The perimeter of the rectangle below is 84 units. Find the length of side VW.
Write your answer without variables.

Answer:

[tex]x=\frac{3\left(1+\sqrt{3}\right)}{2},\:x=\frac{3\left(1-\sqrt{3}\right)}{2}[/tex]

Step-by-step explanation:

[tex]x_{1,\:2}=\frac{-\left(-6\right)\pm \sqrt{\left(-6\right)^2-4\cdot \:2\left(-9\right)}}{2\cdot \:2} < - InsertQuadraticFormula[/tex]
[tex]x_{1,\:2}=\frac{-\left(-6\right)\pm \:6\sqrt{3}}{2\cdot \:2}[/tex]
[tex]x_1=\frac{-\left(-6\right)+6\sqrt{3}}{2\cdot \:2},\:x_2=\frac{-\left(-6\right)-6\sqrt{3}}{2\cdot \:2} < - Separate THE Solutions[/tex]
[tex]x=\frac{3\left(1+\sqrt{3}\right)}{2},\:x=\frac{3\left(1-\sqrt{3}\right)}{2}[/tex]

Answer:

x = 7, y = 45

Step-by-step explanation:

[tex]7x+13=6x+20[/tex]

[tex]x=20-13\\x=7[/tex]

Angle

[tex]7(7)+13=49+13=62^{0}[/tex]

supplementary angle

180 - 62 = 118°

[tex]3y-17=118[/tex]

[tex]y=\frac{118+17}{3} =135/3=45[/tex]

Hope this helps

Answer:

x = 3.25

Step-by-step explanation:

Use the Rule of 3 to solve this

Work in picture

[tex]\sqrt{10^2 - 3^2}=\boxed{\sqrt{91} \text{ ft}}[/tex]

We get that the equation of the line PQ will be 2 x - 7 y + 17 = 0.

A) We know that the equation of the line is:

y - y₁ = m (x - x₁)

where m = y₂ - y₁ / x₂ - x₁

Now, we have:

P = ( x₁, y₁) = (2, 3)

Q = (x₂, y₂) = (9, 5)

We get m by substituting the values as:

m = 5 - 3 / 9 - 2 = 2 / 7

The equation then will be:

y - y₁ = 2 / 7 (x - x₁)

Substituting the values, we get that:

y - 3 = 2/7 ( x - 2)

7 y - 21 = 2 x - 4

2 x - 7 y - 4 + 21 = 0

2 x - 7 y + 17 = 0

B) When PQ will intersect x-axis, then the point will be = ( x, 0)

2 x - 7 y + 17 = 0

2 x - 7 (0) + 17 = 0

2 x = -17

x = - 17 / 2

Point = (-17 / 2 , 0)

Therefore, we get that the equation of the line PQ will be 2 x - 7 y + 17 = 0.

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Add -9 to both sides.

Solve Absolute Value.

No solutions. (Absolute value cannot be less than 0.)

Answer:

x^21/5

Step-by-step explanation:

To change this expression to an expression with a rational exponent, we need to change the radical to a rational (fractional) exponent. Just as square root is a one half power and cuberoot is a one-third power, a fifth root is a one-fifth power.

Once the radical is changed to a fraction, we will just use the exponent rule that says when you raise a power to a power, you multiply exponents.

see image.

Answer:

y=1 x=1

×[[×[+[[+[+[+[+[+[+[+[+[+[[

The approximate number of guests that were children are 172 and adults are 278

From the complete question, we have the following system of equations

25x + 12y = 9014

x + y = 450

Make y the subject in x + y = 450

y = 450 -x

Substitute y = 450 - x in 25x + 12y = 9014

25x + 12(450 - x) = 9014

Expand the expression

25x + 5400 - 12x = 9014

Evaluate the like terms

13x = 3614

Divide both sides by 12

x = 278

Substitute x = 278 in y = 450 -x

y = 450 - 278

Evaluate

y = 172

Hence, the approximate number of guests that were children are 172 and adults are 278

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Answer:

1st one is the right option

Step-by-step explanation:

the average change rate for a function g(x) is defined for an interval of x values as

(g(interval end) - g(interval begin))/(interval end - interval begin)

in our case that is

(g(2013) - g(2008))/(2013 - 2008) =

= (24 mil. - 186 mil)/5 = -162 mil./5 =

= -162,000,000 / 5 = -32,400,000

that means that as a mean value there were 32,400,000 digital cameras shipped less every year.

in other words, fewer and fewer digital cameras are sold. the demand is strongly declining.

actually, following the mean values and their trend, there should have been no new digital cameras shipped in 2014 anymore (as 24 mil. - 32.4 mil is less than 0).

The slope of Line 1 is m = -2

The slope of Line 2 is m = -2

For Line 1;

(x₁, y₁) = (1, 1);

(x₂, y₂) = (-2, 7);

m₁ = (7-1)/(-2-1) = -2;

For Line 2;

(x₃, y₃) = (-1, 4);

(x₄, y₄) = (1, 0);

m₂ = (4-0)/(-1-1) = -2;

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According to this the temperature in February = 4.5°F.

The absolute value (or modulus) of a real number x is its non-negative value regardless of its sign. For example, 5 has an absolute value of 5, and 5 has an absolute value of 5. A number's absolute value can be conceived of as its proximity from zero along the real number line.

The temperature on the same day in February has the same absolute vale as the temperature in the January, but is not the same temperature according to this the temperature in February = 4.5°F.

The absolute value is the same but not the same temperature:

|-4.5| = 4.5

So,

Its 4.5°F

According to this the temperature in February = 4.5°F.

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The sum of the ball's kinetic energy and potential energy remains the same. as the ball rolls from point A to E.( if there is no friction between the ball and the ground).

based on the law of mechanical energy's conservation, the sum of both kinetic and potential energies i.e. the total amount of mechanical energy remain conserved even in the absence of dissipative forces ( friction or air resistance) in a bound system.

the kinetic energy is when ball goes downward but potential energy decreases and reverse happens when ball goes up. but in these case, the sum energy would be constant one.

The ball would not change the energy.

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Answer:

21

Step-by-step explanation:

Just substitute -3 in for a and 2 in for b

[tex]a^2 + 6b\\-3^2 + 6(2)\\9 + 6(2)\\9 + 12\\21[/tex]

When you square a negative number, the answer is positive. Good luck, and have a great day!

Also, Jesus loves you!!!!

If points E,F,G are collinear, then,

EF+FG = EG

5x+10 = 10x

10 = 10x-5x

10 = 5x

5x = 10

x = 10/5

x = 2

So,

As a check, EF+FG = 10+10 = 20 = EG to help confirm the answer

Answer:

EF = 10

Step-by-step explanation:

EF = 5x

FG = 10

EG = 10x

Answer:y=mx+b

Step-by-step explanation:

Answer:

Let x be the amount invested in funds that earned 8%.

Then the amount invested in stock that suffered 3% loss is 18,000 - x.

The profit from investment in funds is 8%x

The loss from investment in stock is 3%(18,000 - x).

The net profit is 8%x - 3%(18,000 - x).

As the net profit given in the problem is $780, we have:

8%x - 3%(18,000 - x) = 780

Step-by-step explanation:

Answer:

b= p-(a+c)

Step-by-step explanation:

An equation that relates the number of bags, x, to the cost, y is y = 5x.

An equation is a mathematical statement that claims that the two sides are equal.

An equation involves two or more variables that require some mathematical operations to obtain their equivalent value.

Therefore, an equation contains numbers, variables, and operators, which show a value after the mathematical operations.

Let the number of bags for the class = x (number of students)

Let the unit cost of a bag = $5

Let y = the total cost

Equation, y = 5x

Thus, an equation that relates the number of bags, x, to the cost, y is y = 5x.

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Answer: 3.32  

Step-by-step explanation:

√11=

3.3166=

3.3166=3.32      ==>When rounding to the hundredth place, if the thousandth's digit is 5 or greater, increase the hundredth's digit by 1.

Answer:

[tex]V=lwh\\\frac{V}{lw} = \frac{lwh}{lw} \\\frac{V}{lw} = h[/tex]

Answer:

12.50m/s

in 2 seconds: 25

im not really good at math but i tried

Step-by-step explanation:

complementary means together they are 90°.

x = 3y - 6

x + y = 90

(3y - 6) + y = 90

4y - 6 = 90

4y = 96

y (the smaller angle) = 24°

x (the larger angle) = 3y - 6 = 3×24 - 6 = 72 - 6 = 66°

Answer:

[tex]-1t+31 +3 \geq -4[/tex]

[tex]-1t +34 \geq -4[/tex]

[tex]-1t \geq 30[/tex]

[tex]t \geq -30[/tex]

Answer:

C.) Equally as distant.

Answer: its c

Step-by-step explanation:

The difference between the payroll of football and baseball is 2.7752 × 10¹¹. Hence, option C is correct.

Equations are logical assertions in mathematics that have two algebraic expressions on either side of an equals (=) sign. The expression on the left and the expression on the right is shown to be equal in reference to one another. LHS = RHS (left hand side = right hand side) appears in all mathematical equations. You can solve equations to determine the value of an unknown variable that represents an unknown quantity.

The payroll of the baseball team is 2.48 × 10⁹ and,

The payroll of the football team is 2.8 × 10¹¹.

So, the football team's payroll is more than the baseball team's payroll by,

(2.8 × 10¹¹) - (2.48 × 10⁹)

= 2.7752 × 10¹¹.

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In linear equation , 2n/7 is Expression for the quotient .

What in mathematics is a linear equation?

Let the number = n

A quotient is the result of a division.

the quotient of twice a number = 2n

= 2n/7

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