The function a represents the cost of manufacturing product A, in hundreds of dollars, and the function b represents the cost of manufacturing product B, in hundreds of dollars.

a(t)=5t+2
b(t)=7t2-2t+4

Find the expression that describes the total cost of manufacturing both products, a(t) + b(t).

A. 7t2 + 7t - 6
B. 7t2 - 3t + 6
C. 7t2 - 7t + 2
D. 7t2 + 3t + 6

Answer:

4

Step-by-step explanation:

Let b represent the number of birds. Then the cost of care for b birds and 16-b cats was ...

4.50b +6.50(16-b) = 96.00

-2.00b = -8.00 . . . . . . . . . . . . simplify, subtract 104

b = 4 . . . . . . . . . . . . . . . . . . . . .divide by -2

The number of birds at the shelter on Thursday was 4.

Answer:

a) (0.08)^6

Step-by-step explanation:

Given in the question,

[tex]\sqrt{0.08^{12} }[/tex]

As we know that

[tex]\sqrt{x} = x^{1/2}[/tex]

So,

[tex]\sqrt{0.08^{12}[/tex] = [tex]0.08^{12(1/2)}[/tex]

[tex]0.08^{12/2}[/tex]

[tex]0.08^{6}[/tex]

Answer:

about 0.08087

Step-by-step explanation:

The statistics functions of your graphing calclulator can help you with that. It is a good idea to learn to use them.

Answer:

A. y = 8.34x + 10

Step-by-step explanation:

The first choice is appropriate to the situation where y=10 when x=0 and where y increases by 83.4 when x increases by 10.

___

The equation of selection D is the same and is also appropriate, but the graph does not match the equation. The equations of the other choices are incorrect, as are the graphs.

The linear equation which represents the data is : y = 8.34x + c. Hence, correct option is A.

The linear equation for the graph can be expressed in the form :

b = change in y / change in x

Change in y :

Change in x :

Hence , slope , b = (83.4 /10) = 8.34

The value of the intercept, c ;

93.4 = 8.34(10) + c

93.4 = 83.4 + c

c = 10

Hence, the linear equation is :

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Answer:

The difference is that the simple interest gives you interest only on the deposited amount in the account while the compound interest is calculated over the deposited amount and the previous interest amount added to the deposited amount.

Step-by-step explanation:

The difference between simple and compound interest is that simple interest is calculated only on the principal amount, while compound interest is earned on past interest.

The difference between simple and compound interest in a savings account is that simple interest is an interest rate calculation only on the principal amount, while compound interest is interest that is earned on past interest. This means that with compound interest, the total amount of savings will grow dramatically over time. To illustrate this, consider the example of putting $1,000 in a savings account with 10% interest. With simple interest, after one year, you will have $1,100. But with compound interest, if you leave the $1,100 in the account and continue to earn 10% interest, you will have $1,210 at the end of year two.

Answer:

A ) subtract the second equation from the first equation

Step-by-step explanation:

2x + 3y = 7

2x - 4y = -5

subtracting the second equation from the first equation we get,

7y = 12

y=12/7

This is the correct option

Answer:

A ) subtract the second equation from the first equation

Step-by-step explanation:

Let's consider the following system of equations.

2x + 3y = 7

2x = 4y - 5

If we subtract the second equation from the first equation, we get:

2x + 3y - 2x = 7 - (4y - 5)

3y = 7 - 4y + 5

7y = 12

y = 12/7

Then, we can use any of the original equations and solve for x.

2x = 4y - 5

2x = 4(12/7) - 5

x = 13/14

Answer:

The length of the edge of the cube = 4 inches

Step-by-step explanation:

* Lets describe the cube

- It has 6 faces all of them are squares

- It has 8 vertices

- It has 12 equal edges

∵ The volume of any formal solid = area of the base × height

∵ The base of the cube is a square

∴ Area base = L × L = L² ⇒ L is the length of the edge of it

∵ All edges are equal in length

∴ Its height = L

∴ The volume of the cube = L² × L = L³

* Now we have the volume and we want to find the

 length of the edges

∵ Its volume = 64 inches³

∴ 64 = L³

* Take cube root to the both sides

∴ ∛64 = ∛(L³)

∴ L = 4 inches

* The length of the edge of the cube = 4 inches

The length of the edges of the cube is 4 inches.

Given that the volume V  is 64 cubic inches, we can set up the equation:

[tex]\[ a^3 = 64 \][/tex]

To solve for a , we take the cube root of both sides:

[tex]\[ a = \sqrt[3]{64} \][/tex]

The cube root of 64 is 4, since [tex]\( 4^3 = 4 \times 4 \times 4 = 64 \).[/tex]

Therefore, the length of the edges of the cube is 4 inches.

Vertex is at (-1,-7), because the |x+1| moves the graph left 1 and -7 moves the graph down 7.

Answer:

the second answer is a

Step-by-step explanation:

edge 2020

When dealing with numbers, we find the LCM by factoring the numbers, and then choosing all the primes appearing, with the highest exponent possible.

Similarly, we will factor the polynomials first:

[tex] x^4+3x^3 = x^3(x+3)[/tex]

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

[tex]x^3+6x^2+9x = x(x^2+6x+9) = x(x+3)^2[/tex]

The following factors emerged:

So, the LCM is

[tex]x^3(x-3)(x+3)^2[/tex]

➷ Find the total data in the first row:

90 + 30 = 120

Now divide each of these values by the total:

(30/120) = 0.25

(90/120) = 0.75

It would be 0.25 in the first box and 0.75 in the second.

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

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Answer:

Group1 .18

Group2 = .54

Step-by-step explanation:

To find the relative frequency, you divide the number by the total number

The total number is 30+90+14+32 = 166

Category 1 Group 1 has 30 in it

The relative frequency is 30/166 = .180722892 = .18

Category 1 Group 2 has 90 in it

The relative frequency is 90/166 =.542168675=.54

Answer: 14 gallons

Step-by-step explanation:

Let's call the total gallons of gas Abdul's tank can hold x.

Then, based on the information given in the problem, you can write the following expression:

[tex]\frac{1}{5}x+7=\frac{7}{10}x[/tex]

Therefore, when you solve for x, you obtain the following result:

[tex]\frac{1}{5}x+7=\frac{7}{10}x\\\\\frac{1}{5}x-\frac{7}{10}x=-7\\\\-\frac{1}{2}x=-7\\\\-x=(-7)(2)\\x=14[/tex]

Answer:

Part A:  A (6 , 11) , B (5 , 6) , C (7 , 1) , D (0 , 8)

Part B:  A (-6 , -11) , B (-5 , -6) , C (-7 , -1) , D (0 , -8)

Step-by-step explanation:

* Lets study the reflection about the two axes X and Y

- The distance between the point and the axes of reflection =

 the distance between its image and the axes

- The point and the its image are on opposite sides of the axes

- If a point (x , y) reflected about x axis, that means the point

  will move vertically

- Moving vertically means we will change the sign of the y-coordinates

∴ The image of (x , y) after reflection about x-axis is (x , -y)

- If a point (x , y) reflected about y axis, that means the point

  will move horizontally

- Moving horizontally means we will change the sign of the x-coordinates

∴ The image of (x , y) after reflection about x-axis is (-x , y)

* Now lets use the explanation above to solve our problem

- At first lets right the original point of the quadrilateral ABCD

∵ A (-6 , 11) , B (-5 , 6) , C (-7 , 1) , D (0 , 8)

Part A: The y-axis is the line of reflection

- Lets change the signs of x-coordinates in all points

∴ The new points after reflection about y-axis is:

  A (6 , 11) , B (5 , 6) , C (7 , 1) , D (0 , 8)

- Note: The point D does not change because x-coordinate is 0

            and there is no sign for the 0

Part B: The x-axis is the line of reflection

- Lets change the signs of y-coordinates in all points

∴ The new points after reflection about x-axis is:

  A (-6 , -11) , B (-5 , -6) , C (-7 , -1) , D (0 , -8)

I’m pretty sure it’s A

Answer: A

Step-by-step explanation:

Answer:

perimeter = (18 +9π) cm

area = (81 -20.25π) cm^2

Step-by-step explanation:

The perimeter of the shaded area is the circumference of the circle added to two sides of the square. The circumference of the circle is π times the diameter, so the perimeter is ...

p = 2(9 cm) + π(9 cm) = (18 +9π) cm

___

The area of the shaded portion is the difference between the area of the square and the area of the circle. The area of the square is the square of the diameter. The area of the circle is π/4 times that value.

A = (9 cm^2) + (π/4)(9 cm^2) = (81 +20.25π) cm^2

_____

Comment on circle area

The formula you often see is ...

A = πr^2 . . . . r is the radius

since r = d/2, where d is the diameter, this can also be written as ...

A = π(d/2)^2 = (π/4)d^2

Here, the diameter of the circle is the same as the side length of its enclosing square, so the area of the circle is π/4 times the area of the enclosing square.

Answer:

Area= [tex]81-\frac{81}{4}\pi[/tex]

Perimeter= [tex]9\pi +18[/tex]

Answer:

both are

Step-by-step explanation:

A number, or a polynomial, is "divisible" by a "factor." Since (k+5) is a factor of (k^2-25), (k^2-25) is divisible by (k+5). Both Eleanor and Isabel are correct in their description.

Answer:

  9.4 ft

Step-by-step explanation:

The formula for the circumference of a circle is ...

  C = πd . . . . . where d represents the diameter

Putting your numbers into this equation gives ...

  C = 3.14·(3 ft) = 9.42 ft

Rounding as required gives the length of fence as 9.4 ft.

To find the length of fencing needed for a circular flower bed, use the formula C = π * d, where C is the circumference and d is the diameter of the circle.

To find the length of fencing needed to go around a circular flower bed, we need to calculate the circumference of the circle. The circumference can be found using the formula C = π * d, where π is approximately 3.14 and d is the diameter of the circle. In this case, the diameter of the flower bed is 3 feet, so the circumference is 3.14 * 3 = 9.42 feet.

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Answer:

y=3/4 *x

Step-by-step explanation:

1. the given equation is the equation of line in slope-interception form (y=kx+b), where 3/4 is 'k' and (-4) is 'b'.

2. if the system of the two equations has no solution, it means, the 2d line is parallel to the given one, then 'k' of the 2d line is the same value.

3. common view of the equation of the 2d line is y=3/4 *x+b, where 'b' is number. For example, y=3/4x; y=3/4 *x+1; y=3/4 *x-5/8, etc.

One example of a linear function that generates a system without a solution is given by:

[tex]y = \frac{3}{4}x + 5[/tex]

A linear function is modeled by:

y = mx + b

In which:

If two equations have the same slope but different intercepts, they never  intersect each other, that is, a system without solutions is generated. Hence, one possible example in this problem is given by:

[tex]y = \frac{3}{4}x + 5[/tex]

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so calculate the Volume of the water that is already in the tank

so l x w x h

4 x 18 x 12

=864cm^3 is in the tank

find the total volume of the tank:

6 x 18 x 12

=1296cm^3

and subtract the current from the total to find what you need:

1296cm^3 - 864cm^3

= 432 cm^3

you can also find how much you need by using the remaining 2cm from the height (6-4=2) and use the volume formula with 2 substituted as the height and you’ll get the same answer

The amount of water needed to fill the tank is 432 cm³.

Volume is a three-dimensional quantity used to calculate a solid shape's capacity. That means that the volume of a closed form determines how much three-dimensional space it can fill.

Volume of cuboid = lwh

The tank is filled with water to a height of 4 centimeters.

The dimension of the tank is width is 18 cm, length is 12 cm, and height 6 cm.

So, the Volume of water present in the tank

= l x w x h

= 4 x 18 x 12

= 864 cm³

Now, the total Volume of tank

= 6 x 18 x 12

= 1296 cm³

So, the amount of water needed to fill the tank

= 1296 - 864

= 432 cm³

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Answer:

5/18

Step-by-step explanation:

The desired fraction can be found by dividing the fraction of distance by the fraction of hours:

(1/6 distance)/(3/5 hour) = (1/6·5/3) distance/hour = 5/18 distance/hour

Then 5/18 of the distance can be covered in one hour.

Answer:

5/18

Step-by-step explanation:

Answer:

48.3 cm^2

Step-by-step explanation:

The area of the enclosing square is that of a square 15 cm on a side, so is ...

square area = (15 cm)^2 = 225 cm^2

The white area is that of a quarter-circle of radius 15 cm, so that area is ...

quarter-circle area = (1/4)πr^2 = (π/4)·(15 cm)^2 = 56.25π cm^2 ≈ 176.7 cm^2

Then the yellow area is the difference ...

yellow area = square area - quarter-circle area

= (225 cm^2) - (176.7 cm^2)

yellow area = 48.3 cm^2

Answer:

22 fish

Step-by-step explanation:

cella has 12 fish. micheal has ten more 12+10=22. combind 22+12=34

Answer:

22 fish

Step-by-step explanation:

Answer:

(2, 5)

Step-by-step explanation:

Dilating 3, means that the values were multiplied by 3.  To find their original location, divide the x and y values of the new point by 3...

(6/3, 15/3) = (2, 5)

In a dilation with a factor of 3, to find the original coordinates from the dilated point (6,15), we divide each coordinate by the dilation factor. The original point A was at (2,5).

In mathematics, dilation is a geometric transformation that resizes a figure, maintaining its shape but changing its size. It involves multiplying the coordinates of each point in the figure by a constant scale factor. If the scale factor is greater than 1, the figure expands, while a scale factor between 0 and 1 results in a reduction. Dilation is commonly used in geometry to study similarity between shapes, where corresponding angles remain equal, and corresponding sides are proportional. It plays a crucial role in various mathematical concepts and applications, such as transformations, similarity, and geometric modeling.

In a dilation, the points move closer or farther away from a certain point, called the center of dilation, by a certain factor. In this case, the dilation factor is given as 3, so the original point is gained by dividing the coordinates of the image by the dilation factor. The image of point A is given as (6,15). To find the original point A, we divide both coordinates by the dilation factor.

So, the original location of point A is (2,5).

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Seven thousand sixty-five fifty six

Answer:

seven hundred sixty-five thousand fifty-six

Step-by-step explanation:

Your Welcome

Answer:

The acute angles of the rhombus are 80°; the obtuse angles are 100°.

Step-by-step explanation:

Since each diagonal bisects the angle of the rhombus, the given conditions are the same as saying the angles of the rhombus are in the ratio 4:5. Adjacent angles add to 180°, and the sum of the ratio units is 4+5=9. So each ratio unit stands for 180°/9=20° of angle, and the angles are ...

80° : 100°

The angles of the rhombus are 80° and 100°.

Answer:

Your answer is

x = -4, 6 or (b)

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~abelxoconda

The solution of the equation for the value of x will be (-4,6).

The polynomial equation with the degree of two will be termed as the quadratic equation or the highest power of the variable is 2 in the quadratic equation.

The given equation is:-

=x²-2x-24

Now we will split the equation

=x²-6x+4x-24

=x(x-6)+4(x-6)

=(x-6)(x-4)

Hence the value of x will be -4 and 6.

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Explanation:

In a function, each x-value has one y-value.

___

That is the definition of a relation that is a function.

Final answer:

Each x-value in a function has exactly one corresponding y-value. Functions map elements of the domain to unique elements in the range, which can be represented graphically and must pass the vertical line test. The derivative in calculus, such as dy/dx, reflects the rate of change between these variables.

Explanation:

In a function, each x-value has one corresponding y-value. This is a foundational concept in mathematics that defines a relationship whereby each input (or x-value) in the function produces exactly one output (or y-value). Essentially, a function maps each element of the domain to exactly one element in the range.

An example of a function is y = f(x), which could represent a linear function like y = 3x + 2. In this case, for every x-value, there is a specific y-value determined by the function's formula. So if x were 1, then y = 3(1) + 2 = 5. The graphical representation of a function, such as its curve or line on a coordinate plane, must pass the vertical line test. That means if you draw a vertical line through any point on the graph, it should intersect the graph at no more than one point, confirming that each x-value has only one y-value.

Understanding functions is pivotal in different areas of mathematics, including calculus where the derivative of a function represents the rate of change of the y-value with respect to the x-value. In the case of the linear function y = 6+3x, the derivative dy/dx is constant at 3, implying that for every unit increase in x, y will increase by 3 units.

Answer:

  $491.37

Step-by-step explanation:

The appropriate formula for the future value of a single investment is ...

  A = P(1 +r/n)^(nt)

where P is the principal invested (389), r is the annual rate (0.039), n is the number of compoundings per year (12), and t is the number of years (6).

Putting the given numbers into the formula, you get ...

  A = 389·(1 +.039/12)^(12·6) = 389·1.00325^72 ≈ 491.37

The total in the account after 6 years will be $491.37.

Answer:

y = 2/3 x -2

Step-by-step explanation:

Slope intercept form is y = mx+b where m is the slope and b is the y intercept

We need to solve for y

2x-3y = 6

Subtract 2x from each side

2x-2x-3y=-2x+6

-3y = -2x+6

Divide  by -3

-3y/-3 = -2/-3x+6 /-3

y = 2/3 x -2

The slope is 2/3 and the y intercept is -2

Answer:

the answer is C.Peter walks at a rate of 13/4 miles per hour.  hope this was helpful

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Answer:

The answer A

Step-by-step explanation:

B: You need a side that is longer than 2 equal sides. B is incorrect.

A: Try

9^2 + 12^2 = 15^2 if that works, A will work.

81 + 144 = 225

This works. I used these numbers because they were easier to see.

0.9^2 + 1.2^2 = 1.5^2

0.81 + 1.44 = 2.25

2.25 = 2.25

That is the answer A

But we have to check the  other two.

C:

0.9^2 = 0.81

1.2^2 = 1.44

1.8^2 = 3.24   This won't work. 3.24 is just too big.

D:

0.9^2 = 0.81

0.6^2 = 0.36

1.5^2 = 2.25   It's too far away.