Part A: Maci made $170 grooming dogs one day with her mobile dog grooming business. She charges $60 per appointment and earned $50 in tips. Write an equation to represent this situation. (4 points)


Part B: Logan made a profit of $210. 00 as a mobile groomer. He charged $75. 00 per appointment and received $35. 00 in tips, but also had to pay a rental fee for the truck at $10. 00 per appointment. Write an equation to represent this situation. (4 points)


Part C: Explain how the equations from Part A and Part B differ. (2 points)

Answer:

Step-by-step explanation:

Standard for of quadratic equation:

We have

Sum of the roots

Product of the roots

We have:

The square of the above is:

Substitute known values and solve for c:

Answer:

c = 3.09375

Step-by-step explanation:

Factored form of a quadratic equation

[tex]y=a(x-r_1)(x-r_2)[/tex]

where:

Given quadratic:

[tex]2x^2-5x+c=0[/tex]

Therefore, the leading coefficient is:

[tex]\implies a=2[/tex]

Substitute the value of a into the formula:

[tex]\implies y=2(x-r_1)(x-r_2)[/tex]

Expand:

[tex]\implies y=2x^2-(2r_2+2r_1)x+2r_1r_2[/tex]

Compare the coefficients of x:

[tex]\implies -(2r_2+2r_1)=-5[/tex]

[tex]\implies 2r_2+2r_1=5[/tex]

[tex]\implies r_2+r_1=2.5[/tex]

If the difference between the roots is 0.25 then:

[tex]\implies r_2-r_1=0.25[/tex]

Add the two root equations to eliminate r₁:

[tex]\implies 2r_2=2.75[/tex]

[tex]\implies r_2=1.375[/tex]

Substitute the found value of r₂ into one of the root equations and solve for r₁:

[tex]\implies 1.375-r_1=0.25[/tex]

[tex]\implies r_1=1.375-0.25[/tex]

[tex]\implies r_1=1.125[/tex]

As c = 2r₁r₂ then:

[tex]\implies c=2(1.125)(1.375)[/tex]

[tex]\implies c=3.09375[/tex]

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Answer:

1.028 × 10⁹

= 1028000000

Answer:

alright, lets say danetta's dinner bill is 20 dollars, and she ordered 4 things, so the equation would be x times 5=20, and edwards would be 25 dollars, so that equation would be x times 5=25

Step-by-step explanation:

Answer:

It's D

Step-by-step explanation:

984.25 g

Answer:

SaS

Step-by-step explanation:

Answer:

x = 3.5

Step-by-step explanation:

Each value is multiplied by 1.5 so 7 times 1.5 is 10.5

10.5/3 = 3.5

Answer:

1.5

Step-by-step explanation:

To find the value of x that makes triangle DEF similar to XYZ, we have to find the scale. To do this find 2 similar sides. I chose 7.5 from XYZ and 5 from DEF. Divide 7.5 by 5 to get 1.5. 1.5 is our scale so this means we will insert 1.5 for x and get 4.5 as our answer.

Answer:

l learnt it but I forgotten sorry

The solution of this system of linear equations is x=3, y=-5.

To solve this system of linear equations, you can use various methods such as substitution, elimination, or matrices. Here is one way to solve using the substitution method:

4((11+y)/2) + 8y = 24

3((11+y)/2) + 2y = 15

y = -5

x = (11 + (-5))/2

x = 3

4(3) + 8(-5) = 24

3(3) + 2(-5) = 15

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The question is -

Solving a system of linear equations in two variables,

Answer:

[tex](x+5)^2+(y+8)^2=6217[/tex]

Step-by-step explanation:

Hi there!

Equation of a circle: [tex](x-h)^2+(y-k)^2=r^2[/tex] where the circle is centered at (h,k) and r is the radius

1) Plug the center of the circle into the equation

Center: (-5,-8)

[tex](x-h)^2+(y-k)^2=r^2\\(x-(-5))^2+(y-(-8))^2=r^2\\(x+5)^2+(y+8)^2=r^2[/tex]

2) Determine r²

Plug in the given point (16,68)

[tex](x+5)^2+(y+8)^2=r^2\\(16+5)^2+(68+8)^2=r^2\\(21)^2+(76)^2=r^2\\441+5776=r^2\\6217=r^2[/tex]

Therefore, r² is equal to 6217. Plug this back into [tex](x+5)^2+(y+8)^2=r^2[/tex]:

[tex](x+5)^2+(y+8)^2=6217[/tex]

I hope this helps!

Answer:

Step-by-step explanation:

so since it’s traveling 9mi/m you need to devide 216 by the rate of 9mi/m to find how long it takes.

216/9=24 so it will take 24 minutes!

Answer:1,944 minutes

Step-by-step explanation:

if the question is a plane is traveling 9 miles per minute how much time is needed to travel 216 miles you need it is clear that you are doing a multiplication problem so multiply that and you get 1,944 minutes

your welcome

Option D. is an obtuse scalene triangle in the given lists of diagrams.

In terms of geometry, an obtuse scalene triangle is one in which one of the angles is less than 90 degrees and the other two are less than 180 degrees, with the one angle measuring greater than 90 degrees but less than 180 degrees. Measurement differences exist for each of the three sides and angles.

Both the obtuse triangle and the scalene triangle's characteristics are present in an obtuse scalene triangle. A scalene triangle has all three sides and angles that are of a different size, whereas an obtuse triangle only has one obtuse angle. The following are the characteristics of an obtuse scalene triangle:

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Answer:

62>j

Step-by-step explanation:

mrk me brainliest plz

Answer: 18

Step-by-step explanation:

18*1=18

18*2=36

Answer:

d

Step-by-step explanation:

Answer: 135 boys

Step-by-step explanation:

Multiply 3*45 since you know the number of boys is 3 times more than the number of girls.

Answer:

Step-by-step explanation:

strategy:  Find the area of the entire dartboard, then subtracted the inner circle from that whole.    we will have the entire outer circle,  so divide that by 2 for half of it.   Next divide the inner circle by 4 . Then add that to the outer circle answer from above.

whole circle = [tex]\pi[/tex]*[tex]20^{2}[/tex] = 1257.142857 [tex]cm^{2}[/tex]

inner circle = [tex]\pi[/tex]*[tex]10^{2}[/tex] = 314.2857143 [tex]cm^{2}[/tex]

1257.142857 - 314.2857143 = 942.8571427 outer circle

942.8571427 / 2 = 471.4285 ( half of the outer circle)

now find quarter of the inner circle

314.2857143 / 4 = 78.57142855

add the two parts together

78.57142855 + 471.4285  = 549.9999

The shaded regions = 550 [tex]cm^{2}[/tex]

The Equation of line F is y= -9/2x  + 59/2.

The Equation of line G  is y = 1/10 x .

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx where, m is the slope

Given:

For Line F:

slope = -9 /2

and, Equation of line F as

y - (-2) = -9/2 (x -(7))

y + 2= -9/2( x- 7)

y = -9/2x + 63/2 -2

y= -9/2x  + 59/2

For Line G:

Slope = (0 -(1))/ ( 0-(10))

slope = 1/10

and, Equation of line G as

y - (1) = 1/10 (x -10)

y-1 = 1/10 x - 1

y = 1/10 x

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If Ahmad took 200 mg of medication and the function [tex]f(t) = 200e^{-0.4t}[/tex] can be used to determine the amount of medication, then He will have only 50 mg of medication left in his system after (c) 3.47 hours .

The Function that is used to determine the amount of medication, f(t), still in his system after t hours. is given as [tex]f(t) = 200e^{-0.4t}[/tex] ,

we have to find the after how many hours there will be only 50 mg of medication left ;

we need to substitute f(t) as 50 ;

we get ;

⇒ [tex]50 = 200e^{-0.4t}[/tex] ;

⇒ [tex]\frac{50}{200} =e^{-0.4t}[/tex] ;

⇒ [tex]\frac{1}{4} =e^{-0.4t}[/tex]

On solving further ,

we get ;

⇒ [tex]t=3.4657..[/tex] hours ;

So , t≈ 3.47 hours .

Therefore , After 3.47 hours there will be 50 mg of medication left .

The given question is incomplete , the complete  question is

Ahmad took 200 mg of a medication. The function [tex]f(t) = 200e^{-0.4t}[/tex] can be used to determine the amount of medication, f(t), still in his system after t hours. To the nearest hundredth, after how much time will Ahmad have only 50 mg of medication left in his system ?

(a) 4.37 hours

(b) 7.47 hours

(c) 3.47 hours

(d) 3.74 hours

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Answer:88

Step-by-step explanation:

The required simplified expression as a monomial is given as -12[z⁶].

A polynomial function is a function that applies only integer dominions or only positive integer powers of a value in an equation such as the monomial, binomial and trinomial, etc. ax+b is a polynomial.

here,

Given an expression, the outcome of the multiplicative depression will be an expression of a monomial.
= [4z³][-3z³]
= 4 × 3 [-z ³⁺³]
= -12[z⁶]

Thus, the required simplified expression as a monomial is given as -12[z⁶].

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Meri will need 696 yards of wood to make 12 birdhouses, as each birdhouse requires 58 yards of wood.

Meri is making birdhouses and each birdhouse needs 58 yards of wood. To find out the total length of wood needed for making 12 birdhouses, we can use the formula:

length of wood per birdhouse x number of birdhouses = total length of wood

So, in this case, we can substitute the given values in the formula:

58 yards x 12 birdhouses = 696 yards

This means Meri needs 696 yards of wood to make 12 birdhouses.

This equation works because it uses the concept of the unitary method, where we find the total length of wood by multiplying the number of birdhouses by the length of wood used in each birdhouse, this way we are able to find the total amount of wood needed.

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Answer:

The table represents a function and the slope is -1/2

Step-by-step explanation:

Here, we want to know if the given table is a function

For a relation to be a function, no two y values have same x value

however, 2 x values can have same y value

Looking at the table, we can conclude that what we have is a function

To find the slope, we select any two points and apply the slope formula

m = (y2-y1)/(x2-x1)

(x1,y1) = (6,-2)

(x2,y2) = (-2,2)

m = (2 -(-2))/(-2-6) = 4/-8 = -1/2

Answer:

737

Step-by-step explanation:

Answer:

Step-by-step explanation:

a.we set the first integers is A, because they are consecutive Integer, so the three Integers are A, A+1, A+2

b.we konw (A+2-A)×4-1=A+1, so A=6

therefore, the three Integer are 6, 7, 8.

Essentially, a contingency table with 10 rows and 11 columns has (D) 90 degrees of freedom.

A contingency table is a matrix-form table that shows how often different combinations of variables appear.

It's really popular in survey research, business intelligence, engineering, and scientific research. Basically, a contingency table with 10 rows and 11 columns has 90 degrees of freedom.

They are also sometimes known as two-way frequency tables and are used to show how often different combinations of variables occur.

A contingency table gives you an idea of how two variables relate to each other.

It displays one categorical variable along the rows and another categorical variable along the columns. It can help point out any interactions between them.

Therefore, essentially, a table with 10 rows and 11 columns has (D) 90 degrees of freedom.

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Complete question:

The degrees of freedom for a contingency table with 10 rows and 11 columns are:

A. 100

B. 110

C. 21

D. 90

Negation means negative of something , in logical mathematics negation is an expression opposite to another operation .

Examples of negation are ,

Logical operations are performed to check the trueness of an expression.

These are generally Boolean expressions or algebraic functions.

A negation of a basic assertion is made by  inserting the word "not" into the original statement. The truth value of the negation will always be the inverse of the truth value of the original assertion.

Under negation, what was true becomes false and the vice - versa.

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A variable-containing expression that divides by a variable, contains fractional or negative exponents, or is enclosed in a radical is not a polynomial.

As long as the polynomial is specified over the real numbers, it is possible for it to have negative coefficients, fractional coefficients, or even radical coefficients.

There cannot be a negative exponent in a polynomial. The exponent of a variable in any term of a polynomial must, by definition, be a nonnegative integer, such as 0, 1, 2, 3, 4, etc. The exponents of variables do not contain fractions, decimals, or negative numbers. There cannot be a variable with a fractional exponent in a polynomial.

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Answer: 813,118 people in the city after 24 years

400,000(1+.03)^24