Which is the best first step and explanation for solving this system of equations?

Answer:

( - 1, 1 )

Step-by-step explanation:

Given the 2 equations

3x - y = - 4 → (1)

x + y = 0 → (2)

Subtract y from both sides in (2)

x = - y → (3)

Substitute x = - y into (1)

- 3y - y = - 4, that is

- 4y = - 4 ( divide both sides by - 4 )

y = 1

Substitute y = 1 into (3)

x = - 1

Solution is (- 1, 1 )

The solution to the system of equations 3x - y = -4 and x + y = 0 is found by substitution, resulting in the solution set (x, y) = (-1, 1).

To find the solution to the equations 3x - y = -4 and x + y = 0, you can use the method of substitution or elimination. Since the second equation easily gives us y in terms of x (that is, y = -x), we can substitute this into the first equation.

Substitute y = -x into the first equation: 3x - (-x) = -4.

Simplify: 3x + x = 4x

hence, 4x = -4

Divide both sides by 4 to solve for x: x = -1.

Now substitute x = -1 into y = -x to find y: y = -(-1) = 1.

The solution to the system of equations is (x, y) = (-1, 1).

Answer:

2 scrapbook pages

I found the answer online

Aylin can create a maximum of 19 scrapbook pages by dividing the total number of items by the number of items on each page.

Aylin wants to set up all the pages of her scrapbook in the same way, with a combination of photos and newspaper clippings on every page.

She wants to make sure that no items are left over.

To find the greatest number of scrapbook pages Aylin can create, we need to divide the total number of items -

= 18 photos + 20 newspaper clippings

= 38 items

Now,

Since she wants each page to have the same combination, we can find the greatest common divisor (GCD) of 18 and 20, which is 2.

Therefore, Aylin can create a maximum of 38/2 = 19 scrapbook pages.

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The graph of the line that contains the point ( − 6 , 1 ) and has a slope of 5 is shown below in the attachment.

How to graph a line?

To graph a line with a given point (-6, 1) and a slope of 5 without explicitly finding the equation, you can start from the given point (-6, 1) and use the slope (5) to find other points.

Move up by 5 units (rise) and to the right by 1 unit (run) from the given point, and you'll get another point on the line. Repeat this process to plot multiple points and then connect them to graph the line.

The graph of the line is attached below.

Answer:

.5

Step-by-step explanation:

1 divided by 2 is .5.

Answer:

0.5

Step-by-step explanation:

1/2 is equal to 5/10, and 5/10 is equal to 0.5.

Answer:

2,300

Step-by-step explanation:

see attached to identify the hundreds digit.

How we round the hundreds digit depends on the number in the tens place.

If the number in the tens places is less than 5, then we keep the hundreds digit the same (i.e we round down)

If the number in the tens place is greater or equal to 5, then we increase the hundreds digit by 1 (i.e round up)

in this case, the digit in the tens place is 1 (i.e less than 5) hence we round down by keeping the hundreds place the same

we end up with 2,300

2,319 rounded to the nearest hundreds is 2,300.

To round the number 2,319 to the hundreds place, follow these steps:

Therefore, the answer is 2,300.

Answer:

g(x) = |x+3| - 5

Step-by-step explanation:

Let y = f(x)

⇒y = |x+3|

When y is replaced by Y + k, the graph of y = f(x) shifts k units down

⇒ y replaced by Y + 5 translates the graph of y = f(x) 5 units down

∴ Y = g(x) is represented by Y + 5 = |x+3|

⇒ Y = |x+3| - 5

or g(x) = |x+3| - 5

Answer:

Step-by-step explanation:

16

The value of x in the equation 3x + 7x + 9 = 35 is 2.6 after simplification and carrying out the necessary algebraic steps.

The subject of your question is Mathematics, specifically algebra. Now, let's solve the equation: 3x + 7x + 9 = 35.

To start, combine like terms on the left side of the equation. That gives us 10x + 9 = 35. Next, subtract 9 from both sides to isolate the term with x. This gives us 10x = 26. Finally, divide both sides by 10 to find the value of x. So, x = 2.6.

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Answer:

They need to make 5 pies for 15 people.

Step-by-step explanation:

15*3=45 slices of pie in total,

each pie is cut into 9 slices,

45/9=5 pies

Answer:

The two cars are at the distance of 21 miles apart .

Step-by-step explanation:

Given as :

The car travel due north to the distance  = 12 miles

The car travel due south to the distance = 9.12 miles

let the distance between the two cars = x miles

So, the total distance between the cars = The distance of north going car + the distance of south going car

Or,  the total distance between the cars = 12 miles + 9.12 miles

or,  the total distance between the cars =  21.12 miles ≈ 21 miles

I.e the total distance between the cars = 21 miles

Hence The two cars are at the distance of 21 miles apart . Answer

Answer:

The radioactive substance will decay in 17.70 hours .

Step-by-step explanation:

Given as :

The rate of decay of radioactive substance = 4 %  per hour

Let The original weight of substance = w

The final weight of substance = [tex]\frac{w}{2}[/tex]

Let the hours for decay of substance = n

Now,

The weight of substance after n years = The original weight of substance × [tex](1- \dfrac{\textrm Rate}{100})^{n}[/tex]

or,

[tex]\frac{w}{2}[/tex] = w × [tex](1- \dfrac{\textrm 4}{100})^{n}[/tex]

Or, [tex]\frac{1}{2}[/tex] = [tex](1- \dfrac{\textrm 1}{25})^{n}[/tex]

or,  [tex]\frac{1}{2}[/tex] = [tex](\dfrac{\textrm 25-1}{25})^{n}[/tex]

or,  [tex]\frac{1}{2}[/tex] = [tex](\dfrac{\textrm 24}{25})^{n}[/tex]

Taking log both sides :

Log  [tex]\frac{1}{2}[/tex] = Log [tex](\dfrac{\textrm 24}{25})^{n}[/tex]

So, Log [tex]\frac{1}{2}[/tex] = n × Log [tex]\frac{24}{25}[/tex]

∴ - 0.301 =  n × ( - 0.017 )

So , n = [tex]\frac{0.301}{0.017}[/tex]

I.e n = 17.70  hours

Hence The radioactive substance will decay in 17.70 hours . Answer

Answer:

0.22 hours

Step-by-step explanation:

Half life is defined as the time taken by a radioactive material to decay to half of its original value.

Mathematically, half-life (t1/2) = ln2/¶ where ¶ is the decay constant.

Before we can get the half life, we need to get the decay constant first. To get ¶, we will use the radioactivity formula. According to the formula,

N/No = e^-¶t where;

N/No is the fraction of the final substance after decay the the original value of the substance = 4% = 1/25

t is the time of decay = 1hour

Substituting into the formula to get the decay constant we have;

1/25 = e^-1¶

Applying ln to both sides, we have;

ln 1/25 = lne^-¶

ln1/25 = -¶

-3.22= -¶

¶ = 3.22

The decay constant is 3.22

Half life = ln2/3.22

Half life = 0.22hours

It will take the substance 0.22hours before it changes to half of its original weight.

Answer:

90°

Step-by-step explanation:

step 1

Find the measure of angle b

we know that

(m∠b+90°)=124° ----> by vertical angles

so

m∠b=124°-90°

m∠b=34°

step 2

Find the measure of angle c

(m∠c+124°)=180° ----> by supplementary angles (form a linear pair)

m∠c=180°-124°

m∠c=56°

step 3

Find the measure of angle a

m∠a=m∠c ----> by vertical angles

so

m∠a=56°

step 4

Find the value of m∠ a + m∠b

m∠a=56°

m∠b=34°

m∠ a + m∠b=56°+34°

m∠ a + m∠b=90°

The percent change is 40%

Step-by-step explanation:

The percent change is given by the formula

[tex]Percent\ change=\frac{New\ value-Original\ value}{Original} * 100[/tex]

Here

New value = 70

Original value = 50

Putting the values in the formula

[tex]Percent\ change=\frac{70-50}{50}*100\\=\frac{20}{50}*100\\=0.4*100\\=40\%[/tex]

The percent change is 40%

Keywords: Percentage

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Answer:

An independent clause is a group of words that contains both a subject and a predicate. It expresses a complete thought and can stand alone as a sentence. It can also be joined to other dependent or independent clauses to make a more interesting and complex sentence.

Step-by-step explanation:

Answer:

Average Speed to complete the journey = 80 km/h

Step-by-step explanation:

Given,

The distance between Sydney and Goulburn = 200 kilometer.

Time to complete the journey = 2 hour 30 minutes

Converting the time into minutes -

2 hour 30 minutes

= (2 x 60) minutes + 30 minutes

= 120 minutes + 30 minutes

= 150 minutes

We know, to determine average speed, we have to divide the distance by time.

Therefore, Speed = [tex]\frac{Distance}{Time}[/tex]

Speed = [tex]\frac{200 km}{150 minutes}[/tex]

Speed = 1.33 km/minutes

Speed = (1.33 km x 60) km/hour (To convert it to hour, we have to multiply by 60)

Average Speed per hour = 80 km/h

For this case we have that by definition, the equation of a line in the standard form is given by:

[tex]ax + by = c[/tex]

According to the statement we have the following equation of the line:

[tex]y + 1 = \frac {2} {5} (x + 3)[/tex]

We manipulate algebraically to write in the standard form. To do this we follow the steps below:

We apply distributive property on the right side of the equation:[tex]y + 1 = \frac {2} {5} x + \frac {6} {5}[/tex]

We subtract [tex]\frac {6} {5}[/tex] on both sides of the equation:

[tex]y + 1- \frac {6} {5} = \frac {2} {5} x\\y- \frac {1} {5} = \frac {2} {5} x[/tex]

We multiply by 5 on both sides of the equation:

[tex]5y-1 = 2x[/tex]

We subtract 5y on both sides of the equation:

[tex]2x-5y = -1[/tex]

Finally, the equation in its standard form is:

[tex]2x-5y = -1[/tex]

Answer:

[tex]2x-5y = -1[/tex]

Answer:

○ A. Graph C

Step-by-step explanation:

Starting from the y-intercept of [tex]\displaystyle [0, -4],[/tex]you do [tex]\displaystyle \frac{rise}{run}[/tex]by either moving one block south over four blocks west or one block north over four blocks east. Now, you have to figure out which graph follows the inequality symbol in the inequality. In this case, two answer choices match this because the less than inequality will result in a dashed line, so we can automatically eliminate answer choices D. and B.. Now, to figure out our graph once in for all, we need to use the zero-interval test [test point [0, 0]] to ensure if we either shade the opposite portion [the portion that does NOT contain the origin] or the portion that DOES contain the origin. We then need to verify it as false or true:

[tex]\displaystyle 0 < \frac{1}{3}[0] - 4 → 0 ≮ -4[/tex]

This is a FALSE statement, so instead of shading above the dashed line, we shade below the dashed line, and that answer choice is A..

>, < → Dashed Line

≥, ≤ → Solid Line

I am joyous to assist you anytime.

Answer:

[tex]-0.4, -\frac{9}{16}, -1\frac{3}{8}, -1.55[/tex]

Step-by-step explanation:

The list of numbers given:

[tex]-1\frac{3}{8}, -0.4, -1.55, -\frac{9}{16}[/tex]

We need to arrange from greatest to least.

In order to arrange the numbers in descending order we will find the equivalent decimal value of each number.

a)[tex]-1\frac{3}{8}=-1.375[/tex]

b) [tex]-0.4[/tex]

c) [tex]-1.55[/tex]

d) [tex]-\frac{9}{16}=-0.5625[/tex]

Arranging the numbers in descending order

[tex]b>d>a>c[/tex]   [since all the numbers are negative, so the number closest to 0 is the greatest]

Thus the correct order from greatest to least is:

[tex]-0.4, -\frac{9}{16}, -1\frac{3}{8}, -1.55[/tex] (Answer)

Answer:

Step-by-step explanation:I could help

Step-by-step explanation:

If [tex]mKg[/tex] of mass is placed on spring with spring constant [tex]k[/tex],

[tex]mg=kx[/tex]

where [tex]g[/tex] is universal gravitational constant

[tex]x[/tex] is the displacement in the spring.

In case 1:

[tex]25g=k(0.15)\\k=\frac{25g}{0.15}[/tex]

In case 2:

[tex]mg=k(0.23)[/tex]

Using  result from case 1,

[tex]mg=\frac{25g}{0.15}\times 0.23[/tex]

[tex]m=[/tex][tex]38.33Kg[/tex]

Answer:

The height of First Copy is 20 cm.

Step-by-step explanation:

Given:

Original Height = 25 cm

First copy is reduce to 80% of Original height.

Therefore to find the height of first copy can be find out by multiplying 80 with original height and then dividing by 100.

∴ Height of First Copy = [tex]\frac{80}{100} \times \textrm{original height}= 0.8\times 25 cm = 20cm[/tex]

Hence Height of first copy is 20 cm

Now Another copy is reduce to 85% of First Copy.

Therefore to find the height of another copy can be find out by multiplying 85 with first copy height and then dividing by 100.

∴ Height of Another Copy = [tex]\frac{85}{100} \times \textrm{first copy height}= 0.85\times 20 cm = 17cm[/tex]

Hence Height of Another copy is 17 cm

Answer:

To find the height of the first​ copy,

multiply 0.8 by 25.

The height of the first copy is

20 cm.

To find the height of the second​ copy,

multiply 0.85 by the height of the first copy.

The height of the second copy is

17 cm.

Step-by-step explanation:

Answer:

The distance between the two buildings is 9.563 yards.

Step-by-step explanation:

See the diagram attached.

AB and CD are two buildings AC distance apart.

Now, AC = ED.

The angle of depression of clothesline BD is 17 Degrees.

Now, given that  BD = 10 yards.

And ∠ OBD = ∠ BDE = 17°  {Alternate angles}

Now, from the right triangle Δ BED, we have  

[tex]\cos 17 = \frac{ED}{BD} = \frac{ED}{10}[/tex]

⇒ ED = 10 cos 17 = 9.563 yards.

Therefore, the distance between the two buildings is 9.563 yards. (Answer)

Using combinations in mathematics, it's found that there are 4 different 3-topping pizzas possible from a selection of 4 toppings, since the order of toppings on a pizza does not matter.

Combination Calculation for Pizza Toppings

When considering the number of different 3-topping pizzas possible from 4 choices, one must use combinations to solve this problem. A combination is a selection of items where the order does not matter, which fits our scenario since the order of toppings on a pizza does not change the pizza's identity. In mathematical terms, we look for the number of combinations of 4 items taken 3 at a time, which is denoted as 4C3.

The formula for combinations is:

C(n, k) = n! / (k!(n-k)!), where n is the total number of items, k is the number of items to choose, and ! denotes a factorial.

Thus, for our pizza topping problem, this becomes:

4C3 = 4! / (3!(4-3)!) = (4×3×2×1) / ((3×2×1)×1) = 24 / 6 = 4 different 3-topping pizzas.

Therefore, there are 4 different ways to select 3 toppings from a choice of 4.

Answer:

$3.50

Step-by-step explanation:

15.00 - 7.00 = 8.00

6 x .75 = 4.50

8.00- 4.5 = 3.50

The equation for the total amount for the fair and rides is given by the relation y = 0.75n + 7  where n is the total number of rides

The amount left after purchasing 6 tokens is $ 3.50

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the total amount be represented as = y

Now , the number of rides be = n

The cost of entry fee = $ 7

The cost for each ride = $ 0.75

The total amount available = $ 15

So , the equation will be

total amount = cost for each ride x number of rides + cost of entry fee

Substituting the values in the equation , we get

Total amount y = 0.75n + 7

y = 0.75n + 7

So , the equation is y = 0.75n + 7

Now , when purchasing 6 tokens , we get the remaining amount as

Substituting the value of n = 6 in the equation , we get

y = 0.75 x 6 + 7

y = 4.5 + 7

y = $ 11.5

So , the amount left = 15 - y

The total amount left = 15 - 11.5

The total amount left = $ 3.50

Hence , The equation for the total amount for the fair and rides is given by the relation y = 0.75n + 7  where n is the total number of rides

The amount left after purchasing 6 tokens is $ 3.50

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Danielle earned $969 last week.

Step-by-step explanation:

Base salary per week = $650

Commission = 7.25%

Worth of electronics sold = $4400

Commission = 7.25% of 4400

[tex]Commission = \frac{7.25}{100}*4400\\Commission = \frac{31900}{100}\\Commission = \$319[/tex]

Earning of last week = Base salary per week + commission

[tex]Earning\ of\ last\ week=650+319=\$969[/tex]

Danielle earned $969 last week.

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Career clusters are groups of related careers. In the example given, careers in biological sciences like microbiologist, ecologist, neurologist, and forensic scientist form one cluster, while allied health professions such as medical technician, medical examiner, and neurophysiologist form another. Matching careers to clusters involves identifying commonalities such as educational requirements, tasks, and industry.

It looks like you are trying to match careers with specific career clusters. Career clusters represent a group of careers that share common features. If we consider biological sciences, we'd have a cluster including careers such as a microbiologist, ecologist, neurologist, and forensic scientist. These professions are heavily involved in studying living organisms and their environments.

On the other hand, if we consider allied health, this would be another cluster including careers like medical technician, medical examiner, and neurophysiologist. These professions are more orientated towards applied sciences in healthcare.

I hope this helps you understand how to match careers with their respective career clusters. A good approach is to identify commonalities between various jobs such as their educational requirements, day-to-day tasks, and the industry they belong to.

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Step-by-step explanation:

In slope intercept form?

Subtract 11x from both sides to get:

13y = -11x + 8

Then divide the entire thing by 13

[tex]y = \frac{ - 11}{13}x + \frac{8}{13} [/tex]

is your new equation

Step-by-step explanation:

1.-92%

2.40%

3.-76%

4.65%

The percent changes for each scenario is: 1. From 1000 to 80: -92% 2. From 45 to 63: +40% 3. From 250 to 60: -76% 4. From 60 to 99: +65%.

To calculate the percent change between two values, we use the formula:

[tex]\[ \text{Percent Change} = \left( \frac{\text{New Value} - \text{Original Value}}{\text{Original Value}} \right) \times 100\% \][/tex]

1. The percent change from 1000 to 80 is calculated as follows:

[tex]\[ \text{Percent Change} = \left( \frac{80 - 1000}{1000} \right) \times 100\% = \left( \frac{-920}{1000} \right) \times 100\% = -92\% \][/tex]

So, the percent change is a 92% decrease.

2. The percent change from 45 to 63 is calculated as follows:

[tex]\[ \text{Percent Change} = \left( \frac{63 - 45}{45} \right) \times 100\% = \left( \frac{18}{45} \right) \times 100\% = \frac{2}{5} \times 100\% = 40\% \][/tex]

So, the percent change is a 40% increase.

3. The percent change from 250 to 60 is calculated as follows:

[tex]\[ \text{Percent Change} = \left( \frac{60 - 250}{250} \right) \times 100\% = \left( \frac{-190}{250} \right) \times 100\% = -76\% \][/tex]

So, the percent change is a 76% decrease.

4. The percent change from 60 to 99 is calculated as follows:

[tex]\[ \text{Percent Change} = \left( \frac{99 - 60}{60} \right) \times 100\% = \left( \frac{39}{60} \right) \times 100\% = \frac{13}{20} \times 100\% = 65\% \][/tex]

So, the percent change is a 65% increase.