60:2000::15:x[/tex]

Product of mean = Product of extreme

[tex]2000*15=60*x\\30000=60x\\60x=30000[/tex]

Dividing both sides by 60

[tex]\frac{60x}{60}=\frac{30000}{60}\\x=500[/tex]

As the new copier is working with old copier, therefore,

Copies made by new printer = 2000 - 500 = 1500

New copier can make 1500 copies in 15 minutes and 2000 copies in x minutes, using proportion

[tex]1500:15::2000:x\\1500*x=15*2000\\1500x=30000[/tex]

Dividing both sides by 1500;

[tex]\frac{1500x}{1500}=\frac{30000}{1500}\\x=20[/tex]

The new copier can create 2000 copies in 20 minutes.

Keywords: ratio, proportion

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The amount deposited in CD is $660

Given that , To save for the purchase of a new car, a deposit was made into an account that earns 8% annual simple interest.  

Let the amount deposited in new car be $ n

Another deposit, $1700 less than the first deposit, was placed in a certificate of deposit (CD) earning 12% annual simple interest.  

Then, amount deposited in CD will be $ (n – 1700)

The total interest earned on both accounts for 1 year was $676

The simple interest is given as:

[tex]\text { Simple interest }=\frac{\text { principal } \times \text {rate} \times \text {time}}{100}[/tex]

Simple interest for purchase of new car:

[tex]\text { S. } \mathrm{I}=\frac{n \times 8 \times 1}{100}=\frac{8 n}{100}[/tex]

Simple interest for CD:

[tex]\text { S.I } =\frac{(n-1700) \times 12 \times 1}{100}=\frac{12(n-1700)}{100}[/tex]

Now, given that S.I for new car + S.I for CD = 676

[tex]\begin{array}{l}{\frac{8 n}{100}+\frac{12(n-1700)}{100}=676} \\\\ {\frac{8 n+12 n-12 \times 1700}{100}=676}\end{array}[/tex]

20n = 67600 – 20400

n = 2360

So money deposited in CD = n - 1700 = 2360 – 1700 = 660

Hence, the CD deposit amount is $660

To find the amount deposited in the CD, set up an equation using the given information. Solve for x to find the amount of the first deposit. Subtract $1700 from the first deposit to find the amount deposited in the CD.

To find the amount of money deposited in the CD, we can set up an equation using the given information.

Let the amount of the first deposit be x.

The second deposit is $1700 less than the first deposit, so it is x - $1700.

Using the formula for simple interest, the interest earned on the first deposit is x * 0.08.

The interest earned on the second deposit is (x - $1700) * 0.12.

According to the given information, the total interest earned is $676. Therefore, we can set up the equation: x * 0.08 + (x - $1700) * 0.12 = $676.

Simplifying and solving for x:

0.08x + 0.12x - $204 = $676

0.20x - $204 = $676

0.20x = $880

x = $4400

Therefore, the amount of money deposited in the CD is $4400 - $1700 = $2700.

So if you're asked to graph a function and its inverse, all you have to do is graph the function and then switch all x and y values in each point to graph the inverse. Just look at all those values switching places from the f(x) function to its inverse g(x) (and back again), reflected over the line y = x.

The equation of the line across which all inverses reflect is y = x. This reflection principle applies to linear functions, hyperbolas, and other mathematical relations where inverses can be found by interchanging the roles of x and y.

The equation of the line that all inverses reflect across is y = x. This is because when you are finding the inverse of a function, you swap the x and y variables, thus mirroring the original function across the line y = x. If you have a linear function in the slope-intercept form (y = mx + b), and you find its inverse, assuming the function is one-to-one and therefore has an inverse, you would essentially swap the x and y coordinates, resulting in the equation of its inverse. This process reflects each point of the original function across the line y = x.

As an example, for a line with an equation y = -x + 1, the inverse when reflected across the line y = x would result in swapping x and y to get x = -y + 1, which when solved for y, gives the inverse function's equation. Conversely, for a function expressed in another form, such as a hyperbola or a set of simultaneous linear equations, the principle is the same: to find the inverse, interchange the roles of the dependent and independent variables. For instance, a hyperbola described by y = a - b/x could have its inverse derived by interchanging x and y, leading to the inverse relation x = a - b/y.

Answer:

The relation to find base is, [tex]base=\frac{area\ of\ the \ parallelogram}{height}=\frac{86}{12}=7.16\ cm[/tex]

Step-by-step explanation:

Given

Area of the parallelogram [tex]=86\ cm^2[/tex]

Height of the parallelogram [tex]=12\ cm[/tex]

We know that the area of the parallelogram [tex]=base\times height[/tex]

So

To find base we have to divide the height on both sides of the equation.

[tex]base=\frac{area\ of\ the \ parallelogram}{height}[/tex]

Plugging the values.

[tex]base=\frac{86}{12} =7.1\ cm[/tex]

So the base in terms of area of the parallelogram and its height is [tex]b=\frac{area}{height} =\frac{86}{12}=7.16\ cm[/tex]

Answer:

[tex]\displaystyle (3, 6)[/tex]

Step-by-step explanation:

{x -4y = −21

{8y - x = 45

_________

[tex]\displaystyle \frac{4y}{4} = \frac{24}{4} \\ \\ [/tex]

[tex]\displaystyle y = 6[/tex][Plug this back into both equations above to get the x-coordinate of 3]; [tex]\displaystyle 3 = x[/tex]

I am joyous to assist you anytime.

Answer:

Multiply the length by the width to find the area in square metres and then multiply that figure by 0.03 Kg to find out how much seed you'll need.

Step-by-step explanation:

Answer:

20 bags of seed is needed for the new lawn

Step-by-step explanation:

To answer this question, first find the area of the lawn and divide the area calculated by the number of square feet per bag of seed.

A  lawn is assumed to have a rectangular shape, the area (A) of the lawn  therefore is

               A = L x W

Where:    A = Area of lawn

                L = Length of lawn

               W =  Width of lawn

                A = L x W

                 L = ?

                W = 60 ft

To find the length, use the formula for the perimeter of a rectangle since the lawn is assumed to a rectangular shape

Perimeter (P) = 2(L+W)

                  P = 300 ft

            300  = 2(L + 60) ft

            300  = 2L + 120

Subtract 120 from both sides

   300 - 120  = 2L + 120 - 120

              180 = 2L

Divide both sides of the equation by the coefficient of L which is 2

         180/2 = 2L/2

             90 = L

              L  =  90 ft

That is, the length of the lawn is 90 ft

To calculate the area of the lawn

              A  = L x W

              L   =  90 ft

              W  = 60 ft

               A  = 90 ft x 60 ft

               A  = 5400 square feet

This means that the area of the lawn is 5,400 square feet

To get the number of bags of seed that will cover the lawn, divide the area of the lawn by the number square feet that a bag will cover.

Number of bags of seed  = Total Area of lawn/Number square feet per bag.

Total Area                          = 5400 square feet

Number square

feet per bag                      = 270

Number of bags               = 5400/270

                                          = 20 bags of grass seed

20 bags of seed is needed for the new lawn

[tex]\bf \textit{internal division of a line segment using ratios} \\\\\\ C(-3,-2)\qquad D(6,1)\qquad \qquad \stackrel{\textit{ratio from C to D}}{2:1} \\\\\\ \cfrac{C\underline{P}}{\underline{P} D} = \cfrac{2}{1}\implies \cfrac{C}{D} = \cfrac{2}{1}\implies 1C=2D\implies 1(-3,-2)=2(6,1)\\\\[-0.35em] ~\dotfill\\\\ P=\left(\frac{\textit{sum of "x" values}}{\textit{sum of ratios}}\quad ,\quad \frac{\textit{sum of "y" values}}{\textit{sum of ratios}}\right)\\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf P=\left(\cfrac{(1\cdot -3)+(2\cdot 6)}{2+1}\quad ,\quad \cfrac{(1\cdot -2)+(2\cdot 1)}{2+1}\right) \\\\\\ P=\left( \cfrac{-3+12}{3}~~,~~\cfrac{-2+2}{3} \right)\implies P=\left( \cfrac{9}{3}~~,~~\cfrac{0}{3} \right)\implies P=(3~~,~~0)[/tex]

Answer:

42 years, 9 months

Step-by-step explanation:

Using the compound interest formula Accrued Amount = P (1 + r/n)^(nt)

where Accrued amount (A) which is quadruple the initial deposit

A = 4 x 500 = $2000

P = principal; $500

r = 3.25% = 0.0325

t = number of years

n = number of times interest is compounded = 12 for monthly

Therefore

2000 = 500 (1 + 0.0325/12)^(12t)

Therefore

(1.002708)^12t = 2000/500

(1.002708)^12t = 4

finding the log of both sides

12t x log 1.002708 = log 4

12t x 0.001174 = 0.6021

12t = 0.6021/0.001174

12t = 512.83

t = 512.83/12

t = 42.7

which is estimated as 42 years, (0.7 x 12 = 9) months

hence it takes about 43 years to quadruple the deposit

The number of years it will take to be the amount by quadruple will be 42.7 years.

Compound interest is applicable when there will be a change in the principal amount after the given time period.

As per the given,

The total amount will be,

A = 4 × 500 = $2000

Principle amount P = $500
Rate of interest r =  3.25% = 0.0325

The time period is t.

n = number of times interest is compounded

n = 12

By compound interest formula,

2000 = 500 [tex](1 + 0.0325/12)^{12t}[/tex]

(1.002708)^12t = 2000/500

(1.002708)^12t = 4

Take logs on both sides,

12t × log 1.002708 = log 4

12t × 0.001174 = 0.6021

12t = 0.6021/0.001174

12t = 512.83

t = 512.83/12

t = 42.7

Thus, the time period will be 42.7 years.

Hence "The number of years it will take to be the amount by quadruple will be 42.7 years.".

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Answer:

see the explanation

Step-by-step explanation:

we know that

To find out how many people voted for each option multiply the percentage in decimal form of each option by the total number of people

so

[tex]84\%=84/100=0.84[/tex] ---> [tex]0.84(6)=5.04=5\ people[/tex]

[tex]16\%=16/100=0.16[/tex] ---> [tex]0.16(6)=0.96=1\ people[/tex]

Answer:

B

Step-by-step explanation:

in B, the expression can be writting in variation form as

y∝1/x

this indicate an inverse variation

Answer:

B) y=6/x

Step-by-step explanation:

I took the test.

Answer:

multiply by 5

Step-by-step explanation:

Note the ratio between consecutive terms is constant, that is

[tex]\frac{0.65}{0.13}[/tex] = [tex]\frac{3.25}{0.65}[/tex] = [tex]\frac{16.25}{3.25}[/tex] = 5

Thus the pattern is multiply by 5

Answer:Multiply by 5

Step-by-step explanation:

I think it's false.... 5/6 is 83.33% as a percent so I don't think it's true.

6/6 ......... 100%

5/6 ..............x%

x = 5/6*100/6/6 = 500/6 = 83,(3)%

Answer:

y + 5 = 3(x + 1) → point-slope form

y = 3x - 2 → slope-intercept form

3x - y = 2 → standard form

Step-by-step explanation:

The point-slope form of an equation of a line:

y - y₁ = m(x - x₁)

m - a slope

(x₁, y₁) - a point on a line

We have

m = 3, (-1, -5) → x₁ = -1, y₁ = -5

Substitute:

y - (-5) = 3(x - (-1))

y + 5 = 3(x + 1) → point-slope form

convert to the slope-intercept form y = mx + b:

y + 5 = 3(x + 1)      use the distributive property: a(b + c) = ab + ac

y + 5 = 3x + 3     subtract 5 from both sides

y = 3x - 2 → slope-intercept form

convert to the standard form Ax + By = C:

y = 3x - 2            subtract 3x from both sides

-3x + y = -2         change the signs

3x - y = 2 → standard form

Answer:

The labor cost per shirt of the American factory is 0.36 times the labor cost per shirt of the foreign company.

Step-by-step explanation:

A textile factory in the United States plays 300 workers a total of $9 million each year to produce 4.5 million shirts.

Therefore, the labor cost per shirt will be

[tex]\frac{9 \times 10^{6}}{300 \times 4.5 \times 10^{6}} = 0.0067[/tex]

Again, a foreign factory employs 225 workers at a total cost of $1,050,000 to produce 2,500,00 shirts.

Therefore, the labor cost per shirt will be

[tex]\frac{1050000}{250000 \times 225} = 0.01867[/tex]

Therefore, the labor cost per shirt of the American factory is 0.36 times (Approximate) the labor cost per shirt of the foreign company. (Answer)

Answer:

Total pay for the week is $924.

Step-by-step explanation:

The per hour rate of weekdays from Monday to Friday =  $15.40

The rate for Saturday = One and Half ( $15.40)

Now,  [tex]1\frac{1}{2}  \times (15.40)  = \frac{3}{2} (15.40) = 23.1[/tex]

So, the per hourly rate for work on Saturday  = $23.1

The rate for Sunday  = 2 x ( $15.40)  = $30.80

So, the per hourly rate for work on Sunday  = $30.80

Now, total hours worked in weekday = 38

So, the rate of 38 hours = 38 x ( Per hour rate) = 38 x ($15.40)  

                                        = $585.2

Now, total hours worked on Saturday  = 8

So, the rate of 8 hours = 8 x ( Per hour rate) = 8 x ($23.1)    = $184.8

Now, total hours worked on Sunday  = 5

So, the rate of 5 hours = 5 x ( Per hour rate) = 5 x ($30.80)    = $154

Hence the total pay = Payment of ( weekday  + Saturday +Sunday)

= $585.2 +  $184.8 +  $154  =  $924

Hence, total pay for the week is $924.

Answer:

He would score 154 points because he averages 14 points per game and 11 times 14 is 154

Data scored 42 points in 3 games, then points scored in 11 games will be equal to 154 points.

The four basic mathematical operations are the addition, subtraction, multiplication, and division of two or even more integers. Among them is the examination of integers, particularly the order of actions, which is crucial for all other mathematical topics, including algebra, data organization, and geometry.

As per information obtained from the question,

Let x points will be obtained in 11 games.

Data scored,

42 points = 3 games

Points earned in 1 game = 42/3 = 14

Then,

Points obtained in 11 games = 14 × 11

x = 154 points.

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Answer:

12 756.2 kilometers

Step-by-step explanation:

12 756.2 kilometers

Good evening ,

Answer:

The set of solutions is IR

Step-by-step explanation:

-2(2x+8)>-16-4x ⇌ -4x-16>-16-4x

Any x∈IR verify the inequality

then The set of solutions is IR.

:)

√6(7+√2)

Use the distributive property:

√6 * 7 + √6 * √2

Move the 7 to the left:

7 * √6 + √6 * √2

Use the product rule for radicals on  √6 * √2

7 * √6 + √(6*2)

Simplify:

7√6 + √12

Rewrite 12 as 2^2*3

7√6 + √(2^2*3)

Pull terms out from under the radical for final answer:

7√6 + 2√3

Answer:

Yes

Step-by-step explanation:

Total Price of all 3 items - $34.19

35 > 34.19

Yes, Kiera will have enough to purchase all three items.

No, $35 will not be enough to purchase all three items.

To determine if $35 is enough to purchase all three items, we need to calculate the total cost of the items and compare it to the amount of money Kiera has.

The cost of each item is as follows:

- Mixing bowl: $14.95

- Spatula: $8.49

- Measuring cups: $10.75

Now, let's add up the costs of these items to find the total cost:

Total cost = Cost of mixing bowl + Cost of spatula + Cost of measuring cups

Total cost = $14.95 + $8.49 + $10.75

To make the calculation easier, we can round each price to the nearest whole number:

- Mixing bowl: $14.95 ≈ $15.00

- Spatula: $8.49 ≈ $8.50

- Measuring cups: $10.75 ≈ $10.75 (already a whole number)

Now, let's calculate the total cost with these rounded numbers:

Total cost ≈ $15.00 + $8.50 + $10.75

Total cost ≈ $34.25

However, even with rounding, the total cost is $34.25, which is still less than $35. Therefore, we need to calculate the exact total cost without rounding:

Total cost = $14.95 + $8.49 + $10.75

Total cost = $34.19

Since the total cost of $34.19 is less than $35, it appears that Kiera has enough money to purchase all three items. However, we must also consider sales tax, which is not included in the given prices. Sales tax rates vary by location, but let's assume a standard rate of 7%.

To calculate the total cost including sales tax:

Total cost with tax = Total cost before tax + (Total cost before tax × Sales tax rate)

Total cost with tax = $34.19 + ($34.19 × 0.07)

Total cost with tax = $34.19 + $2.3933

Total cost with tax ≈ $34.19 + $2.40 (rounded to the nearest cent)

Total cost with tax ≈ $36.59

After including the sales tax, the total cost is approximately $36.59, which is more than the $35 Kiera has. Therefore, $35 will not be enough to purchase all three items once sales tax is included.

Answer:

x is less than 6 so that is correct because 24 divided by 4 is 6