Here’s another one for you math lovers!

Answer:

m<4=40º

Step-by-step explanation:

11x+8=12x-4

-x=-12

x=12

(11•12)+8+x=180

140+x=140

x=40

2^5 = 32

Hope this helps! :)

Answer:

32

Step-by-step explanation:

\(2^{5}\)

= 2 × 2 × 2 × 2 × 2

= 4 × 4 × 2

= 16 × 2

= 32

Answer:

56

Step-by-step explanation:

56 would be the arc. reasoning is because line CG form an arch of 56 and Angle A and C also form a angle of 34

the sale price of the $495 television on sale for 20% off is $396.

the sale price by multiplying the original price of $495 by 20% (which is 0.20), which equals $99. Then you subtract $99 from the original price of $495, which gives you the sale price of $396. In conclusion, the sale price of the $495 television on sale for 20% off is $396.

The sale price of the $495 television on sale for 20% off is $396.


To find the sale price, you need to calculate the discount amount and subtract it from the original price. Follow these steps:

1. Convert the percentage discount (20%) to a decimal: 20% ÷ 100 = 0.2
2. Multiply the original price ($495) by the decimal discount: $495 × 0.2 = $99
3. Subtract the discount amount ($99) from the original price: $495 - $99 = $396


The sale price of the television is $396 after applying the 20% discount.

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Lola is correct because each expression has a value of 1. Option A is correct.

The expression is the relationship between variables and represented as y = ax + b is an example of a polynomial expression.

here,
Given expression
A = \([[a /b]^{-4}]^0\)
B = \([[a /b]^{0}]^{-4}\)

Since we know that,
a⁰ = 1

So,
A = [1]
B = 1⁻⁴ = 1

Thus, Lola is correct because each expression has a value of 1. Option A is correct.

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Answer:

8\(\pi\)

Step-by-step explanation:

area=\(\pi\)\(r^{2}\)

\(\pi\)\(4^{2}\)

16\(\pi\)

since it is a semicircle, cut that number in half.

Answer:

25.12units squared

Step-by-step explanation:

A = \(\frac{\pi r^2}{2}\) or \(\frac{3.14r^2}{2}\)

r = 4

3.14 x 4^2 = 50.24

50.24/2 = 25.12

Answer:

-137.8

^^^^^Hope this Helps!

The f(x) has a degree of 1, hence it is linear in nature while g(x) is a polynomial function because of the third degree.

The key features that they have in common are the y-intercept, domain, and range

Linear and quadratic equations

Linear equations are equations that has a degree of 1 while polynomial equations are equations that has a degree of 2 and above.

Given the following functions

f(x) = –4x + 5 and;

g(x) = x^3 + x^2 – 4x + 5

Since the f(x) has a degree of 1, hence it is linear in nature while g(x) is a polynomial function because of the third degree.

The key features that they have in common are the y-intercept, domain and range

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The  Trigonometric Identity sin² x + cos²x = 1 is: A. Pythagorean Identity.

The Pythagorean Identity which  tend to asserts that for every angle x, the sum of the squares of the sine and cosine of x is equal to one  is known as or called a  trigonometric identity.

The  Pythagorean identity can be expressed as:

sin² x + cos² x = 1

This identity is crucial to understanding trigonometry and tend to have several uses in numerous branches of science and engineering.

Therefore the correct option is A.

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The expression that represents the profit Justin made is 1.31c + 1.66m + 1.6b ( option C)

A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power. In other words, none of the exponents can be greater than 1. For example, x² is a variable raised to the second power, but x is a variable raised to the first power.

Justin earned $1.50c selling cookies but he spent $0.19c. Therefore the profit on cookies = $(1.5-0.19)c. = $1.31c

He earned $2.25m by selling muffins and spent $0.59m on the ingredients. Therefore the profit He made on muffins = $(2.25-0.59) = $1.66m

He earned $1.90b selling brownies and he spent $0.30b on ingredients. The profit he made on brownies = $1.90-$0.30 = $1.60b

Therefore the expression for the total profit = $(1.31c+ 1.66m+1.6b)

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Answer:

6 (I believe so)

Step-by-step explanation:

9n-24=4n+6

9n=4n+30

5n=30

n=6

Answer:

n=6

Step-by-step explanation:

9n - 24 = 4n + 6

-4n          -4n

5n - 24 = 6

     +24    +24

5n = 30

divide both sides by 5

n = 6

hope this helps!!!

Answer:

Yes

Step-by-step explanation:

If we need to find the distance between two points on a number line, we subtract one of the points from the other. We then take the absoulte value of the difference. You done this right.

The Volume of Remaining block is  (l w h - 1125) cm³

We have,

Edge of cube = 15 cm

So, Volume of cube

= 15 x 15 x 15

= 1125 cm³

Now, Volume of Remaining block

= Volume of cuboid - Volume of cube

= l w h - 1125 cm³

Here we just have to put the dimension of cuboid in place of l w h.

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The total surface area of the cylinder in question is 428.93 m².

How are the parameters of a cylinder determined?
A cylinder is a three-dimensional solid with a parallel circular base and top. The overall height of the cylinder is the perpendicular distance between the top and base.
The area with just curved surfaces, leaving the circular top and base, is referred to as the curved surface area.
Total Surface Area is the combined area of the bases and the curved surface.
Mathematically, curved surface area = 2πrh, where r = radius, h = height of cylinder;
Total surface area = 2πrh + 2πr², where r = radius, h = height of cylinder.

Given, the curved surface area of the cylinder = 352 m²
Height of the cylinder = h = 16 m
Using the formula established above, we have 2πrh = 352 --(i)
Substituting other values in (i), we get 2*3.14*r*16 = 352 ⇒ r = 3.50 m
Again, total surface area of cylinder = 2πrh + 2πr²
Substituting all values, we get TSA = (2*3.14*3.50*16) + (2*3.14*3.50²)
= 428.93 m²
Thus, the total surface area of the cylinder in question is 428.93 m².

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Answer:

Attached to this answer are some of the ways you could rewrite \(4*10^{-3}\)

Answer: 10 is your answer

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

Just keep looking at the faces.

Hopefully im correct, this is my 1st one :)

The perimeter of a semicircle the radius 3cm give you answer I’m terms of pi is P = 6 + 3pi.

The complete length of a semicircle's boundary is referred to as the circumference of a semicircle, which is another name for its perimeter. The diameter's length and one-half of the original circle's circumference are added to determine it. Linear units such as "inches," "feet," "metres," or "centimetres," etc. are used to indicate the circle's circumference.

Given that the radius of the semicircle is 3cm.

The formula for the perimeter of a semicircle is:

P = pi(r) + 2r

Substituting the value of r = 3 we have:

P = pi(3) + 2(3)

P = 6 + 3pi

Hence, the perimeter of a semicircle the radius 3cm give you answer I’m terms of pi is P = 6 + 3pi.

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Answer:

D

Step-by-step explanation:

The perimeter P of a rectangle is calculated as

P = 2l + 2w ( l is the length and w the width ) , then

2l + 2(9) = 5364

2l + 18 = 5364 ( subtract 18 from both sides )

2l = 5346 ( divide both sides by 2 )

l = 2673

Then

A = lw = 2673 × 9 = 24057 m² → D

(a) (i) (4+10i)² = -84 + 80i (ii) there are no solutions to the quadratic equation 2² + 6iz + 12 - 20i = 0 (b) The solution to the quadratic equation 2² + 6z + 5 = 0 is z = -3/2.

(a) (i) To calculate (4+10i)², we can use the formula for squaring a complex number

(4 + 10i)² = (4 + 10i) × (4 + 10i)

Expanding using the distributive property

= 4 × 4 + 4 × 10i + 10i × 4 + 10i × 10i

= 16 + 40i + 40i + 100i²

Since i² is equal to -1

= 16 + 40i + 40i - 100

= -84 + 80i

Therefore, (4+10i)² = -84 + 80i.

(ii) Now, let's solve the quadratic equation 2² + 6iz + 12 - 20i = 0 using the calculated value from (i).

2² + 6iz + 12 - 20i = 0

4 + 6iz + 12 - 20i = 0

16 - 20i + 6iz = 0

-84 + 80i + 6iz = 0

Comparing the real and imaginary parts, we have:

Real part: -84 + 6iz = 0

Imaginary part: 80i = 0

From the imaginary part, we see that

80i = 0, which implies that i = 0 (since i cannot equal zero).

Substituting i = 0 into the real part: -84 + 6(0)z = 0 -84 = 0

Since -84 does not equal zero,

there are no solutions to the quadratic equation 2² + 6iz + 12 - 20i = 0.

(b)The quadratic equation

2² + 6z + 5 = 0

2² + 6z + 5 = 0

4 + 6z + 5 = 0

9 + 6z = 0

6z = -9

z = -9/6

z = -3/2

Therefore, the solution to the quadratic equation 2² + 6z + 5 = 0 is z = -3/2.

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\( \huge \boxed{\mathfrak{Question} \downarrow}\)

\( \large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}\)

Given,

Now, we have to find f (-5). To find this, we just need to substitute -5 in the place of x.

So,

\( \sf \: f(x) = {3x}^{2} + x \\ \\ \sf \: \: Substitute \: x \: as \: - 5. \\ \\ \sf \:f( - 5) = 3( - 5) ^{2} + ( - 5) \\ \\ \sf \:Calculate \: -5 \: to \: the \: power \: of \: 2 \: and \: get \: 25. \\ \\\sf \: 3\times 25+5 \\ \\ \sf \:Multiply \: 3 \: and \: 25 \: to \: get \: 75. \\ \\\sf \: 75+5 \\ \\\sf \:Add \: 75 \: and \: 5 \: to \: get \: 80. \\ \\ = \boxed{\boxed{ \bf \: 80}}\)

Since there wer two penalties, each of five yard, the total change in yards due to the penalties is:

there was a change of 10 yards due to the penalties

Answer:

x=26

Step-by-step explanation:

4x+4+4x-32=180

8x-28=180

8x=180+28

x=26

Answer:

Step-by-step explanation:

(a) To find the initial population, we can set up a proportion based on the given information:

400 bacteria after 2 hours corresponds to the initial population P(0).

50,000 bacteria after 8 hours corresponds to P(8).

Using the proportion, we have:

(400 bacteria) / (P(0)) = (50,000 bacteria) / (P(8))

Cross-multiplying and solving for P(0), we get:

P(0) = (400 bacteria) * (P(8)) / (50,000 bacteria)

(b) To find an expression for the population after t hours, we can use the formula for exponential growth:

P(t) = P(0) * e^(kt),

where P(0) is the initial population and k is the constant relative growth rate. To find k, we can use the information given:

P(8) = P(0) * e^(k * 8)

Solving for k:

k = ln(P(8) / P(0)) / 8

Substituting this value of k into the equation for P(t):

P(t) = P(0) * e^((ln(P(8) / P(0)) / 8) * t)

(c) To find the number of cells after 3 hours, we can substitute t = 3 into the expression for P(t):

P(3) = P(0) * e^((ln(P(8) / P(0)) / 8) * 3)

(d) To find the rate of growth after 3 hours, we can take the derivative of the population function with respect to t:

P'(t) = (d/dt)(P(0) * e^((ln(P(8) / P(0)) / 8) * t))

(e) To find when the population will reach 200,000, we can set up the equation:

200,000 = P(0) * e^((ln(P(8) / P(0)) / 8) * t)

Solving for t will give us the time in hours.

Note: The values for P(0), P(8), and ln(x) should be substituted based on the specific information given in the problem.

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The main advantage of using a graphic calculator is that it speeds up the process of solving more difficult arithmetic problems for students.

A graphing calculator, often known as a graphics calculator or graphic display calculator, is a portable computer that can plot graphs, solve many equations at once, and carry out other variable-related activities. The most common graphing calculators are programmable calculators, which let the user design unique programs, generally for scientific, technical, or educational purposes. They feature big screens that show computations and several lines of text.

Numerous graphing calculators may be connected to sensors such as accelerometers, electronic thermometers, pH meters, weather stations, decibels, light meters, and other devices to operate as data recorders and as monitoring, polling, and communication tools with teachers. The use of such data in student laboratory tasks improves their understanding of math, particularly statistics and mechanics. 

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Answer:

Cost of 20 boxes = RS. 188

Step-by-step explanation:

Given:

Length of box = 30 cm  = 0.3m

Width of box = 40 cm = 0.4 m

Height of box = 50 cm = 0.5 m

Cost per m² = Rs. 10

Find:

Cost of 20 boxes

computation:

TSA of box = 2[lb + bh + hl]

TSA of box = 2[(0.3)(0.4) + (0.4)(0.5) + (0.5)(0.3)]

TSA of box = 2[0.12 + 0.2 + 0.15]

TSA of box = 0.94 m²

Cost of 20 boxes = 0.94 x 20 x 10

Cost of 20 boxes = RS. 188

Answer:

\(\dfrac{dV}{dt} =-4 \pi k (\dfrac{3}{4 \pi})^\dfrac{2}{3} }}V^{\dfrac{2}{3}}\)

k = 3.022

Step-by-step explanation:

Given that:

A spherical raindrop evaporates at a rate proportional to its surface area.

The surface area SA of a spherical object is given by the relation:

SA = 4πr²

Write down a differ- ential equation for its volume as a function as a function of time.

So; to differentiate Volume (V) in respect to time (t) ;then:

\(\dfrac{dV}{dt} =-k( 4 \pi r^2)\)

Likewise; we know known that the volume of a sphere V = \(\dfrac{4}{3} \pi r^3\)

Thus, from above;

\(3V = 4 \pi r^3\)

\(\dfrac{3V}{4 \pi} = r^3\)

\(r^3 = (\dfrac{3}{4 \pi })^{\dfrac{2}{3}}V^{\dfrac{2}{3}}\)

\(r^2 = 4 \pi( \dfrac{3}{4 \pi})\dfrac{2}{3}V\dfrac{2}{3}\)

Thus; solving the differential:

\(\dfrac{dV}{dt} =-k( 4 \pi * 4 \pi( \dfrac{3}{4 \pi})\dfrac{2}{3}V\dfrac{2}{3})\)

\(\dfrac{dV}{dt} =-4 \pi k (\dfrac{3}{4 \pi})^\dfrac{2}{3} }}V^{\dfrac{2}{3}}\)

So;

we are to find the constant proportionality K

If Volume V = 1 cm³ and the time = 10 sec

\(\dfrac{1}{10} =-4 \pi k (\dfrac{3}{4 \pi})^\dfrac{2}{3} }}(1)^{\dfrac{2}{3}}\)

0.1 =  - 4π k (0.3848 × 1)

0.1 =  - 4π k × 0.3848

4π k = 0.3848/0.1

4π k  = 3.848

k = 3.848/4π

k = 3.022

864 ounces of A grade coffee and 1008 ounces of B grade coffee. The quantity of A-grade coffee is 864 ounces, and the quantity of B-grade coffee is 1008 ounces.

The coffee house blends A-grade and B-grade coffee into two distinct packages: Economy blend and superior blend.

The economy blend contains 2 ounces of A grade coffee and 7 ounces of B grade coffee while the superior blend contains 6 ounces of A grade coffee and 3 ounces of B grade coffee.

Let x be the number of economy blend packages sold and y be the number of superior blend packages sold respectively.

The profit on the sale of each economy blend is $4, and the profit on each superior blend package is $5.The cost price of 1 economy blend = 2(0.72) + 7(0.28) = $2.48

The cost price of 1 superior blend = 6(0.72) + 3(0.28) = $5.16.

The revenue earned from the sale of x economy blend packages and y superior blend packages respectively are:

Revenue earned from the sale of x economy blend packages = 4xRevenue earned from the sale of y superior blend packages = 5y

The total amount of A-grade coffee used in x economy blend packages and y superior blend packages respectively are:

Amount of A-grade coffee in x economy blend packages = 2x + 6y

Amount of A-grade coffee in y superior blend packages = 7x + 3y

The total amount of B-grade coffee used in x economy blend packages and y superior blend packages respectively are:

Amount of B-grade coffee in x economy blend packages = 7x + 3y

Amount of B-grade coffee in y superior blend packages = 1008 - (7x + 3y) = 1008 - 7x - 3y

Total ounces of coffee in a package = 16 ounces, since 1 pound is equal to 16 ounces. The maximum profit is obtained when the total profit is maximized. The total profit earned is given by:

Total Profit, P = Revenue - Cost

P = (4x + 5y) - (2.48x + 5.16y)

P = 1.52x - 0.16y

To maximize the profit, differentiate P with respect to x and equate to 0. dp/dx = 1.52

Equating dp/dx to 0, we get:

dp/dx = 1.52 = 0x = 1.52/0.16 = 9.5

To maximize the profit, the coffee house should make 9 economy blend packages and (16-9) 7 superior blend packages. Answer: Economy Blend = 9, Superior Blend = 7.

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The maximum profit of $700 is obtained by making 96 packages of the economy blend and 112 packages of the superior blend.

Given that for a given week, Lena's Coffee House has available 864 ounces of A grade coffee and 1008 ounces of 8 grade coffee. These are blended into l-pound packages as follows:

an economy blend that contains 2 ounces of A grade coffee and 7 ounces of B grade coffee, and a superior blend that contains 6 ounces of Agrade coffee and 3 ounces of B grade coffee.

Let's assume the number of packages of the economy blend to be x and the number of packages of the superior blend to be y.

The objective is to find the number of packages of each blend it should make to maximize its profit for the week.

The total amount of A-grade coffee in the economy blend would be 2x ounces while that in the superior blend would be 6y ounces.

The total amount of A-grade coffee that Lena's Coffee House has for the week is 864 ounces.

This can be represented by the inequality 2x + 6y ≤ 864.

The total amount of B-grade coffee in the economy blend would be 7x ounces while that in the superior blend would be 3y ounces.

The total amount of B-grade coffee that Lena's Coffee House has for the week is 1008 ounces. This can be represented by the inequality 7x + 3y ≤ 1008.

The profit from selling an economy blend package is $4 while that from selling a superior blend package is $5. The total profit can be given by the equation, Profit = 4x + 5y.

The objective is to maximize the profit Z subject to the given constraints:

Maximize Z = 4x + 5y

Subject to the constraints:2x + 6y ≤ 8647x + 3y ≤ 1008x ≥ 0, y ≥ 0.

Rewriting the constraints in slope-intercept form,

2x + 6y ≤ 864y ≤ -1/3x + 1447x + 3y ≤ 1003y ≤ -7/3x + 336

Now, we have to find the corner points of the feasible region. These corner points will be the solutions of the two equations given by the lines passing through the vertices of the feasible region.

Let's find the corner points by solving the system of equations,

2x + 6y = 864

7x + 3y = 1008

x = 0,

y = 0

x = 0,

y = 336/3

x = 144,

y = 0

x = 96,

y = 112/3

Now, substituting the values of x and y in the objective function, we can calculate the profit at each of the corner points as follows:

At (0, 0),

Z = 0At (0, 336/3),

Z = 560At (96, 112/3),

Z = 700At (144, 0),

Z = 576

Therefore, the maximum profit of $700 is obtained by making 96 packages of the economy blend and 112 packages of the superior blend.

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Answer:

615.44 cm^2

Step-by-step explanation:

here r, radius is 14 cm and π as 3.14

area of circle = π\(r^{2}\)

3.14 * 14^2

3.14 * 14 * 14

615.44cm^2

Answer:

The area of the hubcap is about \(\boxed{\tt{615.44}}\) cm².

Step-by-step explanation:

Here's the required formula to find the area of hubcap :

\(\longrightarrow{\pmb{\sf{Area_{(Circle)} = \pi{r}^{2}}}}\)

Substituting all the given values in the formula to find the area of hubcap :

\(\longrightarrow{\sf{Area_{(Hubcap)} = \pi{r}^{2}}}\)

\(\longrightarrow{\sf{Area_{(Hubcap)} = 3.14{(14)}^{2}}}\)

\(\longrightarrow{\sf{Area_{(Hubcap)} = 3.14{(14 \times 14)}}}\)

\(\longrightarrow{\sf{Area_{(Hubcap)} = 3.14{(196)}}}\)

\(\longrightarrow{\sf{Area_{(Hubcap)} = 3.14 \times 196}}\)

\(\longrightarrow{\sf{Area_{(Hubcap)} = 615.44}}\)

\(\star{\underline{\boxed{\sf{\purple{Area_{(Hubcap)} = 615.44 \: {cm}^{2}}}}}} \)

Hence, the area of hubcap is 615.44 cm².

\(\rule{300}{2.5}\)

Answer:

Step-by-step explanation:

Example it’s called the sum