During a cake-eating contest, Dave ate three and a half pizza and Daisy
ate two-thirds of a pizza. How many pizzas did they eat altogether?

HELP EXPLAIN STEP BY STEP!

Answer:

8x^4y^2

Step-by-step explanation:

Just plug it in to the calculator and that will be your result.

Percent of residents have at least one traffic violation with 80% held a valid driver’s license,10% has at least one traffic violation and 30% does not have valid license is 14%.

As given,

A=Person has a driver license

A'=Person does not have a driver license

P(A)=0.80

P(A')=0.20

For A, 10% has at least one traffic violation

For A', 30% had at least one traffic violation.

Probability with at least one traffic violation

=Probability of( A and one traffic violation +A' and one traffic violation)

=0.80(0.10)+0.20(0.30)

=0.08+0.06

=0.14

=14%

Therefore, percent of the residents with at least one traffic violation is 14%.

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Answer:

see explanation

Step-by-step explanation:

calculate the slope m using the slope formula and equate to the given slope

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

(a)

(x₁, y₁ ) = (- 3, - 4 ) and (x₂, y₂ ) = (0, y )

[tex]\frac{y-(-4)}{0-(-3)}[/tex] = [tex]\frac{y+4}{0+3}[/tex] = [tex]\frac{y+4}{3}[/tex] , then

[tex]\frac{y+4}{3}[/tex] = 2 ( multiply both sides by 3 )

y + 4 = 6 ( subtract 4 from both sides )

y = 2

ordered pair is (0, 2 )

(b)

(x₁, y₁ ) = (- 2, 2 ) and (x₂, y₂ ) = (x, 5 )

[tex]\frac{5-2}{x-(-2)}[/tex] = [tex]\frac{3}{x+2}[/tex] , then

[tex]\frac{3}{x+2}[/tex] = [tex]\frac{3}{7}[/tex] ( cross- multiply )

3(x + 2) = 21 ( divide both sides by 3 )

x + 2 = 7 ( subtract 2 from both sides )

x = 5

ordered pair is (5, 5 )

(c)

(x₁, y₁ ) = (x, 5 ) and (x₂, y₂ ) = (1, - 5 )

[tex]\frac{-5-5}{1-x}[/tex] = [tex]\frac{-10}{1-x}[/tex] , then

[tex]\frac{-10}{1-x}[/tex] = [tex]\frac{-5}{2}[/tex] ( cross- multiply )

- 5(1 - x) = - 20 ( divide both sides by - 5 )

1 - x = 4 ( subtract 1 from both sides )

- x = 3 ( multiply both sides by - 1 )

x = - 3

ordered pair is (- 3, 5 )

(e)

(x₁, y₁ ) = (- 6, y ) and (x₂, y₂ ) = (8, 2 )

[tex]\frac{2-y}{8-(-6)}[/tex] = [tex]\frac{2-y}{8+6}[/tex] = [tex]\frac{2-y}{14}[/tex] , then

[tex]\frac{2-y}{14}[/tex] = - [tex]\frac{1}{7}[/tex] ( cross- multiply )

- 7(2 - y) = 14 ( divide both sides by - 7 )

2 - y = - 2 ( subtract 2 from both sides )

- y = - 4 ( multiply both sides by - 1 )

y = 4

ordered pair is (- 6, 4 )

The runner should run for roughly around 54 minutes.

To find how many minutes must the runner run:

Minutes required are:

Therefore, the runner should run for roughly around 54 minutes.

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Answer:

36 cm

Step-by-step explanation:

The area of one wall of the room is 72 square feet.

The area of a square is given by -

A{S} = a²

where -

{a} is side of square.

Given is a square room has a floor area of 144 square feet. The height of the room is 6 feet.

It is given that -

floor area = 144

a² = 144

a = √(144)

a = √(12 x 12)

a = 12

The area of the wall will be equivalent to -

A{W} = h x a

A{W} = 6 x 12

A{W} = 72 square feet.

Therefore, the area of one wall of the room is 72 square feet.

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Answer:

KM = 1.5

Step-by-step explanation:

The first piece of info we get is that L is the midpoint of JM. This means that L = JM/2. The second piece of information provided is that K is the midpoint of JL, which means K = JL/2. We know that JL = 1, so we can plug it into the equation to help us figure out the problem. You can also illustrate to solve this problem, as I do here.  

Since JL = 1...

K = 1/2, K = 0.5

________________________________________________

J                       K(0.5)                        L                                          M                                                                                                  

 ___________           __________

        0.5                               0.5

Now with this information, we know that 0.5 represents the distance of 1/4 of JM. We know that KM is 3/4 of the number line, and we know that 1/4 of the line is 0.5. We multiply 0.5 * 3 to get our final answer.

FINAL ANSWER: KM = 1.5

Answer:

Animal bread

food dog

animal— dog

food — bread

slope = Y2 - Y1

————

X2 - X1

Usando una función lineal, tenemos que:

Con cada año adicional, la cantidad en la cuenta es incrementada en 60.

Una función lineal es modelada por:

y = mx + b

En el cual:

En este problema, hay que la pendiente es de 60, puesto que en cada año la cantidad aumenta en $60, por eso:

Con cada año adicional, la cantidad en la cuenta es incrementada en 60.

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Answer:

-12

Step-by-step explanation:

Distribute

20y+20-y=16y-16

Combine like terms

19y+20=16y-16

subtract 16y from 19y and subtract 20 from -16

3y=-36

Divide by 3

y=-12

4x+6y=5 and 2x+4y=3 are the 2 supplied lines. We must solve two simultaneous equations in order to determine the location at where these two lines cross.

When we multiply the second equation by two, we obtain the result 4x+8y=6. Next, we subtract this from the first equation to get -2y = -1, which equals y=1/2. N's coordinates are therefore (+1/2, +1/2).

The line we need to identify now goes through this point and is perpendicular to the line x+2y=0; its slope is -1/2 (the slope of the line [tex]ax+by+c=0[/tex] is -a/b). With m1*m2=-1, the line perpendicular to this one has a slope of 2. Consequently, the line that we must identify The slope of the equation is 2, and it goes through N. In order to simplify the equation, (y-1/2) = 2*(x-1/2), which results in 2y-1 = 2*(2x-1) and 2y-1 = 4x-2 and 4x-2y-1=0. The necessary equation is as follows.

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Lambert calls the difference between the angle-sum of a triangle and 180 degrees the defect.

Therefore, Lambert calls the difference between the angle-sum of a triangle and 180 degrees the defect.

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Answer:

75%

Step-by-step explanation:

15 over 20 is equal to 3/4 and 3/4 is 75%

Step-by-step explanation:

-2x - 7 > 1

-2x > 8

-x > 4

x < -4

that is a continuous line from -4 all the way to the left, and the dot on -4 is empty (meaning : it is not included due to the "<" symbol).

x - 2 >= -1

x >= 1

that is a continuous line from +1 all the way to the right, and the dot on +1 is filled (meaning : is IS included due to the ">=" symbol.

Answer:

A person will pay $5.37

Step-by-step explanation:

6.8 pounds of bananas x $0.79 per pound = $5.37.

I hope this helps and have a blessed day! :)

The equation representing Main Street if Main Street passes through the point (5, 2) is; y = 2x - 8

We are given the linear equation that represents 5th Avenue as;

y = 2x - 3

Now, main street is parallel to 5th avenue and as such will have the same slope.

Thus, equation of the line passing through (5, 2) representing main street is;

y - 2 = 2(x - 5)

y - 2 = 2x - 10

y = 2x - 10 + 2

y = 2x - 8

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Answer:64

Step-by-step explanation: 12 x 2 = 24 and 20 x 2 = 40 and if you add it all up it equals 64 cubic yards please tell me if i'm wrong

Answer:

=> 7+u = 14; u = 7

Step-by-step explanation:

The sum of 7 and u is 14

=> u + 7 = 14

=> u = 14-7

=> u = 7

In order for Abraham to receive an A, he will need to earn a total of 1.5 points, which is the rational number that may be used to represent that amount.

It is important to keep in mind that a number is considered rational if it can be expressed in the form of a fraction.

It is possible when decimals and numbers have worked effectively.

In light of the fact that Abraham must get a grade of A– in mathematics in order to achieve an A, the rational number that can be used to symbolize the number of points that Abraham must earn in order to get an A will be the number 1.5.

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Mansi can cover 1 mile of the distance in just 12 minutes.

The unit rate can be expressed in any unit for instance minute per mile, miles/hour, etc

There is independent quantity, and a quantity which depends on it (dependent quantity). When independent quantity moves by a unit measurement (single unit increment), the increment in dependent quantity is called rate of increment of dependent quantity per unit increment in independent quantity.

Lets consider Mansi covers 3 miles in 36 minutes, her unit rate in minutes per mile is expressed as:

Unit rate = 36min/3miles

Unit rate = 12 minutes/mile

Here,

This shows that Mansi can cover 1 mile of the distance in just 12 minutes.

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Answer:

1

Step-by-step explanation:

The amount Juan & Jaquan each had in sales in July is approximately $725 and the equation for Juan's Earning is 525 + 1.75x and the equation for Jaquan's Earning 609 + 1.015x.

Unitary method:

Unitary method is defined as the process by which we find the value of a single unit from the value of multiple units and the value of multiple units from the value of a single unit.

Given,

Juan and Jaquan work for separate companies.

Juan earns $15 for each sale plus 5% commission.

Jaquan earns $21 for each sale plus 3.5% commission.

In July, Juan made 35 sales and Jaquan made 29 sales.

They made the same total salary.

Here we need to find the amount Juan & Jaquan each had in sales in July.

Let x be the total number of sales in July.

So, based on the given details we can written it as,

Juan earns,

=> 15 + 5%x

=> 15 + 0.05x

And Jaquan earns,

=> 21 + 3.5%x

=> 21 + 0.035x

So, in July, Juan made 35 sales and Jaquan made 29 sales,

Then

=> 35(15 + 0.05x)

=> 525 + 1.75x  -----------(Juan's Earning)

=> 29(21 + 0.035x)

=> 609 + 1.015x -----------(Jaquan's Earning)

And also in July, they made the same total salary.

So,

Juan's Earning = Jaquan's Earning

Then,

=> 525 + 1.75x = 609 + 1.015x

=> 1.75x - 1.0.15x = 609 - 525

=> 0.735x = 84

=> x = 84 / 0.735

=> x = 114.28

So, the total amount they earned in July is,

=> 525 + 1.75(114.28) = 609 + 1.015(114.28)

=> 525 + 199.99 = 609 + 115.99

=> 724.99 = 724.99

So, they earned approximately $725 in July.

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Answer:

21

Step-by-step explanation:

Subtract 7 from both sides to get the answer.

Answer:

[tex]x=\sqrt{13}[/tex]

Step-by-step explanation:

[tex]x^{2} - 6 - 7 = 0 \\x^{2} =13\\x=\sqrt{13}[/tex]

The solution for the system of equations 3x + 6y = 6 and 2x + 2y = 6 is

B) There is one unique solution, (4, -1).

The solutions for a system of equation is the intersecting points between them

We know that system of equations has an infinite number of solutions when they coincide with each other as every point of a line falls into another line.

Systems of equations have a unique solution when they intersect each other and that intersecting point is the solution.

The system of equations has no solution when they are parallel to each other.

So, now we'll graph this system of equations and observe where they lie in XY coordinate.

Observing the graphs of both of these equations we can conclude that they have a unique solution (4,-1).

We can also solve these equations by multiplying equation(ii) by 3 and subtracting it from equation(i) and obtaining the values of (x,y).

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Answer:

24 25 26

Step-by-step explanation:

guess and check..................

Answer is h(x) =[tex]\frac{1}{2}[/tex] cos ([tex]\frac{2}{3}[/tex]π +[tex]\frac{2}{3}[/tex]π ) - [tex]\frac{1}{2}[/tex]

∵The maximum point (- 2π. 3 )

        minimum point (- π / 2 , - 4)

and h(x) = a cos (b x + c)+ d

∴ a + d = 3                                d = - 1/ 2

                                  ⇒  

 -a + d = -4                              a = 7 / 2

{solve the equation}

and   -2πb + c = 0                      b = 2 / 3

                                       ⇒

       - ( π/ 2) b + c =  λ              c = 4 / 3 π

∴ h(x) =[tex]\frac{1}{2}[/tex] cos ([tex]\frac{2}{3}[/tex]π +[tex]\frac{2}{3}[/tex]π) - [tex]\frac{1}{2}[/tex]

Trigonometric functions are also known as Circular Functions can be simply defined as the functions of an angle of a triangle. It means that the relationship between the angles and sides of a triangle are given by these trig functions. The basic trigonometric functions are sine, cosine, tangent, cotangent, secant and cosecant

here detail explanation:

Sine Function

Sine function of an angle is the ratio between the opposite side length to that of the hypotenuse. From the above diagram, the value of sin will be:

Sin a =Opposite/Hypotenuse = CB/CA

Cos Function

Cos of an angle is the ratio of the length of the adjacent side to the length of the hypotenuse. From the above diagram, the cos function will be derived as follows.

Cos a = Adjacent/Hypotenuse = AB/CA

Tan Function

The tangent function is the ratio of the length of the opposite side to that of the adjacent side. It should be noted that the tan can also be represented in terms of sine and cos as their ratio. From the diagram taken above, the tan function will be the following.

Tan a = Opposite/Adjacent = CB/BA

Also, in terms of sine and cos, tan can be represented as:

Tan a = sin a/cos a

Secant, Cosecant and Cotangent Functions

Secant, cosecant (csc) and cotangent are the three additional functions which are derived from the primary functions of sine, cos, and tan. The reciprocal of sine, cos, and tan are cosecant (csc), secant (sec), and cotangent (cot) respectively. The formula of each of these functions are given as:

Sec a = 1/(cos a) =  Hypotenuse/Adjacent = CA/AB

Cosec a = 1/(sin a) = Hypotenuse/Opposite = CA/CB

cot a = 1/(tan a) = Adjacent/Opposite = BA/CB

Note: Inverse trigonometric functions are used to obtain an angle from any of the angle’s trigonometric ratios. Basically, inverses of the sine, cosine, tangent, cotangent, secant, and cosecant functions are represented as arcsine, arccosine, arctangent, arc cotangent, arc secant, and arc cosecant.

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The number of the sheets in a ream of paper is a 500 sheets.

According to the statement

We have to find that the number pf paper sheets in a one ream.

So, For this purpose, we know that the

The standard form of a number is a way of writing the number in a form that follows certain rules.

From the given information:

A standard ream of paper plus another half ream of paper contains 750 sheets of paper.

It means

total number of sheets = 750 sheets

Then

one full ream + half ream = 750 sheets

Let x be a number of sheets

then

x + x/2 = 750

2x+x /2 = 750

3x/2 = 750

3x = 1500

x = 1500/3

x = 500.

So, The number of the sheets in a ream of paper is a 500 sheets.

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She invested $5,000 at 7% and $4,000 at 9%

How much is invested at each rate of return?

The amount invested at 7% can be assumed to be x, such that the amount invested at 9% would be total investment of $9000 minus x, which has been invested at the initial rate of 7%

total interest at 7%=interest rate*amount invested

interest rate=7%

amount invested=x

total interest at 7%=7%*x=0.07x

total interest at 9%=9%*(9000-x)

total interest at 9%=810-0.09x

total interest on both accounts=0.07x+810-0.09x

total interest on both accounts=810-0.02x

total interest earned=$710

710=810-0.02x

0.02x=810-710

0.02x=100

x=100/0.02

x=amount invested in the account which earns 7%=$5,000

amount invested at 9%=$9000-$5000

amount invested at 9%=$4,000

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