Simplify the rationalising the denominators

Let's consider the first number to be [tex]f[/tex] and the second number to be [tex]s[/tex]. Based on the information in the problem, we can create the following equations:

[tex]f + 2s = 1[/tex]

[tex]2f + s = 14[/tex]

Now, we can solve the equations through systems of equations. One way of doing this is by multiplying one of the equations so that there is a term in both equations which can be removed by addition or subtraction. In our case, we can multiply the entire first equation by 2 to get:

[tex]2f + 4s = 2/tex]

[tex]2f + s = 14[/tex]

Now, subtract [tex]2f[/tex] from both equations to get:

[tex]3s = -12[/tex]

[tex]s = -4[/tex]

Now that we have found [tex]s[/tex], "plug" it back into an equation to find [tex]f[/tex]:

[tex]f + 2(-4) = 1[/tex]

[tex]f - 8 = 1[/tex]

[tex]f = 9[/tex]

Our answers are s = -4 and f = 9.

Hey there!!

Let's take the first number as ' x '

Let's take the second number as ' y '

First number + twice the second number is 1

x + 2y = 1 ------------ ( 1 )

Twice the second number + second number is 14.

2x + y = 14 ----------- ( 2 )

Now let's get them all together...

...................................................................................................................................................................

x + 2y = 1 --- ( 1 )

2x + y = 14 --- ( 2 )

Now, let's multiply the first equation with 2 ...

...................................................................................................................................................................

2x + 4y = 2 --- ( 1 )

2x + y = 14 --- ( 2 )

Now, let's subtract the second equation from the second...

...................................................................................................................................................................

2x + 4y = 2 --- ( 1 )

- ( 2x + y ) = - ( 14 )

...................................................................................................................................................................

2x + 4y = 2 --- ( 1 )

-2x - y = -14 --- ( 2 )

...................................................................................................................................................................

3y = -12

Divide by 3 on both sides...

y = -4

The second number is -4.

We have the first equation x + 2y = 1

We got the y value, now substitute the value of y to get the value of x

...................................................................................................................................................................

x + 2y = 1

x + 2 ( -4 ) = 1

x - 8 = 1

Add 8 on both sides

x = 9

Hence, the second number is 9.

...................................................................................................................................................................

Hope my answer helps!!

Answer:

25$

Step-by-step explanation:

4h+ 150= 250

subtract the 150 from 250 to get 100

4h =100

then divide 100 by 4

h=25

Answer:

25$

Step-by-step explanation:

$25 for each additional rental hour.

4h + 150 = 250

4h = 100

h = 25

[tex]-11(9b-8)=(-11)(9b)+(-11)(-8)=-99b+88[/tex]

[tex]x=1.\overline{34}\\\\x=1.343434...\qquad|\cdot100\\\\100x=134.343434...\\\\100x-x=134.343434...-1.343434...\\\\99x=133\qquad|:99\\\\x=\dfrac{133}{99}[/tex]

1. 12*100 - 12*5

You would use the distributive property to get this equation (it is equivalent to the original one)

2. Um... There's no actual story for this problem; sorry I can't solve this problem

Answer:

1. 12*100 - 12*5

You would use the distributive property to get this equation (it is equivalent to the original one)

2. Um... There's no actual story for this problem; sorry I can't solve this problem

Step-by-step explanation:

Your answer (C, the line is vertical) is correct

Your line would have to be horizontal. A vertical line yields an undefined slope.

Slope is rise over run. For a horizontal line you would have 0 rise and X amount of run or 0/x. 0 divided by anything = 0

For a vertical line, you would have the opposite, X rise and 0 run or x/0. You cannot divide by 0. It is impossible.

Therefore, your answer is the second option.

Given problem is:

[tex](7.14\times10^{10})+(3.21\times10^{10})[/tex]

step by step solution:

we will add similar elements.

[tex]10^{10}(7.14+3.21)[/tex]

= [tex]10^{10} (10.35)[/tex]

Now converting [tex]10^{10}[/tex] in decimal form we get 10000000000 (10 zeroes)

Now multiplying 10.35 with 10000000000 we get 103500000000 (8 zeroes)

or we can change it to exponential form like [tex]1.035\times10^{11}[/tex]

11 because when you count from the extreme right end '0' and come counting to the left side, you skip 11 numbers till you reach the first number '1'. And when you put a decimal after 1st number, so the last '0' is at the 11th place, that is why it is [tex]10^{11}[/tex] .

Hello!

To find the answer to this question we first need to find the weekly average.

If we divide 4,320 by 9, we are given an average of $480 per week.

Since we are given the information that Robin works 50 weeks during the year, we can multiply that value by 50 which equal to $24,000.

Hope this helps.

The formula C = 0.35y efficiently calculates the total cost of y apples at $0.35 each. It demonstrates a straightforward linear relationship between cost and quantity.

To find the total cost (C) of y apples priced at $0.35 each, you can use the equation C = 0.35y. This formula multiplies the cost per apple ($0.35) by the number of apples (y) to give you the total cost. For instance, if you want to buy 10 apples (y = 10), the calculation would be C = 0.35 * 10, which equals $3.50.

This equation works because it represents a simple linear relationship between the cost and the quantity of apples. Each apple adds $0.35 to the total cost. Therefore, by multiplying the cost per apple by the number of apples, you get the overall cost.

Remember, this formula assumes a constant price per apple. If the price were to change, the equation would need to be adjusted accordingly. This calculation is useful for budgeting and understanding the cost implications of buying a specific quantity of apples at a given price.

Complete question:

What is the answer to y apples at $0.35 each

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First multiply 5 on both sides to get rid of the five on the bottom.

[tex]\frac{1-7n}{5*5}[/tex][tex]>10*5[/tex]

[tex]1-7n>50[/tex]

Subtract 1 from both sides of the inequality.

[tex]1-1-7n>50-1[/tex]

[tex]-7n>49[/tex]

Divide -7 on both sides, and flip the inequality sign since we are dividing by a negative.

[tex]\frac{-7n}{7}[/tex][tex]>\frac{49}{-7}[/tex]

[tex]n<-7[/tex]

The solution to the inequality is n<-7.

[tex]Solution, \frac{1-7n}{5}>10\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x<-7\:\\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:-7\right)\end{bmatrix}[/tex]

[tex]Steps:[/tex]

[tex]\mathrm{Multiply\:both\:sides\:by\:}5, \frac{5\left(1-7n\right)}{5}>10\cdot \:5[/tex]

[tex]\mathrm{Simplify}, 1-7n>50[/tex]

[tex]\mathrm{Subtract\:}1\mathrm{\:from\:both\:sides}, 1-7n-1>50-1[/tex]

[tex]\mathrm{Simplify}, -7n>49[/tex]

[tex]Multiply\:both\:sides\:by\:-1\:\left(reverse\:the\:inequality\right), \left(-7n\right)\left(-1\right)<49\left(-1\right)[/tex]

[tex]\mathrm{Simplify}, 7n<-49[/tex]

[tex]\mathrm{Divide\:both\:sides\:by\:}7, \frac{7n}{7}<\frac{-49}{7}[/tex]

[tex]\mathrm{Simplify}, n<-7[/tex]

The correct answer is n<-7

Hope This Helps!!!

The answer is the number 12. This is because if 12 is added to 24 it equals 36 and if 12 is multipled by 3 it is 36.

If a certain number is added to 24, the result is the same as if the number were multiplied by 3 the certain number is 12.

Let's assume the certain number is represented by "x."

According to the given information, if the number is added to 24, the result is the same as if the number were multiplied by 3. This can be written as the following equation:

x + 24 = 3x

Now, let's solve for "x":

Subtract "x" from both sides to isolate the "x" term on one side:

x + 24 - x = 3x - x

24 = 2x

Now, divide both sides by 2 to solve for "x":

x = 24 / 2

x = 12

Therefore, the certain number is 12.

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Answer:A,C,D

Step-by-step explanation:

Took test

the answer is 62 units because of the way the kite looks. a kite has 5 to 4 sides and if you divide that you will get sixty two units per unit.

The perimeter of kite ACBO is 62 units. Therefore, option C is the correct answer.

The perimeter of a shape is defined as the total distance around the shape. It is the length of the outline or boundary of any two-dimensional geometric shape. The perimeter of different figures can be equal in measure depending upon the dimensions.

From the given kite ACBO, OB=7 uints and OC=25 units.

Here, ∠OBC=90° (Angle between radius and tangent is 90°)

By using Pythagoras theorem,  

BC²=OB²+OC²

25²=7²+OC²

625=49+OC²

OC²=625-49

OC²=576

OC=24 units

So, perimeter=2(a+b), where a and b are adjacent sides

= 2(7+24)

= 2×31

= 62 units

Therefore, option C is the correct answer.

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Answer:

Edison will be paid $15,112 for the first three months.

Step-by-step explanation:

We know that Edison receives an annual fixed pay of $45,448. Therefore, his fixed pay for each month will be [tex]\frac{45448}{12}=\$3787.33[/tex]

Therefore, his fixed pay for the 3 months will be [tex]3787.33*3=\$11362[/tex].

Now let us compute the commission that Edison received. For that we will compute the 15% of the total sales for those 3 months. Total sales for the 3 months is $25000. Therefore, his commission would be [tex]0.15*25000=\$3750[/tex]

Therefore, total pay that Edison received during first 3 months would be:

[tex]11362+3750=\$15,112[/tex]

Edison will be paid $48,862 for the first 3 months.

To calculate Edison's total payment for the first 3 months, we need to consider both his annual pay and the commission he earns from his sales.

First, let's calculate the commission Edison earns from his sales. He makes sales of $250,000 in the first 3 months, and the commission rate is 15% of the total sales. The commission can be calculated as:

[tex]\[ \text{Commission} = \text{Total Sales} \times \text{Commission Rate} \] \[ \text{Commission} = \$250,000 \times 0.15 \] \[ \text{Commission} = \$37,500 \][/tex]

Next, we need to calculate Edison's base salary for 3 months. Since his annual pay is $45,448, we divide this by 4 to get the quarterly pay (as there are 4 quarters in a year):

[tex]\[ \text{Quarterly Pay} = \frac{\text{Annual Pay}}{4} \] \[ \text{Quarterly Pay} = \frac{\$45,448}{4} \] \[ \text{Quarterly Pay} = \$11,362 \][/tex]

Now, we add the quarterly pay to the commission to find the total payment for the first 3 months:

[tex]\[ \text{Total Payment for 3 Months} = \text{Quarterly Pay} + \text{Commission} \] \[ \text{Total Payment for 3 Months} = \$11,362 + \$37,500 \] \[ \text{Total Payment for 3 Months} = \$48,862 \][/tex]

Hey there!!

How do we find slopes ?

Slope = [tex]\frac{y2-y1}{x2-x1}[/tex]

We are given with two co-ordinates :

(-1,8) and (3,-4)  

Hence, the slope is :

[tex]\frac{-4-8}{3+1}[/tex]

... [tex]\frac{-12}{4}[/tex] = -3

The slope is -3.

Hope my answer helps!

Answer:

The correct option is A.

Step-by-step explanation:

Total number of students at the school is 2,500.

In the given pi chart Pink, Yellow and Sky Blue color represent the percentage of students that under reported, accurately reported, and over reported their heights respectively.

From the graph we can conclude that the yellow portion is approximately one fifth of whole circle. It means the number of students that accurately reported their height is one fifth of total number of students.

[tex]2500\times \frac{1}{5}=500[/tex]

Therefore the number of students that accurately reported their height is 500. Option A is correct.

Answer:

Option A) 500

Step-by-step explanation:

We are given the following information:

Total number of students = 2500

From pie chart:

[tex]\text{Under Reported }= \displaystyle\frac{1}{5}\times 100\% = 20\%\\\text{Accurately Reported }= \displaystyle\frac{1}{5}\times 100\% = 20\%\\\text{Over Reported }= \displaystyle\frac{3}{5}\times 100\% = 60\%[/tex]

We have to find the number of students whose height were accurately reported =

[tex]\text{Number of students whose height were accurately reported }= \\\text{Number of students}\times \text{Percentage of students whose height were accurately reported}\\= 2500\times 20\%\\\\= 2500\times \displaystyle\frac{20}{100} = 2500\times \frac{20}{100} = 500[/tex]

500 students report their height accurately.

Answer:

They place more emphasis on science.

Step-by-step explanation:

The enlightenment emerged in 18th-century, which brought ideas that were deeply influenced by reason, empiricism and classics.  It restructured the old Greek and Roman ideas to make new inventions, and was changing ideas due to reasoning. It was the idea behind the invention of sculpting, a new way of passing ideas or information to people more than through paintings.

Enlightenment initially started with assembling of ordinary materials by a process termed sculptural construction, did not mean exactly the same thing to everybody.

During the enlightenment, artists placed more emphasis on science.

Artists during the Enlightenment shifted from Rococo to Neoclassicism and used their works to convey political messages.

Artists during the Enlightenment played a crucial role in spreading Enlightenment concepts and inspiring rational thinking. The dominant artistic style shifted from Rococo to Neoclassicism, focusing on clarity, logic, and order. Artists like Jacques-Louis David depicted themes of democracy and political statements in their works.

Pretty sure it is A - a parallel line to a given line from a point not on the line

I'm working on the same test :)

Answer:

The construction is a parallel line to a given line  from a point not on the line.

Step-by-step explanation:

For a given figure,

To construct a parallel line

Step 1 : Draw transversal line through any point not on line which is given.

Step 2: Using construction copy an angle, construct same angle formed by transversal line and given line.

Step 3: This is the last step in which when the copy of an angle completed draw a line parallel to the line.

Fran's fudge recipe, originally calling for [tex]2\frac{1}{2}[/tex] cups of sugar, would require [tex]2\frac{9}{10}[/tex] cups after she increases the sugar by 2/5 of a cup. The process involves converting mixed numbers to improper fractions, finding a common denominator, and then adding the fractions together.

If Fran's fudge recipe calls for [tex]2\frac{1}{2}[/tex] cups of sugar and she increases it by 2/5 of a cup, we first need to find the common denominator to combine these two fractions. To do this, we express [tex]2\frac{1}{2}[/tex] cups as an improper fraction, which is 5/2 cups (since [tex]2\frac{1}{2}[/tex] = 5/2). Then, we add 2/5 of a cup to it.

Steps:

Convert 2 1/2 cups to an improper fraction: [tex]2\frac{1}{2}[/tex] = 5/2.

Add 2/5 cup to 5/2 cups: To add these, we need a common denominator, which is 10. So, we convert 5/2 to 25/10 and 2/5 to 4/10.

Add the two fractions: (25/10) + (4/10) = (29/10).

Convert 29/10 back to a mixed number: 29/10 = [tex]2\frac{9}{10}[/tex].

Therefore, Fran uses [tex]2\frac{9}{10}[/tex] cups of sugar in her fudge recipe after the increase.

[tex]\vee=or\\\\therefore\\\\p:x < -3\ ; q:x > 3\\\\p\vee q\to x < -3\ or\ x > 3[/tex]

[tex]\wedge=and\\\\\Rightarrow=if\ ...,\ then\ ...\\\\\Leftrightarrow=if\ and\ only\ if[/tex]

Answer:

the one with or just got it right

Step-by-step explanation:

The right answer is 15t times 2.

The right answer is 15t times 2.

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

here, we have,

The garden club earned, $15 per hour by weeding neighborhood gardens for t hours.

A generous donor has agreed to double their earnings.

now,

hence, The right answer is 15t times 2.

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Answer:

x = 5

Step-by-step explanation:

First, we need to move all the x's onto one side:

-7x-3x+8x = -8-2

Then, we simplify:

-2x = -10

To find x, we need to divide each side by -2:

So then x = 5

1. 1/9

2. 0

3. -9

4. -1

Reasoning: To get the opposite of a number just add a negative sign or take it away. This can be done to all numbers other than 0

Steps for solving for x.

Step 1. Add 6y to both sides

x = -30 + 6y

Step 2. Regroup terms

x = 6y - 30

Steps for solving for y.

Step 1. Subtract x from both sides

-6y = -30 - x

Step 2. Divide both sides by -6

y = -30 - x/6