Solve the system of linear equations by graphing. x−y=7, 0.5x+y=5

Answer:

Step-by-step explanation:

he used distributive property.

Answer:

Jack used distributive property

It ΔABC and ΔXYZ are similar, then the sides of the triangles are in proportion.

[tex]\dfrac{AB}{XY}=\dfrac{BC}{YZ}=\dfrac{AC}{XZ}[/tex]

We have BC = 8, AC = 7, Y = 28, XZ = 49 and YZ = 56. Substitute:

[tex]\dfrac{AB}{XY}=\dfrac{BC}{YZ}\to\dfrac{AB}{28}=\dfrac{8}{56}\qquad\text{cross multiply}\\\\56AB=(8)(28)\qquad\text{divide both sides by 56}\\\\AB=\dfrac{224}{56}\\\\\boxed{AB=4}[/tex]

To match the numbers to the letters for the equivalents, we can simplify each expression:

3(4x + 2) = 12x + 6 (A)

(2x + 3) - (4x + 5) = 2x + 3 - 4x - 5 = -2x - 2 (B)

8x + 5 - x + 4 = 8x - x + 5 + 4 = 7x + 9 (C)

7(3x - 2) = 21x - 14 (D)

Matching the numbers to the letters for the equivalents:

Expression 1 is equivalent to option A.

Expression 2 is equivalent to option B.

Expression 3 is equivalent to option C.

Expression 4 is equivalent to option D.

To map triangle RST to triangle DEF, perform a translation, rotation, and possibly a reflection.

To map triangle RST to triangle DEF using rigid motions, we need to use a combination of translations, rotations, and reflections.

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Answer:

1) Multiplying powers with the same base would be product rule. It where you just add the exponents. Dividing powers with the same base would be the quotient rule. Its where you subtract the exponents.

2)Where you multiply the two exponents together

3)The negative law is where for example, if it were in the numerator, then it would be placed at the denominator with a positive exponent whereas if it were in the denominator it would be on the numerator with the positive exponent. The zero law just states the anything to the power to zero is one.

Step-by-step explanation:

1) 3^3 x 3^4 = 3 ^3+4 = 3^7

3^9 ÷3² = 3^9-2 = 3^7

2) (3^2)^2 = 3^2×2 =3^4

3) 1/3^-5 = 3^5                 \

3^-7 =1/3^7

2^0 = 1

The exponent laws for multiplying and dividing powers with the same base involve adding or subtracting exponents, respectively. The power of a power law states you should multiply exponents. Negative and zero exponent laws indicate how to deal with powers that are negative or zero.

In mathematics, especially when dealing with exponents, there are specific laws that streamline the process of multiplication, division, and dealing with different powers. Below are the laws related to your questions:

Multiplying and Dividing Powers with the Same Base

For multiplication: When two powers with the same base are multiplied, you add the exponents. For example, a^m × a^n = a^(m+n).

For division: When two powers with the same base are divided, you subtract the exponents. For example, a^m ÷ a^n = a^(m-n), where a ≠ 0.

Power of a Power Law

When raising a power to another power, you multiply the exponents. This is known as the power of a power law. So, (a^m)^n = a^(m*n).

Negative and Zero Exponent Laws

A negative exponent indicates division by that base and the exponent turned positive, such as a⁻ⁿ = 1/aⁿ. For a zero exponent, any non-zero base raised to the power of zero equals one, signified as a⁰ = 1.

Answer: 16.5 gallons of water should be mixed to make a 20% solution of [tex]H_2SO_4[/tex]

Step-by-step explanation: We are given the concentration of the solution in percentage, it can be taken as the molarity of the solution.

Now, to calculate the volume of water required, we use the formula:

[tex]M_1V_1=M_2V_2[/tex]

where,

[tex]M_1\text{ and }V_1[/tex] are the initial molarity and volume of the solution.

[tex]M_2\text{ and }V_2[/tex] are the final molarity and volume of the solution.

Given:

[tex]M_1=55\%\\V_1=6gallons\\M_2=20\%\\V_2=?gallons[/tex]

Putting values in above equation, we get:

[tex]55\times 6=20\times V_2\\V_2=16.5gallons[/tex]

Answer:

10.5 gallons of water should be added.

Step-by-step explanation:

Let [tex]C_{1} * V_{1} = C_{2} * V_{2}[/tex], where [tex]C_{i}[/tex] are the concentration of the solution and [tex]V_{i}[/tex] are the volume of the solution for i=1,2.

Now, substituting values, we have,

55*6 = 20*[tex]V_{2}[/tex]

i.e. [tex]V_{2}[/tex] = (6*55)/20

i.e. [tex]V_{2}[/tex] = 16.5

So, the final volume is 16.5 gallons.

Hence, we need to add 16.5 - 6 = 10.5 gallons of water.

Answer:

Multiplication and Division in order from left to right

Step-by-step explanation:

PEMDAS

Parentheses

Exponents

Multiplication and Division in order from left to right

Addition and Subtraction in order from left to right

Final answer:

The operation that should be performed immediately after evaluating exponents using the order of operations is multiplication and division in order from left to right.

Explanation:

The operation that should be performed immediately after evaluating exponents using the order of operations is multiplication and division in order from left to right.

In the order of operations, exponents are evaluated first, followed by multiplication and division from left to right, and finally addition and subtraction from left to right. This means that after evaluating exponents, you should perform any multiplication or division operations in the expression if they exist.

For example, if you have the expression 2³ times 4 + 6, you would first evaluate 2³ = 8 and then perform the multiplication: 8 times 4 = 32. Finally, you would add the resulting 32 to 6 to get the final answer.

Answer:

.70p  

p(1-.30)

Step-by-step explanation:

Tony plans to purchase a jacket that costs p dollars. In a week the jacket will go on sale for 30% off.

Tony writes althea following expression

p - .30p

Here P  or 1P  are same

So expression becomes 1p - 0.30p

Both are like terms

so we can subtract it

1p - 0.30p = 0.70p

Also we can write 1p - 0.30p  as  p(1-0.30)

We can take out p that is in common

Equivalent expression is .70p  and p(1-.30)

Answer:

B

Step-by-step explanation:

Because Im MATHS SUPER MAN

Answer:

$82.55

Step-by-step explanation:

65 + (0.07×65) + (0.2×65)

Answer:

Given equation: [tex]Px+5 = -4x+ Q[/tex]

Add 4x on both sides we get;

Px + 5 + 4x = -4x + Qc+ 4x

Simplify:

Px +4x + 5 = Q

or

x(P+4) = Q - 5

Divide P+4 on both sides we get;

[tex]x = \frac{Q-5}{P+4}[/tex]

If we set Q-5 = 0 and P +4 = 0, there will be no solutions.

Since, No solution would mean that there is no answer to the equation.

⇒[tex]Q -5 = 0[/tex]

or

Q = 5

and

⇒[tex]P +4 = 0[/tex]

or

P= -4

Therefore, the values of P = -4 and Q = 5 results in an equation with no solutions.

Answer: P = -4 and Q = -5

Answer:

f(x) = 2/3x +4

Step-by-step explanation:

The initial value is another name for the y intercept, so b = 4

Rate of change is another name for slope so m = 2/3

We can use the equation y =mx+b

y = 2/3 x + 4

We want it in function form

f(x) = 2/3x +4

Answer:

$86.25

Step-by-step explanation:

You need to calculate 15% of $75, and then add it to $75.

To find a percent of a number, change the percent to a decimal and multiply by the number. To change a percent to a decimal, divide the percent by 100, which the same as moving the decimal point of the percent two places left.

For example, 15% = 15/100 = 0.15 (by dividing 15 by 100).

15% = 0.15 (by moving the decimal point of 15 two places to the left).

Now back to the problem. First, we find 15% of $75.

15% of $75 =

= 15% * $75

= 0.15 * $75

= $11.25

The tip of 15% of $75 was $11.25.

The total amount spent is the bill total, $75, plus the $11.25 tip.

Total spent = $75 + $11.25 = $86.25

Answer:

its probably 8.5

Step-by-step explanation:

Answer:

Option B.

Step-by-step explanation:

Trigonometric area formula is Area = [tex]\frac{1}{2}\times absin(C)[/tex]

Where a and b are two sides of the triangle and C is the angle between these two sides.

As given in the figure, side a = 6 units, c = 2√2 units and ∠B = 80°

Then area of the triangle will be defined by the formula

Area = [tex]\frac{1}{2}\times acsin(B)[/tex]

        = [tex]\frac{1}{2}\times acsin(B)[/tex]

        = [tex]\frac{1}{2}\times 6\times 2\sqrt{2}\times sin(80)[/tex]

        = 6√2×sin80°

        = 6×(1.414)×0.9848

        = 8.36 square units

        ≈ 8.4 square units

Option B is the answer.

Answer:39/4

Step-by-step explanation: What I'd do first is set the question up as an ordered pair, for example (x,y) have the uniforms be represented by x and the cost be represented by y. We know that the cost of five uniforms is $66, so we can substitute (x,y) into (5,66). We can then do the same for nine uniforms which is 105 (9,105). The equation we are going to use to find the slope is y2-y1/x2-x1 = 105-66/9-5.

This should result in 39/4. Make sure to always simplify when needed, in this case we don't have to.

Hope this helped.

Answer:

< 8 = 60

<1 and <5 are corresponding angles

Step-by-step explanation:

<2 = <3  vertical angles

<3 = <6  alternate interior angles

<6 + <8 = 180  supplementary angles

120 + <8 = 180

Subtract 120 from side

120-120 + <8 = 180-120

< 8 = 60

<1 and <5 are corresponding angles

Corresponding angles occupy the same relative position at each intersection.

Answer:

The measure of [tex]\angle 8[/tex] is 60°

[tex]\angle 1[/tex] and [tex]\angle 5[/tex] are corresponding angles.

Step-by-step explanation:

Given that, [tex]m\angle 2= 120\°[/tex]

In the given diagram, [tex]\angle 2[/tex] and [tex]\angle 6[/tex] are corresponding angles and their measures are same.

So, [tex]m\angle 6= 120\°[/tex]

Now, [tex]\angle 6[/tex] and [tex]\angle 8[/tex] are pair of linear angles.

That means......

[tex]m\angle 6+m\angle 8= 180[/tex]°

[tex]\Rightarrow 120\°+m\angle 8=180\°\\ \\ \Rightarrow m\angle 8= 180\°-120\°\\ \\ \Rightarrow m\angle 8=60\°[/tex]

So, the measure of [tex]\angle 8[/tex] is 60°

The type of angles for [tex]\angle 1[/tex] and [tex]\angle 5[/tex] is corresponding.

Answer:55

Step-by-step explanation: Whenever you see the word "sum" it means to add. So, 5+7+9+3+1+3+9+8+5+2+3=55

By adding each game's score in Samara's game sequence, we find that the total score of all 11 games is 55 points.

To find the total score of Samara's games, we need to add all the points she got from each game. We do this by performing the addition of the numbers in the number sentence she wrote down:

Thus, the total number of points for 11 games is 55.

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The original price before a 25% discount, when the sales price is $40, is calculated as $40 divided by 0.75, resulting in $53.33.

To find the original price before a 25% discount, we can set up the equation where original price minus 25% of the original price equals the sales price. Let's call the original price 'P'. Then 0.25P is the amount discounted. The equation is P - 0.25P = $40. This simplifies to 0.75P = $40. To find P, divide both sides by 0.75, giving us P = $40 / 0.75. So, the original price P = $53.33.

The original price is $53.33.

If you have the sales price and the percent of discount, you can calculate the original price using the following steps:

To find the original price, we set up the equation:

0.75P = 40

Next, solve for P by dividing both sides by 0.75:

P = 40 / 0.75

P = $53.33

So, the original price of the item was $53.33 before the 25% discount was applied.

Answer:

the integers are: 87, 89, and 91

Step-by-step explanation:

n+n+2+4=267

3n+6=267

3n=261

n=87.

can you please tell me where you got this question from

Final answer:

The three consecutive odd integers that sum up to 267 are 87, 89, and 91. By setting up an equation, we find the first integer and then determine the next two by adding 2 to each consecutive integer.

Explanation:

The sum of three consecutive odd integers is 267. To find these integers, let's first represent them algebraically. Assume the smallest integer is x. Then the second integer, being consecutive and odd, would be x + 2, and the third would be x + 4. The sum of these three integers is given by:

x + (x + 2) + (x + 4) = 267

Simplify this equation to find the value of x:

3x + 6 = 267

Subtract 6 from both sides:

3x = 261

Divide both sides by 3:

x = 87

Now that we have the smallest integer, the second and third integers are 87 + 2 = 89 and 89 + 2 = 91, respectively.

The three consecutive odd integers are 87, 89, and 91.

The effective annual yield for a certificate of deposit with a 6% annual interest rate compounded quarterly is approximately 6.14%.

To find the effective annual yield, we need to use the formula:

Effective Annual Yield = (1 + (interest rate / number of compounding periods))^number of compounding periods - 1

In this case, the interest rate is 6%, which is equivalent to 0.06. The number of compounding periods is 4 per year. Plugging these values into the formula, we get:

Effective Annual Yield = (1 + (0.06 / 4))^4 - 1

Calculating this, we find that the effective annual yield is approximately 6.14%.

Answer:

18 times

Step-by-step explanation:

6/10= .6

So 60% of 30 is 18

Answer:

3 and 6 as well as 4 and 5

Step-by-step explanation:

interior angles are the ones between perpendicular lines. I do belive you choose the ones oposite from one another. JUst look for the definiotn of angles on google and you'll find plenty of helpful awnsers to solving you equasions.

[tex]\underline{+\left\{\begin{array}{ccc}4x+5y=16\\-4x-10y=4\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad\qquad-5y=20\qquad\text{divide both sides by (-5)}\\.\qquad\qquad\boxed{y=-4}\\\\\text{Put the value of y to the first equation:}\\\\4x+5(-4)=16\\4x-20=16\qquad\text{add 20 to both sides}\\4x=36\qquad\text{divide both sides by 4}\\\boxed{x=9}\\\\Answer:\ \boxed{x=9\ and\ y=-4\to(9,\ -4)}[/tex]

ANSWER:

y = -2/3x + 2

ABOUT SLOPE INTERCEPT FORM:

You have to isolate or get y by itself:

2x + 3y = 6

-2x           -2x

3y = -2x + 6

3             3

y = -2/3x + 2 --- IN SLOPE INTERCEPT FORM

Hope this helps you!!! :)

Answer:

y=-2/3x +2

Step-by-step explanation:

y=mx+b

2x+3y-6

3y-6=-2x

3y=-2x+6

y=-2/3x+2

x, y - the numbers

x + y = 19

x - y = 3        add both sides of the equations

2x = 22      divide both sides by 2

x = 11

Substitute the value of x to the first equation:

11 + y = 19     subtract 11 from both sides

y = 8

The sum of the two numbers is 19 and their difference is 3. The two numbers are 11 and 8.

Let's use a system of equations to solve this problem.

Let's say the first number is x and the second number is y.

According to the given information, we have the following equations:

x + y = 19  (equation 1)

x - y = 3  (equation 2)

We can solve these equations simultaneously by either substitution or elimination method.

Let's use the elimination method.

Adding equation 1 and equation 2, we get:

(x + y) + (x - y) = 19 + 3

2x = 22

x = 11

Substituting the value of x in equation 1, we get:

11 + y = 19

y = 8

Therefore, the two numbers are 11 and 8.

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Answer:

a.  4y =12x  the constant of variation is 3

Step-by-step explanation:

The equation for direct variation is y=kx

a.  4y =12x

 Divide each side by 4

4y/4 = 12x/4

 y = 3x

This is direct variation and the constant is 3

Equations b ,c, d  all have a constant added which make them something other than a direct variation

Answer:

A Constant of variation is 3

Step-by-step explanation:

Remark

Direct variations have an equation that looks like y = kx There is NO y intercept, or the y intercept = 0. If you solve for the slope of choices B C and D you get a y intercept that is not 0. For example Take C

Solution

Your only possible answer is A

The constant of variation =

Answer: 1584.1875

Step by Step Explanation:

Step 1. Multiply the fraction

71 x 89.25/4

Step 2. Multiply the numbers 71 x 89.25.

= 6336.75/4

Step 3. Divide the number 6336.75/4.

= 1584.1875

Hope I could help! :)