Claire and Richard are both artists who use square canvases. Claire

uses the polynomial 50%? + 250 to decide how much to charge for her paintings

and Richard uses the polynomial 40x² + 350 to decide how much to charge for

his paintings. In each polynomial, x is the height of the painting in feet.

a. How much does Claire charge for a 20-foot-tall painting?

b. How much does Richard charge for a 15-foot-tall painting?

c. To the nearest tenth, for what height will both Claire and Richard charge

the same amount for a painting? Explain how to find the answer.

d. When both Claire and Richard charge the same amount for a painting,

how much does each charge?

Answer:

Perimeter = 8x - 12

Step-by-step explanation:

The perimeter of a square is:

p = 4(side length)

on this case:

p = 4(2x-3)

p = 4*2x + 4*-3

p = 8x - 12

Answer:

19.9 cm²

Step-by-step explanation:

The following data were obtained from the question:

Angle at the centre (θ) = 150°

Diameter (d) = 7.8 cm

Area of sector =.?

Next, we shall determine the radius.

This can be obtained as illustrated below:

Radius (r) = Diameter (d) /2

r = d/2

Diameter (d) = 7.8 cm

Radius (r) =.?

r = d/2

r = 7.8/2

r = 3.9 cm

Finally, we shall determine the area of the sector as follow:

Angle at the centre (θ) = 150°

Radius (r) = 3.9 cm

Pi (π) = 3.14

Area of sector (A) =.?

A = θ/360 × πr²

A = 150/360 × 3.14 × 3.9²

A = 15/36 × 3.14 × 15.21

A = 19.9 cm²

Therefore, the area of the sector is 19.9 cm²

Answer:

20°

Step-by-step explanation:

The measure of the inscribed angle is equal to the half of the arc it sees

Since AC is the diameter the measure of arc ABC is 180°

and since A sees arc BC and C sees the arc AB

A< + C< = 90° so angle C = 20°

Answer:

[tex] x = \sqrt {40}[/tex]

Step-by-step explanation:

Given is an isosceles triangle, dotted line is the bisector of top angle which is also perpendicular bisector of the base of the triangle. Hence, by Pythagoras theorem:

[tex] {x}^{2} = {6}^{2} + ({ \frac{4}{2} })^{2} \\ = 36 + 4 \\ = 40 \\ \therefore \: x = \sqrt{40} \\ [/tex]

Answer:

D. x = sqrt(52).

Step-by-step explanation:

Since the line measuring 6 units bisects the top angle, there are two right angles. We can use the Pythagorean Theorem to solve for x.

a^2 + b^2 = x^2

4^2 + 6^2 = x^2

16 + 36 = x^2

52 = x^2

x = sqrt(52)

x = sqrt(2 * 2 * 13)

x = 2sqrt(13)

x = 7.211102551.

Hope this helps!

Answer:

The third option: x= [tex]\frac{8}{3} \pi[/tex]

Step-by-step explanation:

Arc length formula=[tex]\frac{Central Angle}{360} * 2\pi r[/tex]

Arc length = [tex]\frac{120}{360} *2\pi (4)[/tex]

=[tex]\frac{8}{3}\pi[/tex]

Answer: find the answer in the explanation.

Step-by-step explanation:

To increase the time the fireworks stays in the air by 2 seconds to build up the suspense, 2 should be added to the time t.

T + 2 = t

T = t - 2

Substitute T for t in the function g(t)

The company will make this happen without changing the length of the fuse by substituting T for t which will lead to

g(t) = -16(t - 2)^2 + 224(t - 2) + 120

How will this affect the maximum height of the firework?

Initially the function is:

g(t) = -16t2 + 224t + 120

Where the time at maximum height is found by using the formula

t = -b/2a

b = 224, a = -16

Substitutes both into the formula

t = -224/2(-16)

t = -224/-32

t = 7

Substitute 7 for t in the first equation

g(t) = -16(7)^2 + 224(7) + 120

g(t) = -16(49) + 224(7) + 120

g(t) = -784 + 1568 + 120

g(t) = 904 metres

But when the time is delayed by 2 seconds in the air, the maximum height will be

g(t) = -16( 7 - 2 )^2 + 224(7 - 2) + 120

g(t) = -16(5)^5 + 224(5) + 120

g(t) = -16(25) + 224(5) + 120

g(t) = -400 + 1120 + 120

g(t) = 840

The effect will surely reduce the maximum height of the fireworks.

[tex]1^4+1^2+1-k=0\\3-k=0\\k=3[/tex]

Answer:

k=3

Step-by-step explanation:

Hello, if p-1 is a factor of

[tex]f(p)=p^4+p^2+p-k[/tex]

it means that f(1)=0, so

1+1+1-k=0

3-k=0

k=3

thank you

Answer:

8p + 24 dollars

Step-by-step explanation:

1 hour = (p+3)

8 hours = 8 (p+3)

=> 8p + 24

In 8 hours, Cheryl earns 8p + 24 dollars.

Answer:

[tex]\boxed{8p + 24}[/tex]

Step-by-step explanation:

Hey there!

Well if Cheryl earns p + 3 per hour and it is asking us to find the amount made in 8 hours, we can make the following,

8(p + 3)

8*p = 8p

8*3 = 24

Together,

8p + 24

Hope this helps :)

Answer:

PEMDAS

Step-by-step explanation:

P - Parentheses (Brackets also!)

E - Exponents

M and D - Multiplication and division. Many people think multiplication has to be done first as said in "PEMDAS" but it doesn't. Do multiplication and division according to which ever one is farthest to the left (left to right).

A and S - Addition and subtraction. Same thing applies here, neither addition or subtraction has to be done first, just do them according to which one is farthest to the left when reading the expression from left to right.

Answer:

1. 38.3 x 10^5

2. 6.67 x 10^9

3. 4.48 x 10^4

Step-by-step explanation:

4.2 X 10 ^6 - 1.2 X 10^5 - 2.5 x 10^5

For the above question, we need to make the exponents equal

=> 42 x 10^5  -  1.2 x 10^5  -  2.5 x  10^5

SInce, all the exponents are equal, we can now add and subtract the normally.

=> (42 - 1.2 -2.5) x 10^5

=> (42 - 3.7) x 10^5

=> 38.3 x  10^5

So, the answer to the 1st question is 38.3 x 10^5

Next question:

=> 3.3 x 10^9 + 2.6 x 10^9 +7.7 x 10^8

=>  we need to make the exponents equal

=> 3.3 x 10^9 + 2.6 x 10^9 + .77 x 10^9

=> All the exponents are equal, we can now add and subtract the normally.

=> (3.3 + 2.6 + .77) x 10^9

=> 6.67 x 10^9

=> So the answer to the 2nd question is 6.67 x 10^9

Next question,

=> 8 X 10^4 - 3.4 x 10^4  - 1.2 x 10^3

=> we need to make the exponents equal

=> 8 x 10^4 - 3.4 x 10^4 - .12 x 10^4

=> All the exponents are equal, we can now add and subtract the normally.

=> (8 - 3.4 - .12) x 10^4

=> 4.48 x 10^4

=> So the answer to the 3rd question is 4.48 x 10^4

The solutions to the expressions are:

[tex]4.2 \times 10^6 - 1.2 \times 10^5 - 2.5 \times 10^5[/tex]=[tex]38.3\times 10^5[/tex]

[tex]3.3 \times 10^9 + 2.6 \times 10^9 + 7.7 \times 10^8[/tex] = [tex]6.67\times 10^9[/tex]

[tex]8.0 \times 10^4 -3.4 \times 10^4 - 1.2 \times 10^3[/tex] = [tex]4.48 \times 10^4[/tex]

[tex]4.2 \times 10^6 - 1.2 \times 10^5 - 2.5 \times 10^5[/tex]

Combine like terms:

[tex]4.2 \times 10^6 - (1.2+2.5) \times 10^5[/tex]

[tex]4.2 \times 10^6 - 3.7 \times 10^5[/tex]

[tex]42 \times 10^5 - 3.7 \times 10^5[/tex]

[tex](42-3.7)\times 10^5[/tex]

[tex]38.3\times 10^5[/tex]

[tex]3.3 \times 10^9 + 2.6 \times 10^9 + 7.7 \times 10^8[/tex]

Convert all terms with same power:

[tex]3.3 \times 10^9 + 2.6 \times 10^9 + 0.77 \times 10^9[/tex]

[tex](3.3+2.6+0.77) \times 10^9[/tex]

[tex]6.67\times 10^9[/tex]

[tex]8.0 \times 10^4 -3.4 \times 10^4 - 1.2 \times 10^3[/tex]

[tex]8.0 \times 10^4 - 3.4 \times 10^4 - 0.12 \times 10^4[/tex]

[tex](8.0-3.4-0.12) \times 10^4[/tex]

[tex]4.48 \times 10^4[/tex]

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Answer:

Step-by-step explanation:

I'm assuming you are trying to solve for x. I'm not sure, but that's what I figured out for the answer, so I'm gonna go with that. : )

We are looking for the value of x to make that statement true. It's going to take some trig manipulations, but if you are at this level of precalc, these identities should definitely NOT be new to you. We will begin by squaring both sides of that equation to get:

[tex]9sin^2(x)+3cos^2(x)=3[/tex]

From here we will factor out a 3 to get:

[tex]3(3sin^2x+cos^2x)=3[/tex] and then divide both sides by 3 to get:

[tex]3sin^2x+cos^2x=1[/tex]

Knowing the Pythagorean identity for the trig ratios, we will replace the sin-squared with what it is equal to in terms of cos-squared. If:

[tex]sin^2x+cos^2x=1[/tex], then

[tex]sin^2x=1-cos^2x[/tex]. Making that replacement gives us an equation with only one trig ratio in it, namely, cos:

[tex]3(1-cos^2x)+cos^2x=1[/tex] and distributing:

[tex]3-3cos^2x+cos^2x=1[/tex] which simplifies down to:

[tex]-2cos^2x=-2[/tex]. Divide both sides by -2 to get:

[tex]cos^2x=1[/tex]. When you take the square root of both sides you get:

[tex]cos(x)=1[/tex] and [tex]cos(x)=-1[/tex]. Here is where we will use the unit circle to see where the cos is 1 and where the cos is -1. You didn't give me an interval in which to work, so I am going to use from 0 degrees to 180. Within that interval, the cos is 1 at 0 degrees; within that interval, the cos is -1 at 180.

Now we need to plug those values into the original equation to see if they work. One of them may be extraneous. Plugging in 0 first:

3sin(0) + √3cos(0) = -√3. We need to see if this is true.

The sin of 0 is 0; the cos of 0 is 1, so

0 + (√3)(1) = -√3?

The left side is √3, not -√3, so 0 doesn't work. Let's try 180 now, shall we?

3sin(180) + √3cos(180) = -√3. We need to see if this is true.

The sin of 180 is 0; the cos of 180 is -1, so

0 + (√3)(-1) = -√3?

The left side is -√3 and so is the right side, so

x = 180°

Answer:

17

Step-by-step explanation:

67 minus 33 leaves 34 red bikes but divided that by half gives you 17

There are approximately 17 red bikes in the bike rack outside the school.

Algebra is the estimation of mathematical representations, while logic is the manipulation of those symbols.

We can solve this problem by setting up an equation to represent the relationship between the number of bikes in the bike rack, the number of silver bikes, and the number of red bikes.

Let's define a variable, r, to represent the number of red bikes. We know that 33 bikes are silver, so the number of bikes that are not silver is 67 - 33 = 34 bikes.

Half of the remaining bikes are red, so we can say that there are r = 34/2 = 17 red bikes.

Therefore, there are approximately 17 red bikes in the bike rack outside the school.

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Answer:

1. 2cm 3cm and 4cm

yes, because 2+3>4

2. 2cm 3 cm 6 cm

no, 2+3<6

3. 90 degrees 45 degrees 45 degrees

yes, 90+45+45 = 180

4. 90 degrees 60 degrees 60 degrees?

no, 90+60+60=210!=180

Answer:

3250

Step-by-step explanation:

so for the first and 2nd show, the attendance is 2580 and 2920.

The average of both these numbers is 2750

the if the third show had 3000 people, the average attendance would only be 2875.

We need the average number to be 3000.

2750 is 250 less than 3000, so the other number must be 250 more.

3250 is how many people should go to the last show.

=====================================

Explanation:

We have 2580 people attend the first show and 2920 attend the second. So far, that's 2580+2920 = 5500 people. Add on another x people to get 5500+x, which represents the sum of all three days attendance figures. Divide this sum by 3 to get the average attendance

average attendance = (sum of individual attendance values)/(number of days)

average attendance = (5500+x)/3

So that's why (5500+x)/3 goes in the first box. The parenthesis are important to ensure that you divide all of "5500+x" over 3. If you just wrote 5500+x/3, then the computer would think you just want to divide x only over 3.

----------------

We set (5500+x)/3 equal to 3000 as we want the average of the three days to be 3000

(5500+x)/3 = 3000

5500+x = 3*3000

5500+x = 9000

x = 9000-5500

x = 3500

We need 3500 people to show up on day 3 so that the average of all three days is 3000.

3500 goes in the second box.

----------------

Check:

The figures for the three days are 2580, 2920, and 3500

They add to 2580+2920+3500 = 9000

Which divides to 9000/3 = 3000, which is the average we're after. So the answer is confirmed.

Answer:

3.1

3.2

3.3

3.4

3.5

3.6

Hope this answer correct :)

Answer:

Now solve these two equations.ull get andwer

The original number will be "63".

Let,

The equation will be:

→ [tex]x=y+3[/tex]...(equation 1)

Original number will be:

→ [tex]10x+y[/tex]

then,

→ [tex]2 (10x+y)-\frac{(10y+x)}{2} = 108[/tex]

→ [tex]\frac{4(10x+y)}{1} -(10y+x) = 216[/tex]

→ [tex]40x+4y-10y-x = 216[/tex]

→ [tex]39x-6y=216[/tex]...(equation 2)

By using (equation 1) and (equation 2), we get

→ [tex]39(y+3)-6y=216[/tex]

→ [tex]39y+117-6y=216[/tex]

→                   [tex]33y=99[/tex]

→                       [tex]y = \frac{99}{33}[/tex]

→                          [tex]= 3[/tex]

Now,

[tex]x = y+3[/tex]

  [tex]=3+3[/tex]

  [tex]=6[/tex]

hence,

The original number will be:

= [tex]10x+y[/tex]

= [tex]10\times 6+3[/tex]

= [tex]60+3[/tex]

= [tex]63[/tex]

Thus the above approach is right.

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Answer:

A'(5, 2), B'(5, -1), C'(6, -1), D'(6, 2)

Step-by-step explanation:

A transformation is the movement of a point from its initial position to a final position. If an object is transformed all its points are also transformed. Types of transformation are reflection, rotation, translation and dilation.

If a point O(x, y) is translated left by h unit, the new coordinate is O'(x-h, y) while if O(x, y) is translated right by h unit the new coordinate is O'(x+h, y)

If a point O(x, y) is translated up by h unit, the new coordinate is O'(x, y+h) while if O(x, y) is translated down by h unit the new coordinate is O'(x, y-h)

The location of the shape as shown in the diagram is:

A(3, 6), B(3, 3), C(4, 3), D(4, 6)

If the points are translated two yards East and four yards south, it means it is translated 2 unit right and 4 unit down i.e. (x+2, y-4). The new coordinates are:

A'(5, 2), B'(5, -1), C'(6, -1), D'(6, 2)

Answer:

ombining the expressions from parts E and F, for any given initial point (x, y), the coordinates of the new point after a translation of two yards east and four yards south are (x + 2, y + (-4)).

Step-by-step explanation:

this is more simple

Answer:

x = -1.29 and -2.71

Step-by-step explanation:

Use the quadratic formula, which is [tex]x=\frac{-b+\sqrt{b^2-4ac} }{2a}[/tex] and [tex]x=\frac{-b-\sqrt{b^2-4ac} }{2a}[/tex]

[tex]\frac{-8+\sqrt{8^2-4(2)(7)} }{2(2)}[/tex] and [tex]\frac{-8-\sqrt{8^2-4(2)(7)} }{2(2)}[/tex]

[tex]\frac{-8+\sqrt{8} }{4}[/tex] and [tex]\frac{-8-\sqrt{8} }{4}[/tex]

Further reduced down to:

[tex]\frac{-8+2\sqrt{2} }{4}[/tex] and [tex]\frac{-8-2\sqrt{2} }{4}[/tex]

In decimal form, to the hundredths place, both of these are:

-1.29 and -2.71

Answer:

x = 1/2

Step-by-step explanation:

Let's represent this in a mathematical way,

(x+1)^2 - x^2 = 2

Ok now we expand,

x^2 + 2x + 1 -x^2 = 2

rearrange,

x^2 - x^2 + 2x + 1 = 2

subtract,

2x + 1 = 2

subtract 1 from both sides,

2x + 1 - 1 = 2 - 1

2x = 1

Now divide 2 from both sides and get your answer,

x = 1/2

Answer:

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

[tex]x {}^{2} + 2x + 1 - x {}^{2} = 2[/tex]

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

[tex]x = 1 \div 2[/tex]

Answer:

[tex]\boxed{2\pm \frac{\sqrt{2}}{2}}[/tex]

Step-by-step explanation:

[tex]2x^2-8x=-7[/tex]

[tex]\sf Add \ 7 \ on \ both \ sides}.[/tex]

[tex]2x^2-8x+7=-7+7[/tex]

[tex]2x^2-8x+7=0[/tex]

[tex]ax^2 +bx+c=0[/tex]

[tex]\sf Apply \ quadratic \ formula.[/tex]

[tex]a=2 \ \ \ b=-8 \ \ \ c = 7[/tex]

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

[tex]x=\frac{-(-8)\pm\sqrt{(-8)^2-4(2)(7)}}{2(2)}[/tex]

[tex]x=\frac{8\pm\sqrt{64-56}}{4}[/tex]

[tex]x=\frac{8\pm\sqrt{8}}{4}[/tex]

[tex]x=\frac{8\pm2\sqrt{2}}{4}[/tex]

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

Answer:

P = 27.2c-7.2d

Step-by-step explanation:

It is given that,

The width of a rectangle is (8.3c-8.4d)

The length of a rectangle is (5.3c+4.8d)

The perimeter of a rectangle is equal to the sum of its all sides i.e.

P = 2(l+b)

P = 2(8.3c-8.4d+5.3c+4.8d)

P = 2[(8.3c+5.3c)+(4.8d-8.4d)]

P = 2(13.6c-3.6d)

⇒P = 27.2c-7.2d

Hence, the expression that represents the perimeter of the rectangle is 27.2c-7.2d.

Answer:

x+5=19

Step-by-step explanation:

i think that right let me know...:/

Answer:

x= 14

Step-by-step explanation:

a number x increased by 5, so it will be x + 5 and is in math means equals to so it becomes

x+5=19

19-5=x

14=x

Answer:

12y

Step-by-step explanation:

product means multiplycation so twelve times y is  12y

Answer:

13x3= 39

Step-by-step explanation:

10x3=30

3x3=9

30+9=39

Hope it helps!

Answer:

30 km/h car

Step-by-step explanation:

From analysis the   car traveling at 30 km/h has greater kinetic energy

we can deduce it from the expression of kinetic energy which is

[tex]KE=\frac{1}{2} mv^2[/tex]

Assuming the mass m= 1 kg

For the 30 km/h

[tex]KE=\frac{1}{2}*1*30^2 \\\\KE=\frac{1}{2}*1*900\\\\\KE=450 J[/tex]

For the 15 km/h

[tex]KE=\frac{1}{2}*2*15^2 \\\\ KE=\frac{1}{2}*2*225 \\\\\ KE=\frac{1}{2}*450 J\\\\\ KE=225 J[/tex]

Though the kinetic energy is a function of mass and velocity, but from our analysis the faster moving object has more KE

Answer:

The total volume of the solid is 1.67 cubic units.

Step-by-step explanation:

Each pyramid with a height of 2 units and a rectangular base with dimensions of 5 units × 0.25 units.

1/3 x (area of base) x height

= 1/3 x (5 x 0.25) x 2= 0.833

Therefore, the volume of each pyramid will be

= cubic units.

So, the total volume of the solid is (2 × 0.833) = 1.67 cubic units. (Answer)

Hope it helped ya!

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Tysmm

The total volume of the solid is 1.67 unit³.

Each thing in three dimensions takes up some space. The volume of this area is what is being measured. The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity.

Given:

Each pyramid has a height of 2 units.

and the rectangular base with dimensions of 5 units × 0.25 units.

So, the Volume of each Pyramid is

= 1/3 x (area of base) x height

= 1/3 x (5 x 0.25) x 2

= 0.833

and, the total volume of the solid

= (2 × 0.833)

= 1.67 cubic units.

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Answer:

A

Step-by-step explanation:

it is A for every output y , there is only one input x

Answer:

A

Step-by-step explanation:

Because all the x-intercepts are different. Whereas all the other ones have repeats of numbers in the x-intercepts.

Answer: C.) mAngleGLI = 2mAngleGLH

Step-by-step explanation:

Hope it helps!!!

For ray LH as the bisector of angle GLI, we can determine that the relation ∠GLI = 2∠GLH holds

An angle is formed from the intersection of two lines. Types of angles are acute, obtuse and scalene.

∠GLI is bisected by LH, hence:

∠GLH = ∠HLI (definition of bisection)

∠GLI = ∠GLH + ∠HLI (angle addition)

∠GLI = 2∠GLH

The information that can be used to determine this is ∠GLI = 2∠GLH

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Answer:

Step-by-step explanation:

Number of class intervals = 7

Class width = 5

Class intervals (heights)        Frequency (Number of boys)

130 - 135                                                     3                        

136 - 140                                                     5

141 - 145                                                      3

146 - 150                                                     5

151 - 155                                                      2

156 - 160                                                     1

161 - 165                                                      1

Therefore, frequency table given above will represent the distribution of the heights and number of students.