Dominic is working two summer jobs, making $10 per hour babysitting and making $6 per hour walking dogs. In a given week, he can work no more than 16 total hours and must earn at least $120. If x represents the number of hours babysitting and y represents the number of hours walking dogs, write and solve a system of inequalities graphically and determine one possible solution.

Answer:

Step-by-step explanation:

b) Figure 1 is 2² = 4 (which is also 2x2=4 or if you count all the squares = 4)

Figure 2 is 3² = 9 (which is also 3x3=9 or if you count all the squares = 9 )

Figure 3 is 4² = 16 (which is also 4x4=16 or if you count all the squares = 16 )

Figure 4 is 5² =25(which is also 5x5=25 or if you count all the squares = 25)

Figure 5 is 6² = 36(which is also 6x6=36 or if you count all the squares =36)

c) Figure 1 add squares in a horizontal row which is your x-coordinate (2)

then add squares in a vertical row which is your y-coordinate (2)

so (x,y) = (2,2). Graph those points. Do the same for each and your line is a diagonal straight line traveling diagonally upward equally.

f) Equation: a² = a x a

Answer: 32 + 18 + 4 + 30 = 8432+30=6262+18=8080+4=84

Step-by-step explanation: i did this question before so i dont know if you can understand it but i got it correct last week

Answer:

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No that is a rational number

There will be 2 people left in the last boat

A group of 408 people are going on a boat tour

The boat hold 7 people each

408/7

= 58.2

Hence 58 boats will be complete with 7 people on each boats and the number of persons in the last boat is 2

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When Olga turns 18, she will have $3032.89 in her account, which earned a monthly compound interest rate of 1.75%.

Compound interest refers to the amount of interest added on the principal amount plus interest. The formula of monthly compound interest is:

B = P(1 + r)^t

where B is the ending balance, P is the principal amount or original balance, r is the monthly interest rate in decimal form, and t is the number of months.

If Olga's uncle invested $2,000 in an account that was locked into a 1.75% interest rate, compounded monthly, using the formula, solve for the ending balance after 2 years.

B = P(1 + r)^t

B = 2000(1+ 0.0175)^24

B = $3032.89

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Answer: 1. linear

2. quadratic

3. linear

4. linear

5. quadratic

6. quadratic

7. linear

Step-by-step explanation:

1. pi and d are constants, so linear.

2. quadratic since (x+3)^2

3. 3^2 is a constant since 3^2=9. x is also a constant, so linear.

4. x is a constant, so linear.

5. Quadratic since the equation's highest degree is 2.

6. Quadratic ==> x(x+3)=x^2+3x

7. 3x and -2 are constants, so linear.

Answer: 2.16

Step-by-step explanation:

87.912 ÷ 40.7=

87.912/40.7=

(81.4+6.512)/40.7=

81.4/40.7 + 6.512/40.7=

2+6.512/40.7=2.16

Answer:

[tex]y=5x-3[/tex]

Step-by-step explanation:

The slope-intercept form of an equation is [tex]y=mx+b[/tex], where [tex]m[/tex] is the slope, and [tex]b[/tex] is the [tex]y[/tex]-intercept.

Distance between the points A and B are equal to distance between points B and C.

So, The given triangle is isosceles.

And, The vertices on a coordinate are plot in figure.

Here,

The vertices of a triangle are A (0, 0), B (2a, b) and C (4a, 0)

We have to check the triangle is isosceles.

And, Plot the vertices on a coordinate grid to model the problem.

What is Isosceles triangle?

When two sides of a triangle are equal then the triangle is said to be isosceles triangle.

Now,

The vertices of a triangle are A (0, 0), B (2a, b) and C (4a, 0)

We have to check the triangle is isosceles.

For this we use distance formula and prove that the two sides of triangle are equal.

Distance between the points A (0, 0) and B (2a, b) is;

[tex]D_{AB} = \sqrt{(2a - 0)^2 + (b-0)^2} = \sqrt{4a^2+b^2}[/tex]

And, Distance between the points B (2a, b) and C (4a, 0) is;

[tex]D_{BC} = \sqrt{(4a - 2a)^2 + (0-b)^2} = \sqrt{4a^2+b^2}[/tex]

Hence, Distance between the points A and B are equal to distance between points B and C.

So, The given triangle is isosceles.

a. The vertices are plot in coordinate grid to model the problem in figure.

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When measuring height, it is necessary to represent both the vertical position and the separation between the minimum and maximum place or location. Rachel is 5 feet 6 inches tall, the tall is her cousin exists 2 feet 9 inches.

In math, tall can be defined as the vertical distance from the top to the base of the object. Tall is the distance between an object's highest and lowest points.

The measurement of an object's height from the base to the top is known as tall. It is sometimes referred to as altitude in geometry. The vertical distance between the lowest and highest point is measured. In coordinate geometry, it is often the measurement along the y-axis of an object.

Rachel/Cousin = Rachel's shadow / Cousin's shadow

5 feet 6/x = 2/1

simplifying the above equation, we get

5ft 6 = 2x

x = 5ft 6/2

x = 66in/2

x = 33 in

x = 2ft 9inch

Therefore, the value of x = 2ft 9inch.

Rachel is 5 feet 6 inches tall, the tall is her cousin exists 2ft 9inch.

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Answer:

x =7

Step-by-step explanation:

hope it helped

Answer:

x=7

Step-by-step explanation:

i just saw that this has been answered but i want to give an explanation incase it is needed:

•3x+4=5x-10

first move the like terms to one side of the = sign. (its best to move the smaller x value to the bigger one.

•4+10=5x-3x

then you just solve the equation on both sides:

• 14=2x

then you have to being the 2 over the = sign so that x is by itself. when you bring a divide value over the = sign it will turn into the opposite operation.

so basically you are dividing 14 by 2

•14/2 = x or 14÷2=x

which finally gives you :

x=7

hope that makes sense...

For the given parabola, we have that:

a) The equation is: f(x) = -16(x - 0.75)² + 18.

b) The function is increasing at a rate of 12 feet per second, while the don't have the final point for the decrease, hence we cannot compute the average rate of change.

The equation of a quadratic function, of vertex (h,k), is given by:

y = a(x - h)² + k

In which a is the leading coefficient.

For this problem, the vertex is at (0.75,18), hence:

h = 0.75, k = 18.

f(x) = a(x - 0.75)² + 18.

When x = 0, y = 9, hence:

9 = 0.5625a + 18

a = -9/0.5625

a = -16.

Hence:

f(x) = -16(x - 0.75)² + 18.

The average rate of change of a function is given by the change in the output divided by the change in the input. Hence, over an interval [a,b], the rate is given as follows:

[tex]r = \frac{f(b) - f(a)}{b - a}[/tex]

It is increasing between x = 0 and x = 0.75, in which f(0) = 9, f(0.75) = 18, hence:

r = 9/0.75 = 12.

The function is increasing at a rate of 12 feet per second, while the don't have the final point for the decrease, hence we cannot compute the average rate of change.

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y = x², y = 4  are  the region enclosed by the given equations is revolved about the y -axis.

What exactly is a closed area?

All space between a floor and ceiling that is enclosed on all sides by solid walls or windows, except doors that stretch from the floor to the ceiling, is referred to as an enclosed area.

What do you mean by the region that a closed curve encloses?

The sum of all infinitely thin rectangles with height f(x), enclosed by the curve y=f(x), and the x-axis between x=a and x=b, is what we mean when we write baf(x)dx.

Whether contained or not?

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The given sequence is geometric, with common ratio = 2.

A geometric progression, sometimes referred to as a geometric sequence in mathematics, is a series of non-zero numbers where each term following the first is obtained by multiplying the preceding one by a constant, non-zero value known as the common ratio.

Given: 10, 20, 40, ...

Here, 20/10 = 40/20 = 2

That is, the given sequence follows the required condition for a sequence to be geometric.

Hence, The given sequence is geometric, with common ratio = 2.

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The median change if the minimum number was removed is a increase by 3. 5 . Option A

Median is simply known as the middle number in a given set of data.

It is also defined as the number separating the greatest number from the least in a given set of data.

Given the data;

54,6,17,49,27,46,18,34

Arrange from least to greatest

6 , 17, 18, 27, 34, 46, 49, 54

The median = 27 + 34/ 2 = 30. 5

Removing the minimum digit which is 6, we have;

17, 18, 27, 34, 46, 49, 54

Median = 34

Find the difference in median= 30. 5 = 34 = -3. 5

Thus, the median change if the minimum number was removed is a increase by 3. 5 . Option A

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Answer: -3

Step-by-step explanation:

bro i was just doing that in math class

If DA = 7.4 centimeters, then the radius of the circle EF is 3.7 inches.

A radius of a circle or sphere is any of the line segments from its center to its perimeter in classical geometry, and in more modern usage, it is also their length. The name is derived from the Latin radius, which means both ray and spoke of a chariot wheel.

The radius of a circle is the distance between the circle's center and any point on its circumference. It is usually represented by the letters 'R' or 'r'. This number is significant in almost all circle-related formulas. A circle's area and circumference are also measured in terms of radius.

Here, DA is a diameter  and EF is the radius.

Radius of a circle = 1/2 diameter

Where, d = 7.4

Radius of a circle, r = 1/2 d

Radius of a circle = 1/2(7.4)

Radius of a circle = 3.7

Therefore, the radius of the circle is 3.7 inches.

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Answer: 2 [tex]\frac{14}{25}[/tex]

Step-by-step explanation:

2.56=

2 + 0.56=

2 + 56/100=

2 + 14/25=2 [tex]\frac{14}{25}[/tex]

The height after the 18th month is 69 cm

The function definition is given as

H(m) = 51 + m

Where m represents the number of months

In this case;

m = 18

So, we have

H(18) = 51 + 18

Evaluate the sum

H(18) = 69

Hence, the height after the 18th month is 69 cm

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The student walked 58.58 meters more than the total displacement from the starting point.

Given that a student walked 100 meters north, then 100 meters west.

We are required to find the number of meters, the student travelled more as compared to the total displacement from the starting point.

We have to find the distance from the starting point to ending point. We have to apply pythagoras theorem to find that distance.

Pythagoras theorem basically says that the square of hypotenuse of right angled triangle is equal to the sum of squares of base and perpendicular.

[tex]H^{2} =P^{2} +B^{2}[/tex]

In our case P is 100 meters and B is 100 meters and we have to find H from the formula given above.

[tex]H^{2} =100^{2} +100^{2}[/tex]

H=[tex]\sqrt{10000+10000}[/tex]

H=[tex]\sqrt{20000}[/tex]

H=141.42 meters

Difference=100+100-141.42

=200-141.42

=58.58 meters

Hence the student walked 58.58 meters more than the total displacement from the starting point.

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   For the given parabola:

 We have the following data.

v = (-4,2)

f = (-4, 2.25)

d  = y = 1.75

We define what a parabola is

 The parabola is a geometric shape that is formed from the intersection of a vertical plane in a cone.

The canonical equation of a parabola is given by

(x - h)² = 4p(y - k)

The parabola is a quadratic function, it is composed of a vertex, or inflection point, a focus and a directrix.

  The parabola equation is:

y = x² + 8x + 18

y - 18  + 16 = x² + 8x + 16

y - 2 = x² + 2(4x) + 4²

y - 2 = (x + 4)²

This means that the vertex of this parabola is

v = (h, k)

v = (-4,2)

f = (-4, 2 + 1/4)

f = (-4, 2.25)

d = y = 2 - 1/4

d  = y = 1.75

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Answer:

48

Step-by-step explanation:

Answer:

Angles U and V and angles T and P

Step-by-step explanation:

The translated and reflected function is:

g(x) = f(-x) - 3 = 3x + 1.

Here we want to transform a function f(x)=  -3x + 4.

First, remember that a vertical translation is written as:

g(x) = f(x) + N

Then a translation of 3 units down is written as:

g(x) = f(x) - 3

Now we want to do a reflection across the y-axis, this just changes the sign of the variable, so we get:

g(x) = f(-x) - 3

Now we replace the actual function f(x) by -3x + 4, we will get:

g(x) = -3*(-x) - 3 + 4 = 3x + 1

g(x) = 3x + 1

We conclude that the transformed function is 3x + 1.

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If you had $150, but you are spending $2 each day, then the algebraic expression model of this situation is 150-2x

Given,

The total amount you had = $150

The amount you spend in each day = $2

Consider the number of days = x

Then the algebraic expression for this situation is 150-2x

Hence, If you had $150, but you are spending $2 each day, then the algebraic expression model of this situation is 150-2x

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Answer/Step-by-step explanation:

2.

5x + 3y = 15

3y = -5x + 15

÷3   ÷3    ÷3

y = (-5/3)x + 5

* = coordinate: (0, 5), (3, 0)

                5  *

                4   -

                3   -

                2   -

                 1   -

-------------------0----|----|----*----|---|------

                 -1  -     1    2   3   4   5

                 -2 -

                 -3 -

                 -4 -

                 -5 -

4.

10x + 8y = -40

8y = -10x - 40

÷8     ÷8    ÷8

y = (-5/4)x - 5

* coordinate: (0, -5), (4, -10)

                5  -

                4   -

                3   -

                2   -

                 1   -

-------------------0----|----|----|----|---|------

                 -1  -     1    2   3   4   5

                 -2 -

                 -3 -

                 -4 -

                 -5 *

                 -6 -

                 -7 -

                 -8 -

                 -9 -

                 -10 -                    *

6.

-3x + 6y = 12

6y = 3x + 12

÷6   ÷6   ÷6

y = (1/2)x + 2

* coordinate: (0, 2), (2, 3)

                5   -

                4   -

                3   -          *

                2   *

                 1   -

-------------------0----|----|----|----|---|------

                 -1  -     1    2   3   4   5

                 -2 -

                 -3 -

                 -4 -

                 -5 -

8. x - y = 5

-y = -x + 5

÷-1   ÷-1  ÷-1

y = x - 5

* coordinate: (0, -5), (1, -4)

                5  -

                4   -

                3   -

                2   -

                 1   -

-------------------0----|----|----|----|---|------

                 -1  -     1    2   3   4   5

                 -2 -

                 -3 -

                 -4 -     *

                 -5 *

I hope this helps!

In the accompanying diagram of ABC, AB ≅ AC,. BD = 1. 3. BA, and CE = 1. 3. CA. Triangle EBC can be proved congruent to triangle.

What do you mean by congruent?

Triangles. Congruent

∆ABC ≅ ∆ DEF.

1. AB ≅ DE

2. BC ≅ EF

3. AC ≅ DF

4. ∠ A ≅ ∠ D

5. ∠ B ≅ ∠ E

6. ∠ C ≅ ∠ F

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