4 Consider the quadratic equation below.[tex]4 {x}^{2} - 5 = 3x + 4[/tex] Determine the correct set-up for solving the equation using the quadratic formula.

To find the step where the error was made, we are going to correctly solve the equation:

We need to solve for x, first we subtract 3 from each side:

We divide by 2 each side:

The first step that shows an error in the solution of the equation is the Step 2, because when we have two negative numbers, we add them, we do not subtract them.

Answer: B. Step 2

Given:

The original selling price of 1 swimsuit = $44.95

The selling price of 1 marked down swimsuit = $16.90

Using the provided formula:

Where,

M is the markdown

S is the original selling price

N is the reduced price

Substituting we have:

Solving for N:

Hence, the reduced price is $28.05

Answer:

$28.05

The map of Roaring River shows1 inch to be an equivalent of 25 miles. If therefore, the river is shown as 5.5 inches long on the map;

The river is "actually" 137.5 miles long

The Pythagorean theorem states:

where a and b are the legs and c is the hypotenuse of a right triangle.

Substituting with c = 9 and a = 5, we get:

Answer:

Yes, because if you divide the two numbers, you get a whole number which means it is. Also, since the last numbers are 56, 8 can go into 56 so yes.

Step-by-step explanation:

Given:

Required:

To find the correct one.

Explanation:

The given quation is:

4 + x +8 =24

Subtract 8 on both sides

4 + x +8 - 8 = 24 -8

4 + x = 16

Final Answer:

Thus the first option is the correct answer.

Answer:

y= 4x +1

Step-by-step explanation:

The equation of a line, in slope-intercept form, is given by y= mx +c, where m is the slope and c is the y-intercept.

Given that the slope is 4, m= 4.

Substitute m= 4 into y= mx +c:

y= 4x +c

To find the value of c, substitute a pair of coordinates the line passes through.

When x= -2, y= -7,

-7= 4(-2) +c

-7= -8 +c

c= -7 +8

c= 1

Substitute the value of c into the equation:

Thus, the equation of the line is y= 4x +1.

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In order to determine which is the equivalent equation, simplify the given expression:

-2x + 5 - 3x = 5x + 25 simplify like terms left side

-2x - 3x + 5 = 5x + 25

-5x + 5 = 5x + 25 subtract 5x both sides and subtract 5 both sides

-5x - 5x = 25 - 5 simplify both sides

-10x = 20

Hence,the equivalent expression is -10x = 20

Answer:

Explanation:

Given the equation:

On observation, the equation cannot be factorized, so we make use of the quadratic formula.

Comparing with the form ax²+bx+c=0: a=1, b=3, c=-7

Substitute these values into the formula.

We then simplify and solve for x.

a) The rate of change of the volume of the box is 8m³/s.

b) The rate of change of the surface area of the box is -19m²/s.

c) The rate of change of the diagonal of the box is 1m/s.

Let the rate of change of  the edge length x, y, and z of a closed rectangular box are:

dx/dt= 1m/s

dy/dt= -2 m/s

dz/dt= 0.5 m/s

a) The volume of the box

From the formula of the volume,

V=xyz

Then,

differentiate w.r.t t

[tex]\frac{dV}{dt} = xy\frac{dz}{dt} + yz\frac{dx}{dt} +xz\frac{dy}{dt}[/tex]

[tex]\frac{dV}{dt} = xy(0.5)+ yz(1)+xz(-2)[/tex]

put the value of x, y, z , then we get

[tex]\frac{dV}{dt} = 2.3.(0.5)+ 3.5.(1)+2.5.(-2)[/tex]

[tex]\frac{dV}{dt} = 3+ 15 - 10[/tex]

[tex]\frac{dV}{dt} = 8m^3/s[/tex]

The rate of change of the volume of the box is 8m³/s.

b) surface area of the box

surface area of the rectangular box is

s = 2xy + 2yz + 2zx

differentiate w.r.t t

[tex]\frac{ds}{dt} = 2(y + z)\frac{dx}{dt} + 2(z + x)\frac{dy}{dt} +2(x + y)\frac{dz}{dt}[/tex]

[tex]\frac{ds}{dt} = 2(y + z)(1) + 2(z + x)(-2)+2(x + y)(0.5)[/tex]

[tex]\frac{ds}{dt} = 2(3 + 5)(1) + 2(5 + 2)(-2)+2(2 + 3)(0.5)[/tex]

[tex]\frac{ds}{dt} = 16 -40 + 5[/tex]

[tex]\frac{ds}{dt} = -19m^2/s[/tex]

The rate of change of the surface area of the box is -19m²/s.

c) diagonal of the box

lengths of  the boxes for the diagonal is

s = 2x² + y² + z²

differentiate equation w.r.t t

[tex]\frac{ds}{dt} = 4x\frac{dx}{dt} + 2y\frac{dy}{dt} +2z\frac{dz}{dt}[/tex]

[tex]\frac{ds}{dt} = 4.2.1+ 2.3.(-2) +2.5.(0.5)[/tex]

[tex]\frac{ds}{dt} = 8 -12 + 5[/tex]

[tex]\frac{ds}{dt} =1m/s[/tex]

The rate of change of the diagonal of the box is 1m/s.

a) The rate of change of the volume of the box is 8m³/s.

b) The rate of change of the surface area of the box is -19m²/s.

c) The rate of change of the diagonal of the box is 1m/s.

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The most appropriate choice for profit will be given by-

Profit percent after selling a bag of garri is 25%

What is profit?

If the selling price of an article is more than the cost price of the article, then the difference between selling price and the cost price of the article gives the profit

Profit = SP - CP

Here,

Cost price of a bag of Garri = N320

Selling price of a bag of Garri = N400

Profit = N(400 - 320)

         = N80

Profit Percent = [tex]\frac{80}{320} \times 100[/tex]

                       = 25%

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Average rate is f(a+266)-f(a))/266

so f(a+266) equals (0.16 x 266) + f(a)

f (a+266)= (0.16 x 266) + 92.39

The time needed to travel a certain distance varies inversely with the rate of speed, so:

8hours----------------------------->36mi/h

xhours----------------------------->60mi/h

4.8 hours or 4 hours and 48 minutes

we have

-6, 1, 8, 15, ...

so

a1=-6

a2=1

a3=8

a4=15

a2-a1=1-(-6)=7

a3-a2=8-1=7

a4-a3=15-8=7

so

the common difference is

d=7

Part 2

write an equation

we have that

The equation of a general aritmetic sequence is equal to

an=a1+(n-1)d

we have

d=7

a1=-6

substitute

an=-6+(n-1)7

an=-6+7n-7

an=7n-13

Part 3

Find 12th term

we have

n=12

a12=-7(12)-13

a12=71

As all the options are the same equation

so, we need to know the type of the sign of the inequality

As shown in the graph

The line is shaded so, the sign is < or >

The shaded area which is the solution of the inequaity is below the line

So, the sign is <

So, the answer is option B) 14x + 7y < 21

Okay, here we have this:

Considering the provided graph, we are going to find the measure of the angle "3", so we obtain the following:

Since angle 3 and 4 form a straight angle, that is to say that these two angles are supplementary, then we have:

Finally we obtain that the correct answer is the option C.

∵ m< OZQ = m[tex]\because m\angle OZP=62[/tex]Substitute the measures of the given angles in the equation above

Subtract 62 from both sides

The measure of angle PZQ is 63 degrees

The distance between the parallel lines is [tex]\frac{3}{5}}[/tex].

The given parallel lines are

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

We have to find the distance between the given parallel lines.

The formula is used to solve the distance between two parallel lines [tex]ax+by+c_{1}=0[/tex] and [tex]ax+by+c_{2}=0[/tex] is

[tex]d=|c_{2} $-$c_{1}|\frac{1}{\sqrt{a^{2}+b^{2}}}[/tex]

The first given line is [tex]y= $-$3x+4[/tex]

We can write that line as [tex]3x$-$y $-$4=0[/tex]

The second given line is [tex]y= $-$3x+1[/tex]

We can write that line as [tex]3x$-$y $-$1=0[/tex]

Comparing the both given parallel lines with the standard equation of line.

After comparing we get

[tex]a=3, b= $-$1, c_{1}= $-$4, c_{2}= $-$1[/tex]

Putting the value in the formula

[tex]d=|(-1) -(-4)|\frac{1}{\sqrt{(3)^{2}+(-4)^{2}}}\\d=|-1+4|\frac{1}{\sqrt{9+16}}\\d=|3|\frac{1}{\sqrt{25}}\\d=\frac{3}{5}}[/tex]

Hence, the distance between the parallel lines is [tex]\frac{3}{5}}[/tex].

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We need to solve the next expressions:

17. 19yd. 28in.- 16yd. 31in

We need to solve subtract each expression.

Then:

19yd. 28in.- 16yd. 31in =

19yd - 16yd and 28in-31in

3yd -3in

Then, we have the next equivalent.

1 yard = 36 in

So:

36 in - 3 in = 33 in

Therefore

19yd. 28in.- 16yd. 31in = 2 yard 33

18 61wk. 4da.- 18wk. 6da.

We need to subtract both expression:

Then

61wk - 18wk = 43kw

4da-6da = -2da

Where 1 week = 7 days

Then

7 da - 2da = 5 da

Hence, 43kw -1 wk = 42 wk.

The result is:

42 wk 5 da

21. 8tbsp. 2tsp. * 15

We need to convert 2ts into tbsp and then multiply the result by 15.

If

1 tsp ------- 0.333tbsp

Then

2tp ------ 2(0.333tbsp)= 0.66666 tbsp

Now

(8tbsp + 0.6666 ) * 15 = 130 tbsp

Paul is the oldest and Fred is the youngest of the three.

Younger is a comparative adjective that generally indicates more youthful.

Similar to old, elder simply indicates older in age. It is a comparative version of old.

Given that x is a natural number, let Bill's age equal x years.

Paul's age is thus calculated as (x + a) Years, where an is any positive integer.

Fred is also younger than Bill.

So, Fred's age is equal to x - k, where k is any positive integer.

As a result, if we arranged Fred, Bill, and Paul's ages, they would be

Bill, Fred, and Paul

x-k < x < x+a

As a result, we can conclude that Paul is the oldest and Fred is the youngest of the three.

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Given the picture, we have:

Enclosed area: A = x*y

Fence Length: F= 2x+y

Answer:

2x+19

Step-by-step explanation:

Let x be the number

2x+19

First, let's distribute the exponent -3 for 2 and ten, like this:

Now, we can apply the next property when we have a number raised to a negative power:

Then:

And when we have a division of the same number raised to different powers we can apply:

then:

Now, as we know, having 10 raised to 6 means that we are multiplying ten by ten 6 times, when we do this we get:

And with 2 raised to three we get:

Then we have:

We have to graph the function F(x) defined as:

We can graph it as:

To see the complete graph we have to show the horizontal axis from x = -30 to x = 30 and the vertical axis from y = -80 to y = 80.

Answer: Option B

The most appropriate choice for geometric series will be given by

The equation is [tex]y = 80 (1.2)^x[/tex] and it is a geometric function.

What is geometric series ?

The series in which the ratio between consecutive terms of the series are same is called geometric series

For example, 2, 4, 8, 16, ... is a geometric series in which ratio between two consecutive terms is 2.

Number of pieces of art in 2004 = 80

Number of pieces of art  in 2005 = [tex]80 \times 1.2[/tex]

Number of pieces of art in 2006 =  [tex]80\times (1.2)^2[/tex]

Number of pieces of art after x years from 2004 = [tex]80 \times (1.2)^x[/tex]

The equation is [tex]y = 80 (1.2)^x[/tex]

This is a geometric function

The graph has been attached here.

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This is a simple question to solve when we use the calculator (as the question allows us to use it).

For this problem when we have :

It can be read as "log base 10 of pi", and using a calculator we find:

And that is the final answer.

NOTE: this result means that:

.

Given that the slope of a line is 2/3, that passes through the point (4, -1), i.e

The formula to find the equation of straight line is

Substitute the values into the formula of the equation of a straight line

Solve for y i.e make y the subject

Thus, the answer is

Thus, the answer is the last option.

Answer: Fanuela walked 2.808 miles.

Step-by-step explanation:

If 3.9 = 100 and we need to work out what 72 is we can do this/

3.9 ÷ 10 = 0.39 which = 10

0.39 ÷ 10 = 0.039 which = 1

so with these calculations we can solve the problem.

To get the 70 in 72 we can do 0.39 x 7 (10 x 7) which = 2.73.

To get the remaining 2 in 72 we can do 0.039 x 2 (1 x 2) which = 0.078.

2.73 + 0.078 = 2.808.

Fanuela walked 2.808 miles.

Hope this helps! Feel free to ask any questions if you're still unsure.

1. Quadratic curve

2. Odd degree function

3. TWO REAL ZEROS