3x+2y=4
8x-3y=-6 solving systems of equations by substitution

Answer:

Julie worked 18 hours at Job A and 17 hours at Job B.

Step-by-step explanation:

1. Let's review the data given to us for solving the question:

Rate per hour at Job A = US$ 6.10

Rate per hour at Job B = US$$ 7.40

Hours at Job A = x

Hours at Job B = 35 - x

Total of hours worked by Julie = 35 hours

Total weekly earnings = US$ 235.60

2. How many hours did she work at each job the week that she made $235.60?

For finding the result, we will use the following formula:

6.10x + 7.4 (35 - x) = 235.60

6.10x + 259 - 7.4x = 235.60

-1.3x = 235.60 - 259 (Subtracting 259 to both sides)

-1.3x = - 23.40

x = -23.4/-1.3 (Dividing by -1.3)

x = 18

Julie worked 18 hours at Job A, so she worked 17 (35 - 18) hours at Job B.

3. Proof that x = 18 is correct.

6.10x + 7.4 (35 - x) = 235.60

6.10 (18) + 7.4 (35 - 18) = 235.60

109.80 + 125.80 = 235.60

235.60 = 235.60

It's proven that x = 18 is correct.

Answer:

Step-by-step explanation:

Let x represent the number of hours worked at Job A and 35-x represent the number of hours worked at Job B.

($6.10 × x) +$7.40 × (35-x) =$235.60

Solving for x

$6.10x + $259 - $7.40x = $235.60

Collect like terms and solve for x

$6.10x-$7.40x=$235.60-$259

-$1.3x=-$23.4

x=18hours for Job A while 35-x=17hours for Job B

Answer:

Ratio of PQC to ABC is 2:9.

Step-by-step explanation:

In ΔBRQ and ΔBPC

∠BQR = ∠BCP (given) and ∠B is common for both triangles, so from AAA similarity ΔBRQ and ΔBPC are similar.

⇒ BQ : QC = BR : RP = 2 : 1    →(1)

now draw perpendiculars from points A and P to BC line segment. Call the projected points as A' and P'.

It is clear that lines AA' and PP' are parallel. So in ΔBPP' and ΔBAA' we have AAA similarity with common angle at B.

⇒PP' : AA' = BP : BA = 2 : 3    →(2) (∵ AP : PB = 1 : 2)

area of ΔPQC = 0.5×PP'×QC

area of ΔABC = 0.5×AA'×BC

area of ΔPQC : area of ΔABC = (0.5×PP'×QC)/(0.5×AA'×BC)

                                               =(PP'/AA')×(QC/BC)

                                               =(2/3)×(1/3) (∵ from (1) and (2))

                                               =2/9.

∴ Ratio of PQC to ABC is 2:9

The simplified expression will be equal to - 6x² - 24x + 12p

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

The Numbers constants, variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols; which can also be used to indicate the logical syntax's order of operations and other features.

Given that 5x - 3( x + 4)2x + 12p

Solving;

5x - 3( x + 4) 2x + 12p

5x - 3(2x² + 8x) + 12p

5x - 6x² - 24x + 12p

- 6x² - 24x + 12p

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Answer:

5 centimeters of snow per hour.

Step-by-step explanation:

We are given an equation d = 5h, where d = depth of snow and h = hours of the snowstorm.

We need to find the number of centimeters of snow that accumulate in 1 hour.

In order to find the number of hours that accumulate the  snow to 1 centimeter, we need to plug d=1 in the given equation.

On plugging d=1, we get

1= 5h.

Dividing both sides by 5, we get

1/5 = h.

Therefore, it would take 1 hour for 5 centimeters of snow to accumulate in Harper's yard.

The amount of snow accumulation per hour varies, ranging from 0.5 cm in light snow to up to 5 cm in heavy snowfall. However, actual snow accumulation can be influenced by various factors such as temperature, wind speed, and humidity.

The amount of snow accumulation per hour can vary greatly depending on the intensity of the snowfall. For example, a light snowfall might result in as little as 0.5 cm of snow per hour while a heavy snowfall could accumulate up to 5 cm of snow per hour. However, it's important to note that these are just average estimates and actual snow accumulation can be influenced by various factors such as temperature, wind speed, and humidity.

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Answer:

4

2

3

1

Step-by-step explanation:

1) [tex](p^6.q^{{\frac{3}{2}}})^{{\frac{1}{3}}}[/tex]

Therefore, [tex]$ p^{\frac{6}{3}}.q^{\frac{3}{2}.\frac{1}{3}} $[/tex]

[tex]$ \implies p^2.q^{\frac{1}{2}} $[/tex]

2) [tex]$ \frac{p^5}{p^{-3}q^{-4}} $[/tex]

[tex]$ = p^5.p^3.q^4 = p^8.q^4 $[/tex]

Now, [tex]$ (p^8q^4)^{\frac{1}{4}} $[/tex]

[tex]$ \implies p^{\frac{8}{4}}.q^{\frac{4}{4}} $[/tex]

[tex]$ = p^2. q $[/tex]

3) [tex]$ (\frac{p^2.q^7}{q^4} )^{\frac{1}{2} $[/tex]

[tex]$ \implies p^{{\frac{2}{2}}}.q^{\frac{3}{2}} $[/tex]

[tex]$ \implies pq^{\frac{3}{2}} $[/tex]

4) [tex]$ \frac{(pq^3)^{{\frac{1}{2}}}}{(pq)^{{\frac{-1}{2}}}} $[/tex]

[tex]$ \implies p^{{\frac{1}{2}}}q^{{\frac{3}{2}}}. p^{{\frac{1}{2}}}.q^{{\frac{1}{2}}}} $[/tex]

[tex]$ = pq^2 $[/tex]

Hence, the answers.

Answer:

605100

Step-by-step explanation:

6.051*10^5=605100

Answer:

160

Step-by-step explanation:

2+2=4

4 x 40= 160

The mile symbol 'm' was commonly used before the widespread adoption of the metric system. The total miles taken by Ashlynn to ride her bike to school and home in 40 days is 160.

A mile is defined as the unit of length which is exactly equal to 5280 feet or 1760 yards and it is standardized as exactly 1609.344 meters. It is the largest unit which is commonly used to measure the distance between places that are far from each other.

Here the total miles covered by the bike is 2 + 2 = 4

The total miles covered by Ashlynn = 4 × 40 = 160

A mile is a customary unit of distance. It is commonly used to express the distance between cities, roads and the lengths of the rivers. The symbol of mile is denoted as 'mi'.

Thus the total miles is 160.

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Answer:

Yes.

Step-by-step explanation:

A rational number is any number that can be expressed as a ratio of two integers. 1 and 3 are integers, and 1/3 is a ratio of them, so 1/3 is a rational number.

Answer: Yes it is

Step-by-step explanation: A rational number is a number that can be written in the form of a fraction, so yes it is a rational number.

Answer:

C

Step-by-step explanation:

Two pyramids are similar. It means that their side lengths are proportional.

So, let's see the proportionality constant from SMALL PYRAMID to LARGE PYRAMID.

The corresponding length of 8 in small pyramid is 24 in large pyramid. We ask ourself:  "8 times WHAT gives us 24?"

This is the proportionality constant (aka "k").

So, 8 times "3" is 24. So the proportionality constant is "3".

k = 3

Now, the height of small pyramid is 6 and height of large pyramid is "x". These sides will be same way proportional. So, we can say:

6 times the proportionality constant (3) would give us x

So,

6 * 3 = x

x = 18

Correct answer is C

Answer:

10. 7n - 1 < -8

Isolate the variable, n. Do the opposite of PEMDAS. Treat the < as equal sign, what you do to one side, you do to the other. First, add 1 to both sides:

7n - 1 (+1) < - 8 (+1)

7n < - 8 + 1

7n < - 7

Isolate the variable, n. Divide 7 from both sides:

(7n)/7 < (-7)/7

n < -7/7

n < -1

n < -1 is your answer.

11. 3 > -7v + 4v

Combine like terms, then isolate the variable, v. First, add -7v and 4v together.

3 > (-7v + 4v)

3 > (4v - 7v)

3 > (-3v)

Isolate the variable, v. Divide -3 from both sides. Note that since you are dividing a negative number, you must flip the sign:

(3)/-3 > (-3v)/-3

3/-3 > v

-1 < v

v > -1 is your answer.

~

Answer:

3 7/12

Step-by-step explanation:

first you have to make both denominators the same through multiplication but remember if you do that you have to multiply the numerator by the same number as the denominator. then after you do that you can add them and if it comes out improper then you need to simplify your fraction and you have the answer.

Answer: 3⁷/₁₂

Explanation:

Numerator- number on top of fraction

Denominator- number on bottom of fraction

First find a common denominator. A number that both denominators can go into. In this case we'll use 12. Because both of the denominators, 6 and 4, fit into 12.

6 goes into 12 twice. And 4 goes into 12 three times.

To convert to a common denominator, multiply both the numerator and the denominator by the same number. Do not multiply the whole number.

So because 6 goes into 12 twice, we multiply by 2.

⁵/₆ x 2 = ¹⁰/₁₂

And because 4 goes into 12 three times, we multiply by 3.

2³/₄ × 3 = 2⁹/₁₂

Okay so now that both numbers have a common denominator, we can add.

¹⁰/₁₂ + 2⁹/₁₂ = 2 ¹⁹/₁₂

Simplified as 3 ⁷/₁₂

(a) D(c) = f + cx    

(b) Delivery fee is $5.

(c) The cost per calendar is $19.

Step-by-step explanation:

Let,

Delivery fee = f

Cost of calendar = x

No. of calendars = c

Total cost with delivery fee = D

Therefore,

The cost of 2 calendars plus delivery fee is $43.

D(c)= f + cx

43 = f + 2x Eqn 1

The cost of 4 calendars plus delivery is $81.

D(c) = f + cx

81 = f +4x    Eqn 2

(a)Write an equation that gives the  total cost as a function of calendars bought.

D(c) = f + cx      

(b)What is the delivery fee?

Multiplying Eqn 1 by 2;

[tex]2(43 = f + 2x)\\86=2f+4x\ \ \ Eqn\ 3[/tex]  

Subtracting Eqn 2 from Eqn 3;

[tex](2f+4x)-(f+4x)=86-81\\2f+4x-f-4x=5\\f=5[/tex]

Delivery fee is $5.

(C)What is  the cost per calendar?

Putting f=5 in Eqn 1;

[tex]43=5+2c\\43-5=2c\\2c=38\\[/tex]

Dividing both sides by 2

[tex]\frac{2c}{2}=\frac{38}{2}\\c=19[/tex]

The cost per calendar is $19.

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Answer:

In 68229 ways can the quiz be selected such that there is atleast three multiple choice questions

Step-by-step explanation:

Given:

Number of True or false questions= 10

Number of multiple choice questions= 20

To Find:

How many ways can 5 questions can be selected if there must be at least three multiple choice questions =?

Solution:

Combination

A combination is a mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter. In combinations, you can select the items in any order.  

The question States there sholud be ATLEAST 3 multiple choice question,

So, we may have

(3 Multiple choice question and 2 true or false question) or

(4 Multiple choice question and 1 true or false question) or

(5 Multiple choice question and 0 true or false question)

Required Number of ways = (20C3 X10C2) +(20C4 X10C1) + (20C5 X10C0)

Required Number of ways [tex]=(\frac{20!}{20!(20-3)!}\times\frac{10!}{10!(10-2)!})+(\frac{20!}{20!(20-4)!} \times \frac{10!}{10!(10-1)!}) +(\frac{20!}{20!(20-4)!} \times \frac{10!}{10!(10-0)!})[/tex]

Required Number of ways = ( 1140 x 42) + (4845 x 10) +(15504 x 1)

Required Number of ways = 47880+48450+15504

Required Number of ways = 68229

[tex](-22)^{\frac{1}{2}}[/tex] and [tex](-10)^{\frac{1}{4}}[/tex] are not real numbers

A real number is any positive or negative number. This includes all integers and all rational and irrational numbers

They are called "Real Numbers" because they are not Imaginary Numbers.

When you take an even root of a negative number, there is no real answer. (2 is an even number)

In the real number set, you can't take an even-indexed root of a negative number.

Given options are:

[tex]\begin{array}{l}{\text { A) }(-22)^{\frac{1}{2}}} \\\\ {\text { B) }(-16)^{\frac{1}{3}}} \\\\ {\text { C) }(-16)^{\frac{1}{5}}} \\\\ {\text { D) }(-10)^{\frac{1}{4}}}\end{array}[/tex]

Looking at the answer choices here, we can see that A and D use even roots, so they will give non-real answers.

Thus [tex](-22)^{\frac{1}{2}}[/tex] and [tex](-10)^{\frac{1}{4}}[/tex] are not real numbers

Answer:

(-16)^1/3 and (-6)^1/5

Step-by-step explanation:

Answer:

The rational zero of the polynomial are [tex]\pm \frac{7}{4}, \pm \frac{1}{4},\pm \frac{7}{2},\pm \frac{1}{2},\pm 7,\pm 1[/tex]  .  

Step-by-step explanation:

Given polynomial as :

f(x) = 4 x³ - 8 x² - 19 x - 7

Now the ration zero can be find as

[tex]\dfrac{\textrm factor of P}{\textrm factor Q}[/tex] ,

where P is the constant term

And Q is the coefficient of the highest polynomial

So, From given polynomial ,  P = -7 , Q = 4

Now , [tex]\dfrac{\textrm factor of \pm P}{\textrm factor of \pm Q}[/tex]

I.e  [tex]\dfrac{\textrm factor of \pm P}{\textrm factor of \pm Q}[/tex] = [tex]\frac{\pm 7 , \pm 1}{\pm 4 ,\pm 2,\pm 1 }[/tex]

Or, The rational zero are [tex]\pm \frac{7}{4}, \pm \frac{1}{4},\pm \frac{7}{2},\pm \frac{1}{2},\pm 7,\pm 1[/tex]

Hence The rational zero of the polynomial are [tex]\pm \frac{7}{4}, \pm \frac{1}{4},\pm \frac{7}{2},\pm \frac{1}{2},\pm 7,\pm 1[/tex]  .  Answer

Answer:

22m²

Step-by-step explanation:

Area of parallelogram is simply the base length x height.

In this case, base length = 4m and height = 5.5m

hence,

Area = 4 x 5.5 = 22m²

Answer:

22 m^2

Step-by-step explanation:

A = (base)(height), so:

A = (4 m)(5.5 m) = 22 m^2

Answer:

Step-by-step explanation:

[tex]\bold{STEP\ 1:}\\\\\dfrac{6}{7}\ of\ 28=\dfrac{6}{7\!\!\!\!\diagup_1}\cdot28\!\!\!\!\!\diagup^4=(6)(4)=24\\\\\bold{STEP\ 2:}\\\\_{\bold{METHOD\ 1}}\\\\p\%=\dfrac{p}{100}\to30\%=\dfrac{30}{100}=0.3\\\\x-\text{a number}\\\\0.3x=24\qquad\text{divide both isdes by 0.3}\\\\\dfrac{0.3x}{0.3}=\dfrac{24}{0.3}\\\\x=80[/tex]

[tex]_{\bold{METHOD\ 2}}\\\\\begin{array}{ccc}30\%&-&24\\\\100\%&-&x\end{array}\qquad\text{cross multiply}\\\\\\(30)(x)=(100)(24)\\\\30x=2400\qquad\text{divide both sides by 30}\\\\\dfrac{30x}{30}=\dfrac{2400}{30}\\\\x=80[/tex]

[tex]_{\bold{METHOD\ 3}}\\\\\begin{array}{cccc}30\%&-&24&\text{divide both sides by 3}\\\\\dfrac{30\%}{3}&-&\dfrac{24}{3}\\\\10\%&-&8&\text{multiply both sides by 10}\\\\(10\%)(10)&-&(8)(10)\\\\100\%&-&80\end{array}[/tex]

The value of the number will be;

⇒ x = 80

What is mean by Percentage?

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

Given that;

The algebraic expression is,

''If 6/7 of 28 is equal to 30% of that number''

Now,

Let the number = x

So, We can formulate;

⇒ 6/7 × 28 = 30% of x

Solve for x as;

⇒ 6 × 4 = 30/100 × x

⇒ 24 = 3/10 × x

⇒ 24 × 10 = 3x

⇒ 240 = 3x

⇒ x = 240/3

⇒ x = 80

Thus, The value of the number will be;

⇒ x = 80

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Answer:

1/12

Step-by-step explanation:

You want to find the compatible numbers with the common denominator so you want to multiply by ones until you get something with the same denominator. In this case it's 12, 1/3 x 4 = 4/12 and 1/4 x 3 = 3/12, Then subtract. Therefore you get your answer 1/12

George ate 1/12 of the pan of brownies.

There are 1/3 pan of brownies. George eats 1/4 of this pan.

In order to find out the fraction of the brownie pan that George ate, you need to multiply the proportion of the pan that still has brownies with the proportion that George ate.

The total fraction of the pan he ate is:

= Amount of pie George has x Amount of brownies he eats

= 1/3 x 1/4

= 1/12 of the pan

This means that out of the whole pan of brownies, George ate 1/12.

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Answer:

1 movie ticket costs $9. I hope this helps!

Step-by-step explanation:

Are you wondering how much the tickets would cost seperatly? If that's the case then you would divide $45 by 5 which would be $9 for each ticket.

Answer:

53 degrees

Step-by-step explanation:

Since we don't know the measure of the radius

UZ =127

UX=127

ZX =154

 360-154=  106

106/2=53

XY=53

YZ=53

Answer:

It's in standard form.

Answer:

Standard Form

Step-by-step explanation:

Answer:

[tex]111\ grams\ of\ zinc[/tex]

Step-by-step explanation:

Let

x -----> grams of zinc

y ----> grams of copper

we know that

[tex]\frac{x}{y}=\frac{3}{17}[/tex] -----> equation A

For y=629 grams of copper

substitute in the equation A and solve for x

[tex]\frac{x}{629}=\frac{3}{17}[/tex]

[tex]x=\frac{3}{17}(629)[/tex]

[tex]x=111\ grams\ of\ zinc[/tex]

Answer:

20 cups

Step-by-step explanation:

15 / 6 = 5/2

8 * 5/2 = 20

20 cups of milk would be required by Brian to prepare 15 dozen brownies. By utilizing ratios and proportions, this conclusion has been obtained.

To solve this problem, we can use both proportions and ratio. Brian uses 8 cups of milk for every 6 dozen (or 72) brownies. This can be written as the ratio 8:72 or the proportion 8/72 = x/180. From the proportion, we know the cross products are equal, so 8*180 = 72*x. Solving for x gives us x = (8*180)/72. Therefore, Brian would need 20 cups of milk to make 15 dozen brownies.

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Answer:

97.5 sq. ft.

Step-by-step explanation:

Im presuming the question asks to find area of the shaded region.

First of all, the total figure is a rectangle. We can write an expression(in words) for the shaded area.

Shaded Area = Area of Rectangle - Area of Small Triangle(White) - Area of Large Triangle(White)

Now, we find respective areas.

Area of rectangle:

length * width = (5+10) * (12) = 15 * 12 = 180

Area of Small Triangle (white):

A = (1/2) * base * height = (1/2) * 5 * (12-3) = (1/2) * 5 * 9 = 22.5

Area of Large Triangle (white):

A = (1/2) * base * height = (1/2) * 10 * (12) = 60

Now, we find area of shaded region:

Shaded Area = Area of Rectangle - Area of Small Triangle(White) - Area of Large Triangle(White)

Shaded Area = 180 - 22.5 - 60 = 97.5 sq. ft.

Answer:

97.5 sq. ft.

Step-by-step explanation:

See the given diagram with given measurements.

The area of the shaded portion is to be determined.

Now, we have to first find the area of the two right triangles formed at the left and right sides.

We know that the area of a right triangle = [tex]\frac{1}{2} \times (\textrm {Base})\times (\textrm {Height})[/tex]

Then the area of the left side triangle = [tex]\frac{1}{2} \times 5 \times (12 - 3) = 22.5[/tex] sq. ft.

Now, the are of the right side triangle = [tex]\frac{1}{2} \times 10 \times 12 = 60[/tex] sq. ft.

Now, the area of non-shaded region = Total are of the two right triangles  

= (60 + 22.5) = 82.5 sq. ft.

Therefore, the area of the shaded region is = (Area of the total rectangle - Area of the non-shaded region)

= [(10 + 5) × 12] - 82.5

= 97.5 sq. ft. (Answer)

Answer:

the equations n + 7= 11

Step-by-step explanation:

if your asking for the same equation

(not totally sure)

Answer:

n=7

Step-by-step explanation:

so move 4 to the other side so subtract cuz it's a positive number so it will be

n=7 so 7+4=11

Answer:

730.36

Step-by-step explanation:

.24 × 589= 141.36

141.36+589=730.36

so the original price would be 730.36

Answer:

We can conclude that Δ XYZ ≅ Δ RST by ASA postulate.

Step-by-step explanation:

Δ XYZ and Δ RST are congruents by ASA postulate because:  

1. Their included sides XZ  and RT are equal.  

2. Their angles ∠Z and ∠T are equal (92° = 92°)

3. Their angles ∠X and ∠R are equal.  

4. Their non-included sides XY and RS are equal.

Now, we can conclude that Δ XYZ ≅ Δ RST by ASA postulate.

Answer:

The Time taken to cover the distance of 3 miles at the speed of 2 miles per hour is 1.5 hours

Step-by-step explanation:

Given as :

The distance cover while walking = 3 miles

The Speed with which it walk 3 miles = 2 miles per hour

Let the time taken to cover the distance = T hours

Now,

∵ Time = [tex]\dfrac{\textrm Distance}{\textrm Speed}[/tex]

Or, T =  [tex]\dfrac{\textrm 3}{\textrm 2}[/tex]

∴ T = 1.5 hours

So, time taken is 1.5 hours

Hence The Time taken to cover the distance of 3 miles at the speed of 2 miles per hour is 1.5 hours  Answer

Answer:

262

Step-by-step explanation:

If x is the first integer, then x+1 is the second, x+2 is the third, and so on.  Meaning the 7th term in the list is x+6.

x + x + 6 = 518

2x = 512

x = 256

The first integer is 256, so the last integer is 262.

Answer:

18 (3) + 18 (X) = 18 (3+X)

Step-by-step explanation:

AB + AC = A ( B + B )

A is the common factor

Factor to find common factor

54 = 2 * 3 * 3 * 3

18 = 2 * 3 * 3 * x

greatest common factor (GCF) = 2 * 3 * 3 = 18

18 (3) + 18 (X) = 18 (3+X)

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