(4 marks)
5. Solve the following equations:
a) x+5 = 7
b) 2x - 8 = 20
c) 4x - 6x = 200
d) x+1= 5
3

Answer:

Step-by-step explanation: 5 times 4 then that times 3 then that times 2.

120

5! = 120.

5! equals 5 x 4 x 3 x 2 x 1 which is equal to 120.

The exclamation mark denotes a factorial, which is the product of all positive integers up to that number.

Answer: im sorry i dont knoey888888888888888888888hjk.

Step-by-step explanation:

Answer:

C≈1256.64in

Step-by-step explanation:

C=πd=π·400≈1256.63706in

Hope this helps!

Answer:

table d is the proportional relationship

Step-by-step explanation:

Answer:

95:95:19

Step-by-step explanation:

1.Divide 209 by 11.(209÷19)

2.Multiply 19×5 since 5/11 of the coins are nickels.(19×5=95)

3.Multiply 19×5 again since 5/11 of the coins are dimes.(19×5=95)

4.Multiply 19×1 since there would be 1/11 left of the coins which are quarters. (19×1=19)

5.Check your awnser by adding 95+95+19.(95+95+19=209)

Answer: [tex]x=2[/tex]

Step-by-step explanation:

Inverse proportion equation has this form:

[tex]y=\frac{k}{x}[/tex]

Where  "k" is the constant of variation.

We know that  "y" is inversely proportional to "x" and when [tex]x=3[/tex], [tex]y=6[/tex]

Then, we can substittute these values into the equation and solve for "k" to  find its value:

[tex]6=\frac{k}{3}\\\\6*3=k\\\\k=18[/tex]

Finally, we need to substitute "k" and [tex]y=9[/tex] into the equation and solve for "x":

[tex]9=\frac{18}{x}\\\\x=\frac{18}{9}\\\\x=2[/tex]

Answer:

x=2

Step-by-step explanation:

y is inversely proportional to x is written as:

x ∝ 1/y

When the proportion is removed, a constant is introduced. We have to find the constant first to find the value of x in y = 9

So,

Removing the proportionality symbol will give us:

x=k/y

As we know that x=3 for y=6 so

3 = k/6

3*6=k

So,

k=8

Hence the value of proportionality constant is 8.

Now putting the value of y which is 9

x=k/y

=>x=18/9

=>x=2

Answer:

a) The equation is (y - 1)² = -8 (x - 4)

b) The equation is (x - 1)²/25 + (y - 4)²/16 = 1

c) The equation of the ellipse is (x - 3)²/16 + y²/4 = 1

Step-by-step explanation:

a) Lets revise the standard form of the equation of the parabola with a

   horizontal axis

# (y - k)² = 4p (x - h), (h , k) are the coordinates of its vertex and p ≠ 0

- The focus of it is (h + p , k)

* Lets solve the problem

∵ The focus is (2 , 1)

∵ focus is (h + p , k)

∴ h + p = 2 ⇒ subtract p from both sides

∴ h = 2 - p ⇒ (1)

∴ k = 1

∵ It opens left, then the axis is horizontal and p is negative

∴ Its equation is (y - k)² = 4p (x - h)

∵ k = 1

∴ Its equation is (y - 1)² = 4p (x - h)

- The parabola contains point (2 , 5), substitute the coordinates of the

 point in the equation of the parabola

∴ (5 - 1)² = 4p (2 - h)

∴ (4)² = 4p (2 - h)

∴ 16 = 4p (2 - h) ⇒ divide both sides by 4

∴ 4 = p (2 - h) ⇒ (2)

- Use equation (1) to substitute h in equation (2)

∴ 4 = p (2 - [2 - p]) ⇒ open the inside bracket

∴ 4 = p (2 - 2 + p) ⇒ simplify

∴ 4 = p (p)

∴ 4 = p² ⇒ take √ for both sides

∴ p = ± 2, we will chose p = -2 because the parabola opens left

- Substitute the value of p in (1) to find h

∵ h = 2 - p

∵ p = -2

∴ h = 2 - (-2) = 2 + 2 = 4

∴ The equation of the parabola in standard form is

  (y - 1)² = 4(-2) (x - 4)

∴ The equation is (y - 1)² = -8 (x - 4)

b) Lets revise the equation of the ellipse

- The standard form of the equation of an ellipse with  center (h , k)

 and major axis parallel to x-axis is (x - h)²/a² + (y - k)²/b² = 1  

- The coordinates of the vertices are (h ± a , k )  

- The coordinates of the foci are (h ± c , k), where c² = a² - b²  

* Now lets solve the problem

∵ Its vertices are (-4 , 4) and (6 , 4)

∵ The coordinates of the vertices are (h + a , k ) and (h - a , k)  

∴ k = 4

∴ h + a = 6 ⇒ (1)

∴ h - a = -4 ⇒ (2)

- Add (1) and (2) to find h

∴ 2h = 2 ⇒ divide both sides by 2

∴ h = 1

- Substitute the value of h in (1) or (2) to find a

∴ 1 + a = 6 ⇒subtract 1 from both sides

∴ a = 5

∵ The foci at (-2 , 4) and (4 , 4)

∵ The coordinates of the foci are (h + c , k) , (h - c , k)

∴ h + c = 4

∵ h = 1

∴ 1 + c = 4 ⇒ subtract 1 from both sides

∴ c = 3

∵ c² = a² - b²

∴ 3² = 5² - b²

∴ 9 = 25 - b² ⇒ subtract 25 from both sides

∴ -16 = -b² ⇒ multiply both sides by -1

∴ 16 = b²

∵ a² = 25

∵ The equation of the ellipse is (x - h)²/a² + (y - k)²/b² = 1

∴ The equation is (x - 1)²/25 + (y - 4)²/16 = 1

c) How to identify the type of the conic  

- Rewrite the equation in the general form,  

 Ax² + Bxy + Cy² + Dx + Ey + F = 0  

- Identify the values of A and C from the general form.  

- If A and C are nonzero, have the same sign, and are not equal  

 to each other, then the graph is an ellipse.  

- If A and C are equal and nonzero and have the same sign, then

 the graph is a circle  

- If A and C are nonzero and have opposite signs, and are not equal  

 then the graph is a hyperbola.  

- If either A or C is zero, then the graph is a parabola  

* Now lets solve the problem

∵ x² + 4y² - 6x - 7 = 0

∵ The general form of the conic equation is

   Ax² + Bxy + Cy² + Dx + Ey + F = 0  

∴ A = 1 and C = 4

∵ If A and C are nonzero, have the same sign, and are not equal  to

  each other, then the graph is an ellipse.

∵ x² + 4y² - 6x - 7 = 0 ⇒ re-arrange the terms

∴ (x² - 6x ) + 4y² - 7 = 0

- Lets make x² - 6x completing square

∵ 6x ÷ 2 = 3x

∵ 3x = x × 3

- Lets add and subtract 9 to x² - 6x to make the completing square

 x² - 6x + 9 = (x - 3)²

∴ (x² - 6x + 9) - 9 + 4y² - 7 = 0 ⇒ simplify

∴ (x - 3)² + 4y² - 16 = 0 ⇒ add 16 to both sides

∴ (x - 3)² + 4y² = 16 ⇒ divide all terms by 16

∴ (x - 3)²/16 + 4y²/16 = 1 ⇒ simplify

∴ (x - 3)²/16 + y²/4 = 1

∴ The equation of the ellipse is (x - 3)²/16 + y²/4 = 1

Find the difference between the two prices:

617.40 - 420 = 197.40

Now divide the difference by the wholesale price:

197.40 / 420 = 0.47 = 47% markup.

The percent markup when retail price is $617.40 and wholesale price is 420.00 is 47%.

To calculate the percent markup on the snowblower, we need to find the difference between the retail price and the wholesale price, and then divide that by the wholesale price. The markup is the amount added to the cost of the goods to cover overhead and profit.

Therefore, the percent markup on the snowblower is 47%.

Answer:

The y-intercept of this line: -4

Step-by-step explanation:

A line passes through the points (8, –1) and (–4, 2).

Slope = (-1 - 2)/(8 + 4) = -3/4

Equation in slope intercept form:

y = mx + b where m = slope and b = y-intercept

Substitute m = -3/4 into the equation to find y-intercept

y = -3/4 x + b

Plug in one of those coordinate points above to find b. In this case, I'm using  (–4, 2)

y = -3/4 x + b

2= -3/4 (-4) + b

-1 = 3 + b

b = -4

Answer:

THE ANSWER IS -4

Step-by-step explanation:

[tex]

L=25,W=105 \\

P=2L+2W=2(L+W)\Rightarrow P=2(25+105) \\

P=2\cdot130=\boxed{260}

[/tex]

Hope this helps.

r3t40

Answer:

[tex]\sqrt{13}\ units[/tex]

Step-by-step explanation:

we have

[tex]R(1, -1), S(6, 1),T(8, 5),U(3, 3)[/tex]

Plot the vertices

see the attached figure

The shorter diagonal is SU

the formula to calculate the distance between two points is equal to

[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]

we have

[tex]S(6, 1),U(3, 3)[/tex]

substitute

[tex]SU=\sqrt{(3-1)^{2}+(3-6)^{2}}[/tex]

[tex]SU=\sqrt{(2)^{2}+(-3)^{2}}[/tex]

[tex]SU=\sqrt{13}\ units[/tex]

Answer:

Man cant really get more in depth than the other answer!

Answer is √(13) :D

Answer:

Jenn

Step-by-step explanation:

Natalie and Beth swim at about the same speed. Kara swims twice as fast as Beth so she also swims twice as fast as Natalie. So Kara is faster than Natalie and Jenn is faster than Kara. Therefore Jenn is faster than Natalie.

Hope This Helps :]

Final answer:

Jenn is faster than Natalie because she swims faster than Kara who swims almost twice as fast as Beth, and Natalie swims about the same speed as Beth.

Explanation:

The question pertains to comparing the speeds of different swimmers, which is a logical, rather than numerical comparison. Kara swims almost twice as fast as Beth, and Natalie swims about the same speed as Beth. Jenn swims faster than Kara.

Therefore, Jenn is the fastest swimmer among the four. Since the comparison is between Natalie and Jenn, and we have already established that Jenn swims faster than Kara, who in turn swims faster than Beth (and Natalie swims at the same speed as Beth), it is logical to conclude that Jenn is faster than Natalie.

Answer:

This should help you !!!

Four 2 bedroom apartments and two 3 bedroom apartments were vacant.

It is given that Campus rentals rents 2 and 3 bedrooms apartments for $700 and $900 a month respectively. Last month they had six vacant apartments and reported $4600 in lost rent.  

We have to find out that how many of each type of apartment were vacant ?

What is algebra ?

Algebra is the branch of mathematics that deals with various symbols and the arithmetic operations and the symbols are called variables.

Let's assume that ;

Number of vacant 2 bedroom apartments = x

Number of vacant 3 bedroom apartments = y

∵ The total number of vacant apartments were 6 ; the equation will be ;

x + y = 6 -------- Equation 1

or

x = 6 - y

The loss reported is $4600.

We can write it as ;

x × 700 + 900 × y = 4600

700 × ( 6 - y ) + 900 × y = 4600

4200 - 700 y + 900 y = 4600

200 y = 400

y = 2

putting this in equation 1 we get ;

x = 6 - 2 = 4

Thus , four 2 bedroom apartments and two 3 bedroom apartments were vacant.

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Answer:

odd

Step-by-step explanation:

Just so you know there are shortcuts for determining if a polynomial function is even or odd. You just to make sure you use that x=x^1 and if you have a constant, write it as constant*x^0 (since x^0=1)

THEN!

If all of your exponents are odd then the function is odd

If all of your exponents are even then the function is even

Now you have -4x^3+4x^1

3 and 1 are odd it is an odd function

This a short cut not the legit algebra way

let me show you that now:

For it to be even you have f(-x)=f(x)

For it be odd you have f(-x)=-f(x)

If you don't have either of those cases you say it is neither

So let's check

plug in -x  -4(-x)^3+4(-x)=-4*-x^3+-4x=-4x^3+-4x

that's not the same so not even

with if we factor out -1 .... well if we do that we get -(4x^3+4x)=-f(x)

so it is odd.

Answer:

-1.25, 2, 3.5

Step-by-step explanation:

(x-2)(2x-7)(4x+5)=0

(2x^2-7x-4x+14)(4x+5)=5

from now on you know that either

(2x^2-7x-4x+14)=0 or

(4x+5)=0

By solving the first eqation (2x^2-7x-4x+14)=0

you get x = 2 or 3.5

By solving the second equation (4x+5)=0

you get x = -1.25

Answer:

x = -8   &   at x = 3

Step-by-step explanation:

This is a rational function.

We can get the values of x at which vertical asymptotes occur by setting the denominator equal to 0 and solving for x.

Let's do this:

[tex]x^2+5x-24=0\\(x+8)(x-3)=0\\x=-8,3[/tex]

Hence, vertical asymptotes occur at x = -8 & at x = 3

Answer:

[tex]\displaystyle \frac{25}{2}\pi \approx 39.3[/tex] inches.

Step-by-step explanation:

The question gives the central angle and radius of an arc and is asking for the length.

An arc is part of a circle. What is the circumference of a circle with a radius 15 inches?

[tex]\text{Circumference} = \pi \times \text{Diameter} = 2\pi \times \text{Radius} = 30\pi[/tex] inches.

However, this wiper traveled only a fraction of the circle. A full circle is [tex]360^{\circ}[/tex]. The central angle of this arc is only [tex]150^{\circ}[/tex]. As a result,

[tex]\displaystyle \frac{\text{Length of this arc}}{\text{Circumference of the circle}} = \frac{150^{\circ}}{360^{\circ}} = \frac{5}{12}[/tex].

The length of the arc will thus be

[tex]\displaystyle \frac{5}{12} \times 30\pi = \frac{25}{2}\pi \approx 39.3[/tex].

In other words, the windshield wiper traveled approximately 39.3 inches.

To find the distance traveled by the end of the windshield wiper making a 150° arc, calculate the circumference of the circle swept and apply the formula to determine the distance traveled.

Distance traveled by the end of the windshield wiper:

Calculate the circumference of the circle swept by the windshield wiper: Circumference = 2πr = 2π(15 in).

Convert the circumference to inches: Multiply the circumference by the angle traversed (150°/360°) to find the distance traveled by the wiper's end.

Distance traveled = Circumference x (150/360) = 15π/2 inches or 23.56 inches.

Answer:

29

Step-by-step explanation:

(5k-3) + (9+k) = 180

6k + 6 = 180

6k = 174

k = 29

mark brainliest please (button next to the thanks button)

Answer:

k equals 29 degrees

Step-by-step explanation:

a line equals 180 degrees so you set the sum of the variables equal to 180 and solve for k

Answer:

The value of (g*h) (-3)  is [tex]=-\frac{112}{3}[/tex]

Step-by-step explanation:

If [tex]g(x) = x+\frac{1}{x}-2[/tex] and [tex]h(x)=4-x[/tex]

We have to find (g*h) (-3)

First multiply g(x) with f(x)

[tex] (x+\frac{1}{x}-2)\times (4-x)[/tex]

[tex]Distribute\:parentheses[/tex]

[tex]=x\cdot \:4+x\left(-x\right)+\frac{1}{x}\cdot \:4+\frac{1}{x}\left(-x\right)+\left(-2\right)\cdot \:4+\left(-2\right)\left(-x\right)[/tex]

[tex]\mathrm{Apply\:minus-plus\:rules}[/tex]

[tex]+\left(-a\right)=-a,\:\:\left(-a\right)\left(-b\right)=ab[/tex]

[tex]=4x-xx+4\cdot \frac{1}{x}-\frac{1}{x}x-2\cdot \:4+2x[/tex]

simplify

[tex]=-x^2+6x+\frac{4}{x}-9[/tex]

Now, put x= -3 in above expression

[tex]=-(-3)^2+6(-3)+\frac{4}{-3}-9[/tex]

[tex]=\left(-\frac{1}{3}-3-2\right)\left(4+3\right)[/tex]

[tex]=\left(-\frac{16}{3}\right)\left(4+3\right)[/tex]

[tex]=7\left(-\frac{16}{3}\right)[/tex]

[tex]=-\frac{16}{3}\cdot \:7[/tex]

[tex]=-\frac{112}{3}[/tex]

Therefore, the value of (g*h) (-3) is [tex]-\frac{112}{3}[/tex]

Answer:

the answer is 2 :)

Step-by-step explanation:

Answer:

B) y=3(1/3)^x

Step-by-step explanation:

Based on the graph, y intercept = 3

So you can plug in x =0 in each functions given in the options to see which one has y-intercept = 3

y= 3 (1/3)^x  ; when x = 0, y = 3 * 3^0 = 3 * 1 = 3

Answer:

The correct option is B) [tex]y=3(\frac{1}{3})^{x}[/tex]

Step-by-step explanation:

Consider the provided graph:

The general formula for equation of exponential decay is: [tex]y=ab^{x}[/tex] where [tex]b<1[/tex]

The graph of exponential decay [tex]y=ab^{x}[/tex] where [tex]b<1[/tex] as shown in figure 1:

From the figure 1, it is clear that a represents the y intercept and the coordinates are (0,a).

Now, consider the provided Graph:

The y intercept is (0,3)

Therefore, the value of a must be 3.

Now, consider the provided options, only option B) has the value of a = 3.

Therefore, the correct option is: B) [tex]y=3(\frac{1}{3})^{x}[/tex] .

Answer:

[tex]-\frac{3}{4}[/tex]  meters

Step-by-step explanation:

From the answer choices, we basically need to find which of them is between   [tex]-\frac{1}{2}[/tex]  and  [tex]-1\frac{2}{3}[/tex]

Converting all of them to decimals would make it really easier:

So we need to find number between -0.5  and -1.67

Answer choice A is -2.33

Answer choice B is  -0.75

Answer choice C is  -0.25

Answer chioce D is  -1.83

So which number, from the choices, is between -0.5 & -1.67?

Clearly, it is -0.75, or,  [tex]-\frac{3}{4}[/tex]  meters

Answer:

Average rate of change = -6

Step-by-step explanation:

The average rate of change over the interval (a,b) is given by;

[ f(b) - f(a)] / (b-a)........................where interval is (a,b)

(a,b) interval =(-3,1)

Where;

f(x)= -12 (x+2)² +5

[tex]f(a)=f(-3)=-12(-3+2)^2+5\\f(a)=f(-3)=-12(-1)^2+5\\f(a)=f(-3)=-12(1)+5\\=-12+5=-7\\\\\\f(b)=f(1)=-12(1+2)+5\\f(b)=f(1)=-12(3)+5\\=-36+5=-31\\\\f(b)-f(a)=-31--7=-24\\\\b-a=1--3=4\\\\f(b)-f(a)/b-a=\frac{-24}{4} =-6[/tex]

Answer:

6

Step-by-step explanation:

2+6=8

8+6=14

14+6=20

20+6=26

Answer:

i  need mesurements

Step-by-step explanation:

It took 45 square units of gold foil to cover the entire pyramid trophy, including the bottom.

To find the amount of gold foil needed to cover the square pyramid-shaped trophy, we need to calculate the total surface area of the pyramid, including the base.

A square pyramid consists of the following surfaces:

1. The base (which is a square)

2. Four triangular faces

First, let's find the area of the base. Since it's a square, we can use the formula for the area of a square:

[tex]\[ \text{Area of the base} = \text{side}^2 \][/tex]

Given that the side of the square base is 3 units, the area of the base is:

[tex]\[ \text{Area of the base} = 3^2 = 9 \text{ square units} \][/tex]

Next, let's find the area of each triangular face. Since it's a regular pyramid, all four triangular faces have the same dimensions and area. We'll use the formula for the area of a triangle:

[tex]\[ \text{Area of a triangle} = \frac{1}{2} \times \text{base} \times \text{height} \][/tex]

Given that the base of each triangular face is the side length of the square base (which is 3 units) and the height of the pyramid is 6 units, the area of each triangular face is:

[tex]\[ \text{Area of a triangle} = \frac{1}{2} \times 3 \times 6 = 9 \text{ square units} \][/tex]

Since there are four identical triangular faces, the total area of all four faces combined is:

[tex]\[ \text{Total area of all four triangular faces} = 4 \times 9 = 36 \text{ square units} \][/tex]

Now, let's calculate the total surface area of the pyramid by adding the area of the base and the total area of all four triangular faces:

[tex]\[ \text{Total surface area} = \text{Area of the base} + \text{Total area of all four triangular faces} \][/tex]

[tex]\[ = 9 + 36 = 45 \text{ square units} \][/tex]

Therefore, it took 45 square units of gold foil to cover the entire pyramid trophy, including the bottom.

Complete question:

Akira receives the prize at the science fair for having the most informative project her trophy is in the shape of a square pyramid and is covered in shiny gold foil how much gold foil did it take to cover the chair free including the bottom​.

Answer:

x=8*2

Step-by-step explanation:

Answer:

[tex]8(2)^{x-1}[/tex]

Step-by-step explanation:

Pacey's computer is infected with a virus. The number of files the virus corrupts doubles every 8 minutes.

That means at every 8 minutes interval sequence becomes 8, 8 × 2, 8 × 2 × 2,.....

So the sequence is a geometric sequence.

Explicit formula of geometric sequence is

[tex]A_{x}=A_{0}(r)^{x-1}[/tex]

When[tex] A_{x}[/tex] = xth term

[tex]A_{0}[/tex] = first term

x = number of term

and r = common ratio

Here [tex]A_{0}[/tex] = 8 and r = [tex]\frac{8\times2}{8}[/tex] = 2

So expression representing the number of files corrupted will be [tex]A_{x}[/tex] = [tex]8(2)^{x-1}[/tex]

The index of a radical is the number indicating what root of a given number should be taken. In the expression '4 radical 8', '4' is the index of the radical, meaning the expression represents the fourth root of 8.

In the expression '4 radical 8', '4' is referred to as the index of the radical. The index of a radical is the number that denotes what root of the number is to be taken. For example, an index of 2 (which is often not written) refers to a square root, an index of 3 refers to a cube root, and so on. In this case, since the expression is '4 radical 8', it means we are looking at the fourth root of 8.

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In 4 radical 8, the given index of the radical 4, means we are looking for a number that, when raised to the power of 4, gives us 8.

The index of a radical is the number that is written just above and to the left of the radical symbol. In your problem, 4 radical 8, the number 4 is the index of the radical. So, the index of the radical in 4 radical 8 is 4. This means that we are looking for a number that, when raised to the power of 4, gives us 8.

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Answer:

The inputs to this formula are:

The equation of this line in point-slope form will be:

[tex]y - 4 = -2(x +11)[/tex].

Step-by-step explanation:

The general form of a 2D line in its point-slope form is:

[tex]l:\; y - y_0 = m(x - x_0)[/tex].

This form of the equation of a line takes two pieces of information:

For this line, the point [tex](x_0, y_0)[/tex] is [tex](-11, 4)[/tex].

The slope of this line is [tex]-2[/tex]. In other words,

Apply the point-slope formula for a 2D line:

[tex]l:\; y - 4 = -2 (x - (-11))[/tex].

[tex]l:\; y - 4 = -2 (x +11 )[/tex].