What is the result of subtracting the second equation from the first?

-4x - 2y = -2

x - 2y = 9

Answer:

A. III only

Step-by-step explanation:

In mathematics, an identity is one of the characteristics of algebraic expressions.

Given variable a and b in an algebraic expression, an identity is defined as an equality that remains the same no matter the values that we choose for either variable a or b.

Identity in mathematics makes it very easy to solve algebraic expressions. The two sides of an identity in an algebra can easily be exchanged for each other.

In the above question, we are given 3 Options.

I) 3(5 + 2x) = 15 + 6x

II) y = x + 3

III) (x² - y²) = (x + y) (x - y)

Option I) 3(5 + 2x) = 15 + 6x

Is showing distributive property in mathematics.

Distributive property is :

a(b + c) = ab + ac

Option I is not an identity , therefore it is wrong.

Option II) y = x + 3 is just an algebraic expression.

Only Option III is an identity. This is because it follows the rule of

(a² - b²) = (a + b) (a - b)

We can prove and confirm this be solving the algebraic expression

(x + y) (x - y)

We expand the bracket

x² - xy +xy - y²

x² - y²

Therefore, option A is the correct option.

Answer:

5/2

Step-by-step explanation:

We take the ratio of a side of ABC over the same side on DEF

AB/ DE

35/14

Divide top and bottom by 7

5/2

Answer:

D

Step-by-step explanation:

3n - 5p + 2n = 10p

Add like terms.

5n - 5p = 10p

Add 5p to both sides.

5n = 10p + 5p

5n = 15p

Divide both sides by 5.

n = 15/5p

n = 3p

The solution of expression for n is,

⇒ n = 3p

We have to given that,

An expression to solve,

⇒ 3n - 5p + 2n = 10p

Now, We can solve the expression for n as,

⇒ 3n - 5p + 2n = 10p

Combine like terms,

⇒ 3n + 2n = 10p + 5p

⇒ 5n = 15p

Divide by 5 both side,

⇒ n = 15p/5

⇒ n = 3p

Therefore, The correct option is,

D. n = 3p

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Answer:

y = (-1/2)x - 3

Step-by-step explanation:

The line y = 2x - 6 has a slope of 2 and so any line perpendicular to it has a slope which is the negative reciprocal of 2:  -1/2.

If this perpendicular line passes through (0, -3), then the slope-intercept equation y = mx + b becomes -3 = (-1/2)(0) + b, or -3 = b, and the desired

equation is

y = (-1/2)x - 3

Answer:

8.29166

Step-by-step explanation:

3.5_0.375+5.166666

Answer:

[tex]8 \frac{7}{24} [/tex]

Step-by-step explanation:

Please see attached picture for full solution.

Answer:

[tex]\dfrac{1}{3}[/tex].

Step-by-step explanation:

In quadrilateral QRST, Q(-1,0), R(5,0), S(3.5,-6), T(-2.5,-6).

In quadrilateral Q'R'S'T', Q'(-1,2), R'(1,2), S'(0.5,0), T'(-1.5,0).

Distance formula:

[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Using distance formula , we get

[tex]QR=\sqrt{(5-(-1))^2+(0-0)^2}=\sqrt{6^2}=6[/tex]

[tex]Q'R'=\sqrt{(1-(-1))^2+(2-2)^2}=\sqrt{2^2}=2[/tex]

Now,  

[tex]\text{Scale factor}=\dfrac{Q'R'}{QR}[/tex]

[tex]\text{Scale factor}=\dfrac{2}{6}[/tex]

[tex]\text{Scale factor}=\dfrac{1}{3}[/tex]

Therefore the scale factor is [tex]\dfrac{1}{3}[/tex].

The given transformation of quadrilateral QRST to quadrilateral Q'R'S'T'

are a dilation and a translation, therefore,  QRST is similar to Q'R'S'T'.

[tex]\mathrm{The \ scale \ factor \ of \ the \ dilation\ between \ QRST \ and \ Q'R'S'T' \ is} \ \dfrac{1}{3}[/tex]

Reasons:

The vertices of the quadrilateral are;

Quadrilateral QRST

Q(-1, 0)

R(5, 0)

S(3.5, -6)

T(-1, 2)

Quadrilateral Q'R'S'T'

Q'(-1, 2)

R'(1, 2)

S'(0.5, 0)

T'(-1.5, 0)

The given transformation that gives quadrilateral Q'R'S'T' from quadrilateral  QRST are a dilation and a translation.

Required:

The scale factor of the dilation

Solution:

[tex]\mathrm{The \ scale \ factor \ of \ the \ dilation} = \dfrac{\mathrm{Length \ of \ \overline{Q'R'} }}{\mathrm{Length \ of \ \overline{QR}} }[/tex]

Length of [tex]\overline{Q'R'}} }[/tex] = 1 - (-1) = 2

Length of [tex]\overline{QR}} }[/tex] = 5 - (-1) = 6

Therefore;

[tex]\mathrm{The \ scale \ factor \ of \ the \ dilation} = \dfrac{2}{6} = \dfrac{1}{3}[/tex]

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Answer:

Let humans be x and horses be y

Both have one head each,so x+y=74 (1)

Humans have 2 legs each and horses 4 legs each…… so 2x+4y=196 (2)

In first equation x+y=74 then y=74~x (3) ……… .By solving both equations we have as under… x+3y=122 x=122-3y (4)…. Now in equation 4 we put the value of y taken from equation 3 so it will be x=122~3(74-x)…. x=122-222+3x…………. bringing x on one side x-3x=122~222 therefore -2x=~100….. x=50… put the value of x in first equation… x+y=74… 50+y=74… y=74~50…..… y=24… Now it is concluded that Humans are 50 and Horses are 24.. Now you put the values of x & y in 1st and 2nd equation … you will get x+y=74.. 50+24=74………..2x+4y=196…2×50+4×24=196.. it is proved thru equation.

Answer:

-1/10115

Step-by-step explanation:

Let x be the rational number.

-7/85 × x = 1/17

x = 1/17 ÷ -7/85

x = 1/(17 × -7 × 85)

x = 1/(-10115)

x = -1/10115

The rational number is -1/10115.

Answer:

- 5/7

Step-by-step explanation:

-7/85*x= 1/17

x= 1/17 ÷ (-7/85)

x= - 1/17 × 85/7

x= - 5/7

Answer:

w-2

Step-by-step explanation:

To file your return, you'll need the following on hand: Your W-2: This form will come from your company and list not only your salary for the year but the amount of taxes withheld along the way. You're required to file your W-2 along with your taxes, so if you're a salaried employee, this form is non-negotiable.

The document you need to have on hand when preparing to file your tax return is Form W-2. The correct option is D.

A tax return is a document filed with the tax authorities by individuals or businesses to report their income, expenses, and other relevant financial information in order to calculate their tax liability or refund.

It is usually filed once a year, and the information on it is used to determine whether the taxpayer owes additional taxes or is eligible for a refund.

Form W-2 is a form that an employer provides to an employee at the end of the year that shows the employee's total earnings as well as the amount of taxes withheld from those earnings.

It is a necessary document for accurately preparing and filing an individual's tax return.

Thus, the correct option is D.

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Answer:

A. 120

Step-by-step explanation:

To find the measure of x, you would need to subtract the major arc minus the minor arc. A circle is 360 degrees so, 360-60=300. That is the major arc. Now, we use the formula, x=1/2(major-minor). When we plug the information in, we get 1/2(300-60)...1/2(240)...x=120.

Hence,

the correct option would be 120.

Hope this helps!!! PLZ MARK BRAINLIEST!!!

Answer:

Choices are not provided, but you can answer the question as follows: take the coordinates of quadrilateral WXYZ and apply:

W(xW, yW) -> W'(-xW, yW-2)

X(xX, yX) -> X'(-xX, yX-2)

Y(xY, yY) -> Y'(-xY, yY-2)

Z(xZ, yZ) -> Z'(-xZ, yZ-2)

For example, if point W is located at (1, 1), W' would be located at (-1, -1)

Step-by-step explanation:

Reflection over the y-axis transforms point (x, y) into (-x, y)

Translation down 2 units transforms point (x, y) into (x, y-2)

Answer:

The first choice hope this helps :)

Step-by-step explanation:

Answer:

V =1620 pi  cm^2

Step-by-step explanation:

The volume of a cylinder is given by

V = pi r^2 h

V = pi ( 9)^2 * 20

V =1620 pi  cm^2

Answer:

AC=2.06cm

Step-by-step explanation:

AC^2=AD^2+CD^2

AC^2=1.5^2+1.4142^2

AC^2=2.25+2=4.25

....

[tex] \sqrt{ac {}^{2} } [/tex]

=

[tex] \sqrt{4.25 = } 2.06[/tex]

Answer:

AC=2.06 cm

Step-by-step explanation:

Answer:

The correct option is;

Choosing 4 neighborhoods at random and poll every home in those neighborhoods

Step-by-step explanation:

Given that the survey relate to how much money people are willing to spend on on concert tickets with the goal of being practical and unbiased, we have;

Required sampling = Random Sampling

The preferable type of random sampling is either;

1) Simple random sampling

Sampling a given percentage of the homes in the area randomly

2) Clustered random sampling

Completely polling entire population of randomly selected area

Given the practicability of sampling concert goers, since people may have different interests, a better representative sample will be to perform the clustered random sampling approach by choosing 4 neighborhoods at random and poll every home in those neighborhoods.

Answer:

Step-by-step explanation:

RHS means on the right hand side

And LHS means on the left hand side

So if x is one the right side of the expression ,it is on the RHS and if it is on the left side of the expression , it is on the LHS

Answer: C. (1, 4)

Step-by-step explanation:

The point where the two lines meet or intersect is the solution to the system of equations graphed. And in this case, the lines intersect at (1, 4).

Answer:

Kobe raised x + 24.55

Amari raised x

DJ raised 2x – 15.60

Answer:

m∠A = 2x = 2*20 = 40

m∠B = 3x = 3*20 = 60

m∠C= 4x = = 4*20 = 80

Step-by-step explanation:

we know sum of angles of triangle is 180 degrees

given

m∠A : m∠B : m∠C = 2:3:4

let the angle be

m∠A = 2x

m∠B = 3x

m∠C= 4x

we have taken such angle by applying rule of indices where

a:b:c = ax:bx:cx

which means that if we multiply all term of ratio by same number ratio remains same

thus,

2x+3x+4x = 180

9x = 180

x = 180/9 = 20

Thus,

m∠A = 2x = 2*20 = 40

m∠B = 3x = 3*20 = 60

m∠C= 4x = = 4*20 = 80

Answer:

x = 6

Step-by-step explanation:

3x - 2 = 16

3x = 16 + 2

3x = 18

x = 18/3

x = 6

Answer:

x=6

Step-by-step explanation:

3x-2=16

+2      +2

3x = 18

÷3    ÷3

x=6

Answer:

00 to 99 are 100 numbers.

If you match the first number only, you win $200. The Probability for this is 1/100.

If you match the first two numbers and not the third, you win $5000. The Probability for this is 1/50.

If you match all three numbers, you win $100,000. The Probability for this is 3/100.

And, If you are a customer, You will think is fair for you.

But if you are the lottery tickets company, you will think is not fair for you.

It depends who you are. 

the game isn't fair because 100,000/3=3333 1/3, so each number should be worth $3333.3333...... dollars but you can't really give 1/3 dollars so the game is impossible to be fair. Also, if you match the first two numbers you apparently get $5000. That's also not fair because each number is worth $50 dollars more than if you get the first number matched. So, the game isn't fair but it will be pretty much impossible to be fair.

Answer:

Yes the Quadrilateral is a Parallelogram.

Step-by-step explanation:

A parallelogram can be defined as a quadrilateral i.e a geometric shape with four sides that has opposite sides parallel and equal in length.

From the question, we are given the following points

P(2, 2), Q(1, -3), R(-4, 2), S(-3, 7)

Given points: (x1, y1) and (x2, y2)

The formula would be

√(x2 - x1)² +(y2 - y1)²

a) P(2, 2), Q(1, -3)

Length PQ = √(1 - 2)² +(-3 - 2)² = √-1² + -5² = √26

b) R(-4, 2), S(-3, 7)

Length RS = √(-3 - (-4))² + (7 - 2) ² = √ 1² + 5² = √26

c) R(-4, 2), Q(1, -3)

Length RQ = √(1 - (-4))² + (-3 - 2)² = √5² + 5² = √(25 + 25) = √50

d) S(-3, 7), P(2, 2)

Length SP = √(2 - (-3))² + (2 - 7)² = √5² +(-5)² = √(25 + 25) = √50

From the above solution, we can see that

Length PQ = Length RS

Length RQ = Length SP

This means the opposite sides are parallel and equal in length, hence it is a Parallelogram.

Answer:

Water a tank can hold = 14 1/2 = 29/2

Volume of bucket 1 1/4 = 5/4

The expresson can be

29/2 / 5/4

No. of buckets used = 29/2 x 4/5

Answer:

b and e

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let the angles be 2x , 6x , 9x , 13x

We know that the sum of quadrilateral is 360°

Now,

[tex]2x + 6x + 9x + 13x = 360[/tex]

Calculate the sum

[tex]30x = 360[/tex]

Divide both sides of the equation by 30

[tex] \frac{30x}{30} = \frac{360}{30} [/tex]

Calculate

[tex]x = 12[/tex]

Replacing the value,

2x = 2 * 12 = 24°

6x = 6 * 12 = 72°

9x = 9 * 12 = 108°

13x = 13 * 12 = 156°

So, the angles are 24° , 72° , 108° , 156°

Hope this helps...

Good luck on your assignment...

Answer:

Below in bold.

Step-by-step explanation:

2+6+9+13 = 30.

Now there are 360 degrees in a a quadrilateral.

So the value of the shortest angle = 2/30 * 360

= 1/15 * 360

= 24 degrees.

In the same way the value of the other 3 angles is:

6/30 * 360,  9/30 * 360 and 13/30 * 360

= 72, 108 and 156 degrees.

Answer:

1a) 15, 7, x+5

1b) 7

2a) 18, 3r

Step-by-step explanation:

1a) Since Claire is 5 years older, she will always be her cousin's age plus 5

1b) Claire is 5 years older, so Claire's cousin is 5 years younger. So, Claire's cousin is Claire's age minus 5

2a) Diego will have the amount of Han's books times 3

Answer:

Clare Questions:

Cousin: 10, Clare: 15

Cousin: 2, Clare: 7

Cousin: x, Clare: x + 5

Cousin: 7, Clare: 12

Diego Questions:

Han: 6, Diego: 18

Han: can't tell if it is a 0 or n, Diego: 0 or 3n, respectively

Step-by-step explanation:

Since Clare is older than her cousin by 5, they will both age at the same rate, thus she will always be 5 years older.

example: if her cousin is 10, Clare will be 10 + 5 years older, therefore being 15.

Since DIego has 3 times as many books than Hans, it multiplies by 3.

example: if Han has 6 books, multiply 6 by 3 and you get Diegos amount, 18.

Answer:

C

Step-by-step explanation:

A. (4, 0) and (4, 3) have the same x coordinate (Can't happen in a function).

B. (2, 5) and (2, 1) have the same x coordinate.

C. It passes the vertical line test on a graph and no x is repeated.

D. (2, 3) and (2, 5) share the same x coordinate.

Answer:

c is correct answer.

a function from set A (x coordinate) to set B (y coordinate) a special type of relation defined from set A to set B if every element of set A is mapped with unique element of set B.

Answer:

[tex]B. f(x) = 5(27)^x[/tex]

Step-by-step explanation:

Well lets graph it first,

Look at the image below ↓

By looking at the image we can tell that answer choice [tex]B. f(x) = 5(27)^x[/tex].

Thus,

answer choice B is correct.

Hope this helps :)

Answer:

The correct result would be f(x) = 5(27)x.

Step-by-step explanation:

If you would like to find an equivalent function to f(x) = 5(3)^(3x), you can do this using the following steps:

f(x) = 5(3)^(3x) = 5(3^(3x)) = 5(27)^x = 5(27)x

hope this helped :)

Answer:

[tex]f(-1) = 3[/tex]

[tex]f(2) = 6[/tex]

[tex]f(12) = 41[/tex]

Step-by-step explanation:

Given

The piece wise function can be split to:-

[tex]f(x) = -2x[/tex]   [tex]x\leq -10[/tex]

[tex]f(x) = x + 4[/tex]   [tex]-10<x\leq 2[/tex]

[tex]f(x) = 4x - 7[/tex]   [tex]x> 2[/tex]

Required

f(-1), f(2) and f(12)

To solve for each of these functions, we first check the range they fall into, then we execute the corresponding function

-1 is within the range of [tex]-10<x\leq 2[/tex]

Hence; we make use of [tex]f(x) = x + 4[/tex]  

Substitute -1 for x

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

[tex]f(-1) = 3[/tex]

2 is within the range of [tex]-10<x\leq 2[/tex]

Hence; we make use of [tex]f(x) = x + 4[/tex]  

Substitute 2 for x

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

[tex]f(2) = 6[/tex]

12 is within the range of [tex]x> 2[/tex]

Hence; we make use of [tex]f(x) = 4x - 7[/tex]  

Substitute 12 for x

[tex]f(12) = 4(12) - 7[/tex]  

[tex]f(12) = 48 - 7[/tex]

[tex]f(12) = 41[/tex]

Answer:

5

Step-by-step explanation:

p(2) - q(2)

3 - (-2)

3 + 2

= 5