Can someone explain this

The properties justify the steps are taken to solve the system 2a+7b=0 3a-5b=31 as Multiplication, Substraction, Division,  Simplify, etc.,

What is the linear equation?

A linear equation is an algebraic equation of the form y=mx+b. where m is the slope and b is the y-intercept.

'The properties that justify the steps taken to solve the system 2a + 7b = 0, 3a - 5b = 31 are:

2a + 7b = 0, 3a - 5b = 31

10a + 35b = 0, 21a - 35b = 217   <-------> Multiplication property of equality.

31a = 217                                      <-------> Substraction property of equality.

a = 7                                            <-------> Division property of equality.

2(7) + 7b = 0,                             <-------> Substitution property of equality.

14 + 7b = 0,                              <-------> Simplify  

7b = -14,                                   <-------> Simplify  

b = -14/7,                                  <-------> Division property of equality.

b = -2

Therefore, the properties justify the steps are taken to solve the system 2a+7b=0 3a-5b=31 as Multiplication, Substraction, Division,  Simplify, etc.,

To learn more about the linear equation visit,

https://brainly.com/question/2030026

#SPJ1

Students raised $225 in the first week and $90 in the second week.

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

Given that, a student club has a goal to raise $750 to buy new books for a library.

In the first week, the club raised 30% of its goal.

Now, 30% of 750

= 30/100 ×750

= 3×75

= $225

In the second week, the club raised 12% of its goal.

Now, 12% of 750

= 12/100 ×750

= 0.12×750

= $90

Hence, students raised $225 in the first week and $90 in the second week.

To learn more about the percentage visit:

brainly.com/question/24159063.

#SPJ9

Answer:

0.75

Step-by-step explanation:

The slope-intercept form is one way to write a linear equation (the equation of a line). The slope-intercept form is written as y = mx+b, where m is the slope and b is the y-intercept (the point where the line crosses the y-axis).

Answer:

Step-by-step explanation:

10

The two-column table that can be used to prove the congruence relationships between the segments of the triangles are presented as follows;

             Statement    [tex]{}[/tex]                                   Reasons

1. [tex]\overline{KN}[/tex] ≅ [tex]\overline{MN}[/tex]                     [tex]{}[/tex]                            Given

 [tex]\overline{NL}[/tex] bisects ∠KNM           [tex]{}[/tex]                          

2. ∠KNL ≅ ∠MNL [tex]{}[/tex]                                        Definition of bisected angle

3. [tex]\overline{NL}[/tex] ≅ [tex]\overline{NL}[/tex]                   [tex]{}[/tex]                               Reflexive property

4. ΔKNL ≅ ΔMNL [tex]{}[/tex]                                         SAS congruence rule

5. [tex]\overline{KL}[/tex] ≅ [tex]\overline{ML}[/tex]         [tex]{}[/tex]                                        CPCTC

6. KL = ML [tex]{}[/tex]                                                    Definition of congruence

C.  

[tex]{}[/tex]               Statement [tex]{}[/tex]                                   Reasons

1.  [tex]\overline{BE}[/tex] ≅ [tex]\overline{CE}[/tex], [tex]\overline{AE}[/tex] ≅ [tex]\overline{DE}[/tex]                               Given

2. ∠AEB ≅ ∠CED [tex]{}[/tex]                                        Vertical angles theorem

3. ΔABE ≅ ΔCED [tex]{}[/tex]                                        SAS congruence rule

4. [tex]\overline{AB}[/tex] ≅ [tex]\overline{CD}[/tex]                                         [tex]{}[/tex]        CPCTC

Congruent segments are segments that have the same lengths.

The details of the reasons used to prove the equivalence of sides KL and ML and the congruence of the segments [tex]\overline{AB}[/tex] and [tex]\overline{CD}[/tex] are presented as follows;

Definition of bisected angles

Bisected angles are angles that are split in two angles of the same measure by a segment passing through their vertex.

Reflexive property

The reflexive property of congruence states that a segment is congruent to itself.

SAS congruence rule

The SAS, Side-Angle-Side congruence rule states that if two sides and an included angle of a triangle are congruent to two sides and an included angle in another triangle, then the two triangles are congruent.

CPCTC

CPCTC is an acronym for Corresponding Parts of Congruent Triangles are Congruent.

Definition of congruence

Geometric figures, such as segment, angles and shapes are congruent when their sizes and measurements are the same.

Vertical angles theorem

The vertical angles theorem states that vertical angles formed by the intersection of two lines are congruent

Learn more about the triangle congruence rule here: https://brainly.com/question/29451135

#SPJ1

Answer:482 in ^2

Step-by-step explanation:

The solution to the equation 3x2 - 30x - 72 = 0 is x = -4 and x = -12.

3x2 - 30x - 72 = 0

3x2 - 30x = 72

3x2 - 24x = 90

3x2 - 24x + 18x = 90 + 18x

3x(x - 8) = 108

x(x - 8) = 36

x = 36 or x = 8

x = -12 or x = -4

The equation 3x2 - 30x - 72 = 0is a second-degree polynomial equation with two solutions. To solve this equation, first use the distributive property to factor out 3x from the first two terms. This yields 3x(x - 8) = 108. Then divide both sides of the equation by 3 to get x(x - 8) = 36. From here, use the quadratic formula to solve for x. This yields x = 36 or x = 8. Since the equation was given in terms of x2, the two solutions are x = -12 and x = -4. To confirm this, substitute these values into the original equation and check that it is true.

Learn more about equation here

https://brainly.com/question/29657992

#SPJ4

The statement "sum of a and b integers is a negative integer" is true given that A and B are both negative integers and A is greater than B.

When we add two negative integers, the sum is always negative. This is because adding a negative number is the same as subtracting its absolute value. Therefore, if A and B are negative integers, then A + B will be negative as well.

Since A > B, the sum A + B will be closer in value to A than to B. However, it will still be negative because A and B are both negative integers.

So, the sum of A and B is a negative integer, and the statement is true.

To know more about Integers:

https://brainly.com/question/1768255

#SPJ4

____ The given question is incomplete, the complete question is given below:

A and B are both negative integers with a>b. Classify this are true or false. sum of a and b integers is a negative integer.

Five packets of marshmallows cost £4. 80. Then, eight packets of marshmallows cost £7.68.

The problem states that five packets of marshmallows cost £4.80. We need to find out how much eight packets of marshmallows will cost.

To solve the problem, we can use the concept of proportionality. If we assume that the cost of marshmallows is directly proportional to the number of packets, then we can set up a proportion between the cost of five packets and the cost of eight packets.

The proportion can be written as follows:

5 packets / £4.80 = 8 packets / x

where x is the cost of eight packets.

To solve for x, we can cross-multiply the proportion and simplify:

5 packets x = £4.80 x 8 packets

5x = £38.40

x = £38.40 / 5

x = £7.68

Therefore, eight packets of marshmallows will cost £7.68.

To learn more about proportionality click on,

https://brainly.com/question/21090477

#SPJ4

Answer:

the answer is 19!

To make it easier you can also use an online calculator or if you have one in real life you can use it! You can also do it on paper!

Have a great day! :) <3

Answer:

  15

Step-by-step explanation:

You want the sum of the numbers in the diagram that belong to exactly 3 circles.

We find it easier to eliminate numbers that do not belong to 3 circles. In the attachment, the red lines strike through numbers belonging to 1 circle, the blue lines strike numbers belonging to 2 circles, and the green line strikes the number belonging to 4 circles. (The numbers inside the smallest circle are also in the larger circle surrounding it.)

The numbers that are in 3 circles only are 1, 3, 11. Their sum is 15.

Answer:

87654321

Step-by-step explanation:

The equation in standard form is D. 4x² - 17x-9=0

To make an equation into standard form is to equate the terms and factors to zero.

Given the expression;

-3x² + 4(x - 2) = 7x(3 - x) + 1

expand the bracket

-3x² + 4x - 8 = 21x - 7x² + 1

Now, collect the like terms

-3x² + 7x² + 4x - 21x = 1 + 8

Add or subtract the like terms

4x² - 17x = 9

Equate equation to zero, we get;

4x² - 17x - 9 = 0

Learn about quadratic equations at: https://brainly.com/question/1214333

#SPJ1

The value of x in the equation is 8 or -27

The exponential function is a mathematical function denoted by f(x)=\exp or e^{x}. Unless otherwise specified, the term generally refers to the positive-valued function of a real variable, although it can be extended to the complex.

X^2/3 + X^1/3 -6 = 0

= X^1/3(2) + X^1/3 -6 = 0

represent X^1/3 by K

= K²+k-6 = 0

(K +3k )(-2k -6)= 0

k(3+k) -2(k+3) = 0

(k+3)(k-2) = 0

k+3 = 0

k -2 = 0

k = -3 or 2

since K = x^1/3

when k =-3

-3 = x^1/3

x = -3³ = -27

when k = 2

x = 2³ = 8

therefore the value of x is -27 or 8

learn more about exponential equation from

https://brainly.com/question/2456547

#SPJ1

The expression for f(x) - g(x) - h(x) is 6x - 5x² + 6.

Option C is the correct answer.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

f(x) = 3x + 5

g(x) = 4x² - 2

h(x) = x² - 3x + 1

Now,

f(x) - g(x) - h(x)

= 3x + 5 - (4x² - 2) - (x² - 3x + 1)

= 3x + 5 - 4x² + 2 - x² + 3x - 1

= 6x - 5x² + 6

Thus,

6x - 5x² + 6 is the expression.

Learn more about functions here:

https://brainly.com/question/28533782

#SPJ9

Answer: Demographic republic of Congo, Uganda and Gabon

Each week, Desiree earns $925 and pays $149 in payroll tax it will take Desiree at least 4 weeks to earn at least $3000 after taxes.

What is Gross earning ?

Gross earnings refer to the total amount of money that an individual earns before any deductions are taken out. These earnings can include regular salary or wages, as well as any bonuses, tips, or commissions that are earned. Gross earnings are usually reported on a paycheck or pay stub, and may be subject to various taxes and other deductions.

Desiree's net earnings after payroll tax can be calculated by subtracting the tax amount from her gross earnings:

Net Earnings = Gross Earnings - Payroll Tax

Net Earnings = $925 - $149

Net Earnings = $776

To earn at least $3000 after taxes, Desiree needs to earn a total of:

Total Earnings = $3000 + Payroll Tax

Total Earnings = $3000 + $149

Total Earnings = $3149

We can now set up an equation to solve for the number of weeks, x, it will take for Desiree to earn at least $3149:

Net Earnings per week * Number of Weeks = Total Earnings

$776 * x = $3149

Solving for x:

x = $3149 / $776

x = 4.05

Therefore, it will take Desiree approximately 4.05 weeks to earn at least $3000 after payroll tax. Since you can't earn partial weeks, we can round up to 5 weeks to ensure that Desiree has earned at least $3000.

Learn more about Gross earning click here:

https://brainly.com/question/21637154

#SPJ1

Answer:

7 and 7x

Step-by-step explanation:

We distributing these factors are the only that can make sense

In stabilizing selection, option (d) The intermediate phenotype becomes rare.

Stabilizing selection occurs when individuals with extreme phenotypes are at a disadvantage, and individuals with intermediate phenotypes have a greater chance of survival and reproduction.

This means that over time, the population shifts towards the intermediate phenotype. Let's take an example to explain this concept.

Suppose we have a population of rabbits with different fur colors, ranging from white to dark brown. Predators are more likely to spot white rabbits in a snowy environment, while brown rabbits are more likely to be seen in a forest environment. This means that the extreme phenotypes (white and dark brown) are at a disadvantage, while the intermediate phenotype (light brown) is more likely to survive and reproduce. Over time, the population will shift towards the light brown phenotype, as it is the most advantageous trait.

In conclusion, stabilizing selection is a mechanism of natural selection that promotes the preservation of the average characteristics of a population. It occurs when individuals with intermediate phenotypes have a higher chance of survival and reproduction, leading to the shift of the population towards the intermediate phenotype. Mathematically, we can represent this concept using the mean and standard deviation of a population.

To know more about population here.

https://brainly.com/question/27991860

#SPJ4

a. The amount of copper in a bronze brooch weighing 360g is 216g.

b. The total weight of the bronze brooch is 745g.

If an item is made of two different items, the ratio of the quantities of those two items contributes to the amount of the compound item. With the help of that ratio, the unknown quantity can be determined.

a.

The ratio of copper to tin in bronze is 9:1.

So, the portion of copper in the bronze is 9 out of 10, that is, 0.9.

The total weight of the bronze brooch is 360g.

Find the amount of copper in that brooch.

360×0.9=324

Therefore, the copper in a 360g bronze brooch is 324g.

b.

The amount of copper in the bronze brooch is 670.5g.

Also, the portion of copper in the bronze is 0.9.

Let, the total weight of the bronze brooch is Xg.

So, the equation becomes 0.9X=670.5.

Find the value of X.

0.9X=670.5

X=745

Therefore, the total weight of the bronze brooch is 745g.

To learn more about the ratio click below :

https://brainly.com/question/28934221

#SPJ1  

Answer:

7

Step-by-step explanation:

35-8-4-2=21

21/3=7

Answer:

7 pounds

Step-by-step explanation:

8+4+2=14

35-14=21

21/3=7

The customer had a 3-hour repair when paying $96 without a coupon.

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

With a coupon, the customer paid $66 for a 3-hour repair.

The coupon gives a 40% discount on the inspection fee, so let's call the original inspection fee "x". Then the customer paid 0.6x + 14*3 = $66.

Solving for x, we get x = $30.

Without a coupon, the customer paid $96.

We want to find out how many hours of repair were done for $96.

Let's use a similar equation to solve for the number of hours:

Let's call the number of hours "h". Then the customer paid 30*0.6 + 14h = $96.

Solving for h, we get h = 3.

Therefore, the customer had a 3-hour repair when paying $96 without a coupon.

To learn more about Algebraic expression from given link.

https://brainly.com/question/28884894

#SPJ1

Answer:

Step-by-step explanation:

The interest rate of 1.25% compounded monthly means that the interest earned each month is 1.25% of the current balance. Here's how you can calculate the final balance in the account after 20 years:

First, calculate the interest earned each month: $200 * 1.25% = $2.50

Then, add the interest earned to the monthly deposit to get the new balance: $200 + $2.50 = $202.50

Repeat this process for 240 months (20 years x 12 months/year).

The final balance in the account after 20 years would be approximately $71,934.24.

To find the total money you will put into the account, simply multiply the monthly deposit by the number of months: $200 * 240 = $48,000.

To find the total interest earned, subtract the initial deposit from the final balance: $71,934.24 - $48,000 = $23,934.24

So, in 20 years, you will have put a total of $48,000 into the account, and you will have earned a total of $23,934.24 in interest.

Answer:

The first term is, x2 its coefficient is 1 .

The middle term is, -9x its coefficient is -9 .

The last term, "the constant", is +16

Step-1 : Multiply the coefficient of the first term by the constant 1 • 16 = 16

Step-2 : Find two factors of 16 whose sum equals the coefficient of the middle term, which is -9 .

-16 + -1 = -17

-8 + -2 = -10

-4 + -4 = -8

-2 + -8 = -10

-1 + -16 = -17

1 + 16 = 17

2 + 8 = 10

4 + 4 = 8

8 + 2 = 10

16 + 1 = 17

The equation of the total cost is C = 3 + 5x and the amount earned after 5 hours is $28.

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("="). For illustration, 2x - 5 = 13.

Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign. Typically, we consider an equation's right side to be zero.

Let us suppose the number of hours = x.

The cost of additional hour is $5.

The cost of x hours is 5x.

Given that, Nicole charges a flat fee of $3, plus $5 per hour.

C = 3 + 5x

If she baby sits for 5 hours, that is x = 5, then:

C = 3 + 5(5)

C = 3 + 25

C = $28

Hence, the equation of the total cost is C = 3 + 5x and the amount earned after 5 hours is $28.

Learn more about equation here:

https://brainly.com/question/29657988

#SPJ1

The expression can be written as the trinomial below.

3x2 - 14x + 15

Here we just need to expand the expression:

(x - 3)*(3x - 5)

Just expanding that product we will get:

(x - 3)*(3x - 5)

x*(3x) - 3*(3x) + x*(-5) - 3*(-5)

3x^2 - 9x - 5x + 15

3x2 - 14x + 15

So we have 3 terms now, thus, this is a trinomial.

Learn more about trinomials at:

https://brainly.com/question/1538726

#SPJ1

Answer: A linear function with a line heading toward negative infinity as x approaches infinity and with a y-int at (0,8/7)

Step-by-step explanation:

The line will be linear as you rearrange the function to be y=

You would do this by moving the 3x over to the right side by subtracting both sides by 3x, giving you 7y=-3x+8. From here, you get y by itself by dividing both sides by 7. Giving a final function of [tex]y=-\frac{3}{7} x+\frac{8}{7}[/tex]

Answer:

The new price is $100.

Step-by-step explanation:

20% of $125 = 0.2 × 125 = $25

New price = Regular price - Discount

New Price = $125 - $25 = $100