Find the distance across the lake. Assume the triangles are similar

Answer:

When x=0 to 400, y=30. This makes ths domain for this inequality 0 to 400 and the range is just 30. When x>400, y=.097x. This makes the domain from 400 to infinity and the range .097(401) to infinity.

Step-by-step explanation:

The price is set between 0 and 400 kWh at $30 dollars flat. The price, however, for any usage of electric greater than 400 kWh is $.097 for every kWh used, making it multiply by the kWh.

The domain (electricity usage) is 0 to infinity kilowatt-hours (0 ≤ kWh < ∞), and the range (cost) has two parts: a fixed cost of $30 (for 0-399 kWh) and a variable cost that starts at $38.80 and can increase infinitely ($30 < Cost < ∞) for usage of 400 kWh or more.

To identify the domain and range of the cost of electricity based on Victoria's usage, let's consider two situations described:

Domain (Electricity Usage in kWh): This refers to the amount of electricity used. Victoria's electricity usage is between 0 kWh and any upper limit (which isn't specified but is typically determined by practical or contractual limits). So, we can express the domain in inequalities as 0 ≤ kWh < ∞ (where ∞ represents infinity).

Range (Cost in $): For the first situation, since the cost is set no matter the usage between 0 and 400 kWh, the range is a single value of $30. In the second situation, the cost starts at $0.097 per kWh for 400 kWh, which is $38.80, and increases as more electricity is used. Thus, the range for the second part is $30 < Cost < ∞.

The domain is specified in kilowatt-hours and is not capped, indicating it's a continuous set of values over a range from 0 to infinity. The range for the cost has two distinct parts: a fixed cost for usage under 400 kWh, and a variable cost that starts at a minimum value and increases potentially without bound for usage above 400 kWh.

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Answer:

[tex]28w^2-476w[/tex]

Step-by-step explanation:

The general rule we are going to use to multiply this out is the distributive property. Which is:

a(b+c) = ab + ac

Note: x * x = x^2

Now multiplying, we get:

[tex]28w(w-17)\\=28w*w-28w*17\\=28w^2-476w[/tex]

This is the multiplied out form, answer.

Answer:

A line with slope 2 and y-intercept 5.

Step-by-step explanation:

y=mx+b is the slope-intercept form of a line with slope,m, and y-intercept ,b.

y=2x+5 is in this exact form.

This means y=2x+5 is a line with slope 2 and y-intercept 5.

You can graph this by first plotting the y-intercept (0,5).

You can then use the slope to find another point.  Keep in my the slope=rise/run so you might want to write it as a fraction.

The slope=2/1, this means you will rise 2 units and go right 1 unit.

So if you start at (0,5) then you can find another point by going to (0+1,5+2)=(1,7).

So if you graph (0,5) and (1,7) and then connect them with a straight-edge you have graphed y=2x+5.

Answer:

the answer is 10^2

thanks. hope full it help you

Answer:

10^2

your welcome :>

Answer:

Step-by-step explanation:

[tex]\text{The domain:}\\\\(x+3)(x-5)\neq0\iff x+3\neq0\ \wedge\ x-5\neq0\\\\x\neq-3\ \wedge\ x\neq5\\\\========================\\\\f(x)=\dfrac{x(x-2)}{(x+3)(x-5)}\\\\\text{The zeros are for}\ f(x)=0\\\\\dfrac{x(x-2)}{(x+3)(x-5)}=0\iff x(x-2)=0\iff x=0\ \vee\ x-2=0\\\\x=0\in D\ \vee\ x=2\in D[/tex]

Answer:

5(x + 4)(x - 2)

Step-by-step explanation:

Start by factoring 5 out of all three terms.  We then have

5(x^2 + 2x - 8), or

5(x^2 + 2x - 8), which is in proper quadratic form.

Note that (4)(-2) = 8 and that 4 - 2 = 2, which match the 3rd and 2nd coefficients of x^2 + 2x - 8.

Thus, in completely factored form, we have 5(x + 4)(x - 2)

Answer:

5 (x -2) (x +4)

Step-by-step explanation:

5x^2 + 10x - 40

Factor out a 5

5(x^2 +2x-8)

We can then factor inside the parentheses

What two numbers multiply to -8 and add to 2

-2*4 = -8

-2+4 = 8

5 (x -2) (x +4)

Answer:

B(-7,-3)

Step-by-step explanation:

When you reflect across the x axis, your y coordinate is multiplied by -1.

(-7,-1(3))

(-7,-3)

The only answer choice that is the same as my result is B.(-7,-3).

Answer:

The first one. 4 times square root of 3.

Step-by-step explanation:

The side of the equilateral triangle that represents the height of the triangle will have a length of because it will be opposite the 60o angle. To calculate the area of the triangle, multiply the base (one side of the equilateral triangle) and the height (the perpendicular bisector) and divide by two.

Answer:

Remember:

Triangle area= [tex]\frac{b*h}{2}[/tex]

h of equilateral triangle = [tex]\frac{\sqrt{3}}{2}*a[/tex]

Step-by-step explanation:

b=4yd

a=4yd

h = [tex]\frac{\sqrt{3}}{2}*a[/tex]

h = [tex]\frac{\sqrt{3}}{2}*4yd[/tex]

4/2=2

h= [tex]2\sqrt{3} yd[/tex]

area= [tex]\frac{b*h}{2}[/tex]

area= [tex]\frac{4 yd*2\sqrt{3} yd}{2}[/tex]

2/2=1

Finally

area= [tex]4\sqrt{3} yd^2[/tex]

Answer:

200

Step-by-step explanation:

12% is the same thing of .12

x = the number you are trying to find

.12(x) = 24     ----- This means that 12% of x is 24.

x = 24/.12

x = 200

To solve this you must use a proportion like so...

[tex]\frac{part}{whole} = \frac{part}{whole}[/tex]

12 is a percent and percent's are always taken out of the 100. This means that one proportion will have 12 as the part and 100 as the whole

We want to know out of what number is 24 12% of. This means 24 is the part and the unknown (let's make this x) is the whole.

Here is your proportion:

[tex]\frac{24}{x} =\frac{12}{100}[/tex]

Now you must cross multiply

24*100 = 12*x

2400 = 12x

To isolate x divide 12 to both sides

2400/12 = 12x/12

200 = x

This means that 12% of 200 is 24

Hope this helped!

~Just a girl in love with Shawn Mendes

Step-by-step explanation:

The political equality of all citizens is an essential principle of democracy. In ademocracy, the just powers of government are based upon the consent of the governed.

D) leaders Must be selected by the citizens rather than inheriting power. (Apex)

Answer:

218,900

Step-by-step explanation:

110,000 x 11%= 12,100

12,100 x 9 = 108,900

110,000+108,900= 218,900

The future value of a present investment of $110,000 at an annual interest rate of 11% compounded for 9 years is approximately $278,984.57.

The question is asking for the future value of a present investment of $110,000 at an annual interest rate of 11% compounded for 9 years. For such a calculation, we can use the formula for compound interest:

FV = PV * (1 + r)^n

Where,

Plugging in the values, we get:

FV = $110,000 * (1 + 0.11)^9

After calculating the above expression, we find that the investment will grow to be approximately $278,984.57 after 9 years.

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[tex]\bf ~\hspace{7em}\textit{rational exponents} \\\\ a^{\frac{ n}{ m}} \implies \sqrt[ m]{a^ n} ~\hspace{10em} a^{-\frac{ n}{ m}} \implies \cfrac{1}{a^{\frac{ n}{ m}}} \implies \cfrac{1}{\sqrt[ m]{a^ n}} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \left( \sqrt{3} \right)\left( \sqrt[5]{3} \right)\implies \left( \sqrt[2]{3^1} \right)\left( \sqrt[5]{3^1} \right)\implies 3^{\frac{1}{2}}\cdot 3^{\frac{1}{5}}\implies 3^{\frac{1}{2}+\frac{1}{5}}\implies 3^{\frac{5+2}{10}}\implies 3^{\frac{7}{10}}[/tex]

for this case we have the following equation:

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

To resolve:

We add x to both sides of the equation:

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

[tex]3x + 5 = 1[/tex]

We subtract 5 on both sides of the equation:

[tex]3x + 5-5 = 1-5\\3x = -4[/tex]

We divide between 3 on both sides of the equation:

[tex]x = - \frac {4} {3}[/tex]

Answer:

We add x to both sides of the equation

Answer:

The correct option is C) add one positive x-tile to both sides.

Step-by-step explanation:

Consider the provided equation.

2x + 5 = -x + 1

Now to solve the above equation first isolate the variables.

To isolate the variables add x to the both the side of the equation.

2x + 5 + x = -x + 1 + x

Now add the like terms.

3x + 5 =  1

Here we add the x tiles to the both the side of the equation.

Now consider the options.

The correct option is C) add one positive x-tile to both sides.

If A and B are mutually exclusive events with P(A) = 0.3 and P(B) = 0.5, then P(A and B) = 0.

If A and B are mutually exclusive events with P(A) = 0.3 and P(B) = 0.5, then P(A and B) = 0.

Mutually exclusive events are events that cannot occur at the same time. This means that if event A happens, event B cannot happen, and vice versa. Therefore, the probability of both A and B occurring together is zero.

Answer:

We need to find the lowest common divisor which is the smallest possible number that is dividable by ALL numbers.

We have the following numbers:

[tex]\frac{25}{3}[/tex]

[tex]\frac{60}{3}[/tex]

[tex]\frac{25}{5}[/tex]

[tex]\frac{60}{5}[/tex]

For the denominators (3, 3, 5, 5) the least common multiple (LCM) is 15.

LCM(3, 3, 5, 5) . Therefore, the least common denominator (LCD) is 15.

Rewriting the original inputs as equivalent fractions with the LCD:

125/15, 300/15, 75/15, 180/15

Answer:

Step-by-step explanation:

[tex]-3x^2-4x-4=0\qquad\text{change the signs}\\\\3x^2+4x+4=0\\\\\text{use the quadratic formula:}\\\\\text{for}\ ax^2+bx+c=0\\\\\text{if}\ b^2-4ac<0,\ \text{then an equation has no solution}\\\\\text{if}\ b^2-4ac=0,\ \text{then an equation has one solution}\ x=\dfrac{-b}{2a}\\\\\text{if}\ b^2-4ac>0,\ \text{then an equation has two solutions:}\ x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

[tex]\text{We have}\ a=3,\ b=4,\ c=4.\\\\\text{Substitute:}\\\\b^2-4ac=4^2-4(3)(4)=16-48=-32<0\\\\\bold{no\ real\ solution}[/tex]

Answer:

discriminant is zero (0)

Step-by-step explanation:

Actually, you have a double root here:  {6, 6}:  "two real, equal roots."  That tells us immediately that the value of the discriminant was zero (0).

Answer:

The discriminant of the equation is zero.

Step-by-step explanation:

The given graph is a quadratic equation. If x = 6 is the only x-intercept of the graph, then the roots must be equal.

The quadratic equation will have two solutions. Here the two solutions are equal x = 6.

If the roots are equal, then the discriminant is zero.

The factors of the quadratic equation (x - 6) (x - 6)

= [tex]x^2 - 6x - 6x + 36[/tex]

= [tex]x^2 -12x + 36[/tex]

Discriminant = [tex]b^2 - 4ac[/tex]

Here a = 1, b = -12 and c = 36

Discriminant = [tex](-12)^{2} - 4.1.36[/tex]

= 144 - 144

= 0

Therefore, the answer is "The discriminant of the equation is zero."

Step-by-step explanation:

[tex]5x-3y=11\\\\x-intercept\ is\ for\ y=0\\\\5x-3(0)=11\\5x-0=11\\5x=11\qquad\text{divide both sides by 5}\\x=\dfrac{11}{5}\\\\y-intercept\ is\ for\ x=0\\\\5(0)-3y=11\\0-3y=11\\-3y=11\qquad\text{divide both sides by (-3)}\\y=-\dfrac{11}{3}[/tex]

Answer:

The area of the prism: 404 square feet.

Step-by-step explanation:

The idea in this exercise is to find the areas of all the geometric figures, and then add them all.

Notice that we have four consecutive rectangles, two smaller with dimension 6 ft by 8 ft and two larger with dimension 11 ft by 8 ft. Then, combined area of this four rectangles is

A_1 = 6*8 + 6*8 + 11*8+11*8 = 48+48+88+88 = 272.

For the other two rectangles, notice that their bases has the same length (11 ft). Their height can obtained using the characteristics of the prism. In this case must be 6 ft, the same length of the base of the previous smaller rectangles. The, the combined area of this rectangle is

A_2 = 6*11 +6*11 = 66 + 66 = 132.

Finally, adding those two area we get the area of the prism: 404 square feet.

Answer:

2.777777 and -7/3

Step-by-step explanation:

2.7182818459 cannot be written in fraction form therefore it is irrational.

2.777777 is rational because it can be written as the fraction 25/9

The square root of 3 is 1.7320508075688772, this number cannot be written as a fraction so it is irrational.

-7/3 is rational because it is already in fraction form.

Answer:

2.777777 and -7/3

Step-by-step explanation:

If a number can be defined in the form of p/q where q≠0, then it is called rational number.

If a decimal number is repeating then it is a rational number because it can be written in the form of p/q.

For example: 1.222, 3/5, 2.5, -1/2, 4.0707007...

All real numbers which are not rational numbers are called irrational numbers.

For example: 0.2357835.., √2, π.

In the given numbers,

Rational numbers = 2.777777,  -7/3

Irrational numbers = 2.7182818459 and √3

Therefore the two rational numbers are 2.777777 and -7/3.

Answer:

They need to sell 9400 pies to reach the break-order point

Step-by-step explanation:

* Lets explain the break-order point

- The break-order point is the point at which total cost and total

  revenue are equal

∴ The total cost = The total revenue

* Lets solve the problem

∵ The equation of the total cost is y = 0.65x + 1410

∵ The revenue equation is y = 0.8x

- To find the break-order point equate the two equations

∴ 0.65x + 1410 = 0.8x

- Subtract 0.65x from both sides

∴ 1410 = 0.8x - 0.65x

∴ 0.15x = 1410

- Divide both sides by 0.15

∴ x = 1410/0.15 = 9400

∵ x is the number of pies

* They need to sell 9400 pies to reach the break-order point

[tex]\bf ~~~~~~\textit{parabola vertex form} \\\\ \begin{array}{llll} \stackrel{\textit{we'll use this one}}{y=a(x- h)^2+ k}\\\\ x=a(y- k)^2+ h \end{array} \qquad\qquad vertex~~(\stackrel{}{ h},\stackrel{}{ k}) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \textit{we know that } \begin{cases} h=2\\ k=-4 \end{cases}\implies y=a(x-2)^2-4 \\\\\\ \textit{we also know that } \begin{cases} y = -3\\ x = -3 \end{cases}\implies -3=a(-3-2)^2-4\implies 1=a(-5)^2 \\\\\\ 1=25a\implies \boxed{\cfrac{1}{25}=a}[/tex]

Answer:

it is not 5

so there are only three options left

The length of BC in the right triangle with sides 9 and 12 is 15.

In a right triangle, the length of the hypotenuse can be found using the Pythagorean theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the other two sides.

In this case, the lengths of the other two sides are given as 9 and 12. Let's label the hypotenuse as BC. We can use the Pythagorean theorem to solve for BC:

a2 + b2 = c2

92 + 122 = c2

81 + 144 = c2

225 = c2

Taking the square root of both sides, we find that the length of BC is 15 units.

Answer:

The correct option is D.

Step-by-step explanation:

The general exponential regression equations is

[tex]y=ab^x[/tex]                      .... (1)

where, a is initial value and b is growth factor.

Using graph calculator, we get

[tex]a=3.5349151766\approx 3.53[/tex]

[tex]b=4.37391527533\approx 4.37[/tex]

[tex]R^2=0.99878148[/tex]

Put the value of a and b in equation (1), to find the exponential regression equation.

Substitute a=3.53 and b=4.37 in equation (1).

[tex]y=(3.53)(4.37)^x[/tex]

[tex]y=3.53(4.37)^x[/tex]

The exponential regression equations that best fits the data is [tex]y=3.53(4.37)^x[/tex].

Therefore the correct option is D.

Answer:

180

Step-by-step explanation:

According to the table, the relationship between the x and the y value is 20, (4*20 = 80) (5*20 = 100) etc.

The graph with the points has a relationship of 35 (2*35 = 70) (4*35 = 140) etc. Therefore, you can figure out what y-value 12 would have for the table and the graph by multiplying 12 by 20 or 35 respectively.

12*20 = 240

12*35 = 420

420-240 = 180

Answer:

180

Step-by-step explanation:

Answer:

1 large truck, 99 small trucks and 180 commercial vans

Step-by-step explanation:

Step 1 : Write the data.

Total amount: 8,000,000

Total trucks needed: 280

Cost of commercial van (x) = $25,000

Cost of small truck (y) = $30,000

Large truck = $40,000 (from my understanding, only 1 large truck has to be bought since the amount given for commercial vans and small trucks is for each of it.

Since they need twice as many vans as small trucks, commercial van will be 2y and small truck will be y

Step 2 : Form two equations

40,000 + 25000(x) + 30000(y) = 8,000,000

25000(x) + 30000(y)  = 7960,000 (equation 1)

1(large truck) + x + y =280

x + y = 279 (equation 2)

Step 3 : Find the value of y

From equation 2:

x = 279 - y

From equation 1:

25000(x) + 30000(y)  = 7960,000

25000(279 - y) + 30000(y)  = 7960,000

-25000y + 30000y + 6975000 = 7960000

5000y = 985000

y= 98.5 rounded off to 99 small trucks

Step 4: Find value of x

x + y = 279

y = 279 - 99

y = 180 commercial vans

Step 5: Answer how many type of each vehicle can they buy.

They can buy:

1 large truck

99 small trucks

180 commercial vans

!!

Answer:

The standard form of the equation is 49t² - 75t + 3 = 0

The solution of the equations are 1.49 and 0.041

Step-by-step explanation:

* Lets explain how to solve the problem

- The standard form of the quadratic equation is ax² + bx + c  = 0,

  where a , b , c are constant and a can not be 0

∵ The quadratic equation is -4.9t² + 7.5t + 1.8 = 2.1

- Lets make the left hand side equal to 0

∵ -4.9t² + 7.5t + 1.8 = 2.1 ⇒ subtract 2.1 from both sides

∴ -4.9t² + 7.5t - 0.3 = 0 ⇒ multiply each term by -10

∴ 49t² - 75t + 3 = 0

* The standard form of the equation is 49t² - 75t + 3 = 0

∵ ax² + bx + c = 0

∴ a = 49 , b = -75 , c = 3

- Lets use the formula [tex]x=\frac{-b+-\sqrt{b^{2}-4ac}}{2a}[/tex] to solve

 the equation

∴ [tex]x=\frac{-(-75)+\sqrt{(-75)^{2}-4(49)(3)}}{2(49)}=1.49[/tex]

∴ [tex]x=\frac{-(-75)-\sqrt{(-75)^{2}-4(49)(3)}}{2(49)}=0.041[/tex]

* The solution of the equations are 1.49 and 0.041

Check the picture below.

Answer:

A)

Step-by-step explanation:

The 30-60-90° triangle has the side lengths of 1, √3, 2, so you should find the triangle that fits this measurement.

A) is your answer for:

Side with measurement 1 (30°): 5

5 is your measurement for the side measurement of 1. The next measurement (60°) must be x √3: 5 x √3 = 5√3 (Side on the bottom).

The last measurement (90°) 2 is twice the measurement of 1: 5 x 2 = 10 (Hypotenuse, side on top).

A) is your answer.

~

Answer:

[tex] x = 2 + \sqrt{42} [/tex]   or   [tex] x = 2 - \sqrt{42} [/tex]

Step-by-step explanation:

[tex] x^2 - 4x - 9 = 29 [/tex]

Subtract 29 from both sides.

[tex] x^2 - 4x - 9 - 29 = 29 - 29 [/tex]

[tex] x^2 - 4x - 38 = 0 [/tex]

There are no two integers whose sum is -4 and whose product is -38, so the trinomial is not factorable. We can use the quadratic formula.

a = 1; b = -4; c = -38

[tex] x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a} [/tex]

[tex] x = \dfrac{-(-4) \pm \sqrt{(-4)^2 - 4(1)(-38)}}{2(1)} [/tex]

[tex] x = \dfrac{4 \pm \sqrt{16 + 152}}{2} [/tex]

[tex] x = \dfrac{4 \pm \sqrt{168}}{2} [/tex]

[tex] x = 2 \pm \dfrac{\sqrt{4 \times 42}}{2} [/tex]

[tex] x = 2 \pm \dfrac{2\sqrt{42}}{2} [/tex]

[tex] x = 2 \pm \sqrt{42} [/tex]

[tex] x = 2 + \sqrt{42} [/tex]   or   [tex] x = 2 - \sqrt{42} [/tex]