Mary is twice as old as Jane was when Mary was as old as Jane is now. The sum of their ages is 28. What is the age of each girl?

Answer:

A.  (3,0)

Step-by-step explanation:

When the equations are graphed, the solution is where the two graphs cross.  For the red line and the blue line, the cross at (3,0)

We can check this by substituting x=3 into both equations and seeing if we get y=0

y = -x+3

y = -3+3

y =0

y = x-3

y = 3-3

y=0

In both cases, we got y=0.  

Therefore (3,0) is a solution to both equations and since it solves both equations, it solves the system.

Answer:

The inverse is sqrt(x+9)

Step-by-step explanation:

f(x)=x^2-9

To find the inverse of the function, we interchange x and y and solve for y

y = x^2 -9

x = y^2 -9

Add 9 to each side

x+9 = y^2 -9+9

x+9 = y^2

Take the square root of each side

sqrt(x+9) = sqrt(y^2)

sqrt(x+9) = y

f^-1 (x) = sqrt(x+9)

Answer:

$51.20

Step-by-step explanation:

A 20% discount makes it 80% of the original price.

80% is 0.8 of something so multiply $64 by 0.8 to get your answer of $51.20

Answer:

D: 54 Divided by 6

Step-by-step explanation:

To find out how many 6 pound bags of food we can give away, we take the total amount of food and divide by 6

54/6

Answer: 32 Rose Arrangements & 8 Tulip Arrangements

Step-by-step explanation: The number of arrangements for each flower is unknown (n) but the total is known, 40 arrangements. There are 4 times as many rose arrangements than tulip meaning 4n rose + n tulip = 40, 4n + n = 40, 5n = 40, 40 ÷ 5 = n, n = 8. Roses = 4n = 4x8= 32. Tulips = n = 8.

[tex]\dfrac{3\ boys}{5\ girls}\to\dfrac{3}{5}\\\\\dfrac{8}{10}=\dfrac{8:2}{10:2}=\dfrac{4}{5}\\\\\dfrac{15}{25}=\dfrac{15:5}{20:5}=\dfrac{3}{5}\\\\\dfrac{9}{15}=\dfrac{9:3}{15:3}=\dfrac{3}{5}\\\\\dfrac{30}{50}=\dfrac{30:10}{50:10}=\dfrac{3}{5}\\\\Answer:\\\\\boxed{\dfrac{3\ boys}{5\ girls}=\dfrac{15\ boys}{25\ girls}=\dfrac{9\ boys}{15\ girls}=\dfrac{30\ boys}{50\ girls}}[/tex]

Answer:

BC = 25

Step-by-step explanation:

If the base angles are equal, then the sides opposite them are as well.

But that's not what you are asked for. You want the value of 2x + 7

Every two triangles are similar. Therefore the sides of triangles are in proportion.

We have the equations:

1.

[tex]\dfrac{3}{5}=\dfrac{3+x}{20}[/tex]    cross multiply

[tex]5(3+x)=(3)(20)[/tex]      divide both sides by 5

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

[tex]3+x=12[/tex]      subtract 3 from both sides

[tex]\boxed{x=9}[/tex]

--------------------------------------

2.

[tex]\dfrac{3}{4}=\dfrac{9}{y}[/tex]      cross multiply

[tex]3y=(4)(9)[/tex]

[tex]3y=36[/tex]      divide both sides by 3

[tex]\boxed{y=12}[/tex]

------------------------------------------

3.

[tex]\dfrac{3}{5}=\dfrac{3+9+u}{60}[/tex]

[tex]\dfrac{3}{5}=\dfrac{12+u}{60}[/tex]    cross multiply

[tex]5(12+u)=(3)(60)[/tex]      divide both sides by 5

[tex]12+u=(3)(12)[/tex]

[tex]12+u=36[/tex]      subtract 12 from both sides

[tex]\boxed{u=24}[/tex]

----------------------------------------------

4.

[tex]\dfrac{3}{4}=\dfrac{24}{v}[/tex]              cross multiply

[tex]3v=(4)(24)[/tex]

[tex]3v=96[/tex]      divide both sides by 3

[tex]\boxed{v=32}[/tex]

Equation for a

a= b/c - 1

Equation for b

b= ca - a

Equation for c

c=  b/a + 1

[tex]\bf \qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]

[tex]\bf \begin{array}{|cc|ll} \cline{1-2} x&y\\ \cline{1-2} \stackrel{-3\cdot 2}{-6}&2\\ \stackrel{-3\cdot 3}{-9}&3\\ \stackrel{-3\cdot 5}{-15}&5\\ \cline{1-2} \end{array}~\hspace{5em}\textit{we know that } \begin{cases} y=3\\ x=-9 \end{cases}\implies 3=k(-9) \\\\\\ \cfrac{3}{-9}=k\implies -\cfrac{1}{3}=k\qquad therefore\qquad \blacktriangleright y=-\cfrac{1}{3}x \blacktriangleleft[/tex]

as you can see above, we can see that "x" can be a product of whatever "y" happens to be, so we know each variable is just a factor away from the other.

Answer:

Direct variation; k = -3; y = -3x  

Step-by-step explanation:

The formula for direct variation is

y = kx     Divide both sides by x

k = y/x

For x = -6, y = 2:

k = -6/2

k = -3

=====

For x = -9, y = 3:

k = -9/3

k = -3

=====

For x = -15, y = 5:

k = -15/5

k = -3

y = -3x

y and x are always in the same ratio, so y varies directly with x.

Answer:

y = [tex]\frac{3}{2}[/tex] x + 3

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c (m is the slope and c the y-intercept )

to calculate m use the gradient formula

y = (y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (- 2, 0) and (x₂, y₂ ) = (0, 3)

m = [tex]\frac{3-0}{0+2}[/tex] = [tex]\frac{3}{2}[/tex]

the line crosses the y-axis at (0, 3) ⇒ c = 3

y = [tex]\frac{3}{2}[/tex] x + 3

Answer:

D. 14 small bottles and 5 large bottles

Step-by-step explanation:

Answer:

Answer is 17.088 seconds

Step-by-step explanation:

We have given,

Speed of helicopter while going down = 10.5feet/sec

Time taken to travel down = 100 sec

Distance covered while going down = speed * time

Distance covered while going down  = 10.5 * 100

Distance covered while going down  = 1050 feet

Now,

Speed of helicopter while going up = 5.2feet/sec

time taken to travel up = 150 sec

Distance covered while going up = 5.2 * 150 =  780 feet

After this 250 second period , the position of helicopter will be:

Position of helicopter = distance covered in downward - distance covered upward

Position of helicopter = 1050 - 780 = 270 feet

That means we need to travel upward a distance of 270 feet at a maximum speed of 15.8feet/sec to reach sea level.

Time taken to reach sea level = distance/ speed = 270/15.8 = 17.088 sec

Hence time taken to reach at sea level with maximum speed is 17.088 seconds.

The minute hand has turned 450 degrees and 1.25 of a full turn.

To find the angle the minute hand has turned, we need to find the elapsed time in minutes and convert it to degrees. Since Brent started his homework at 4:00 pm, we need to determine the elapsed time from 4:00 pm to the completion time. Let's say he completed his homework at 5:15 pm, which means 1 hour and 15 minutes have passed. There are 60 minutes in an hour, so the total elapsed time is 60 minutes + 15 minutes = 75 minutes.

To convert minutes to degrees, we need to know that the minute hand completes a full revolution (360 degrees) in 60 minutes. Therefore, we can set up a proportion: 75 minutes is to x degrees as 60 minutes is to 360 degrees. Solving for x, we get:

x = (75 minutes * 360 degrees) / 60 minutes = 450 degrees

So, the minute hand has turned 450 degrees.

As a fraction of a full turn, we can divide the angle turned in degrees (450 degrees) by 360 degrees (a full turn), giving us:

450 degrees / 360 degrees = 1.25

Therefore, the minute hand has turned 1.25 of a full turn.

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We need the time Brent completed his homework to calculate the angle turned by the minute hand and express it as a fraction of a full turn.

To determine the angle turned by the minute hand and express it as a fraction of a full turn, we need to know the time taken to complete the homework. Without that information, we cannot calculate the angle and fraction accurately. Please provide the time Brent completed his homework so we can calculate the desired values.

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Answer:

its 4 2/25 :P

Step-by-step explanation:

hi!!!

Answer: 13

Step-by-step explanation:

3X5=15, (0+2)=2, -4

15+2-4=13

Answer:

M = (a/2, 0) and N = (0, b/2)

Step-by-step explanation:

The x coordinate of the M = midpoint of AB = a/2. y coordinate = 0.

Coordinates of M are (a/2, 0)

The y coordinate of the N  = midpoint of AC = b/2. x coordinate = 0.

Coordinates of N are (0, b/2))

The question concerns Geometry, a branch of mathematics focused on points, lines, surfaces, and solids. Students should learn foundational concepts like the Pythagorean theorem and properties of shapes to succeed. Detailed, practice-oriented help can be provided for specific problems.

The subject of the question relates to Geometry, which is a branch of mathematics concerned with the properties and relations of points, lines, surfaces, and solids. Geometry can be a challenging subject, but by breaking down problems into smaller parts and understanding the fundamental concepts, you can solve complex problems more easily.

For example, when learning about triangles, you will need to understand concepts such as the Pythagorean theorem, which deals with the relationship between the lengths of the sides of a right triangle. In Geometry, you will also encounter various shapes and figures, learn to calculate areas and volumes, and understand theorems that describe the properties of these shapes. It's essential to grasp these foundational ideas to advance in the subject.

If you have a specific Geometry problem or concept that you are struggling with, feel free to ask for detailed help. Remember, practice is key to mastering Geometry, so keep working through problems and utilize resources that can aid your understanding.

Final answer:

We find that there are 6 rows in the array.

Explanation:

To solve the student's question, we need to find the number of rows in an array made with 24 tiles, where the number of rows is 2 more than the number of tiles in each row.

Let's denote the number of tiles in each row as x, and the number of rows as y.

According to the problem statement, y = x + 2.

Also, the total number of tiles in the array is the product of the number of rows and the number of tiles per row, hence 24 = x * y.

Substituting the expression for y from the first equation into the second equation, we have

24 = x * (x + 2).

To find the value of x, we need to solve this quadratic equation. Starting with simplification, we get

x^2 + 2x - 24 = 0.

This factors to (x + 6)(x - 4) = 0, so x could be -6 or 4.

Since the number of tiles in a row can't be negative, we disregard -6, leaving us with x = 4.

Hence, y = 4 + 2 = 6 rows.

Answer:

Volume = 7.66* side^3

side^3 = Volume / 7.66

side^3 = 30 / 7.66

side^3 = 3.9164490862

side = 1.5762707925

side = 1.58 feet (rounded)

Step-by-step explanation:

1.38 feet rounded to the nearest hundredth is correct actually :)

A secant is a line that intersects a circle at two points.

Therefore your answer is

[tex]\boxed{D.\ \overline{AD}}[/tex]

OB - radius

DE - tangent

FC - chord

AB - some segment

Answer:

The standard deviation of the numbers is 16.154.

Step-by-step explanation:

The given observations are

77,45,72,56,98,60,70,89,50,80,95,70,34,77,65,70,70,82,86,86

Average or mean of the data is

[tex]\bar{X}=\frac{\text{Sum of observations}}{\text{Total number of observations}}[/tex]

[tex]\bar{X}=\frac{1432}{20}=71.6[/tex]

The Standard deviation of the data is

[tex]\sigma=\sqrt{\frac{\sum (X-\bar{X})^2}{n}}[/tex]

[tex]\sigma=\sqrt{\frac{5218.8}{20}}[/tex]

[tex]\sigma=\sqrt{260.94}[/tex]

[tex]\sigma=\sqrt{16.154}[/tex]

Therefore standard deviation of the numbers is 16.154.

Answer:

Step-by-step explanation:

1 mph = 1.6 kph

30 ÷ 1.6 = 18.75 mph

18.75 mph x 4 hours = 75 miles

The speed of the cyclist is 18.75 miles per hour and he will travel 75 miles in 4 hours.

To convert the speed from kilometers per hour to miles per hour, we divide the speed in kilometers per hour by 1.6 (since 1 mile is equal to 1.6 kilometers). So, the speed of the cyclist in miles per hour is 30 / 1.6 = 18.75 miles per hour. Cyclist rides at this speed.

To find out how many miles the cyclist will ride in 4 hours, we multiply the speed in miles per hour by the number of hours. So, in 4 hours, the cyclist will travel 18.75 * 4 = 75 miles.

Remember, these answers are precise as we did not round them.

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Hi there! :)

Answer:

The answer is D. 83°

Step-by-step explanation:

You should know that the interior angles of a triangle always add up to 180°.

So, what you will need to do, is add all 3 angles together and create an equation (equal to 180). Then you need to solve this equation by isolating "x":

(8x + 12) + (55 - 3x) + (10x + 23) = 180

Get rid of all the parentheses

8x + 12 + 55 - 3x + 10x + 23 = 180

Add all similar terms together

8x - 3x + 10x = 15x

12 + 55 + 23 = 90

15x + 90 = 180

Subtract "90" from each side of the equation → 180 - 90 = 90

15x = 90

Divide each side of the equation by "15" → 90 ÷ 15 = 6

x = 6

Since you now know that the value of "x" is 6, you can now find the measure of the angle at George's position by replacing the "x" by 6:

10x + 23 = Measure of the angle at George's position

10(6) + 23

Multiply 10 by 6 → 10 × 6 = 60

60 + 23

Add 60 and 23 together → 60 + 23 = 83

83 = Measure of the angle at George's position

There you go! I really hope this helped, if there's anything just let me know! :)

Answer:

B. area = x^2 + 2xy + y^2

Step-by-step explanation:

Area of square with side s is s^2.

This square has side x + y, so

area = (x + y)^2

area = (x + y)(x + y)

area = x^2 + xy + xy + y^2

area = x^2 + 2xy + y^2

Answer:

B

Step-by-step explanation:

area of a square = s² ( s is the side length )

here s = x + y, hence

area = (x + y)² ← expand using FOIL )

        = x² + xy + xy + y² = x² + 2xy + y² → B

Answer:

18 number of glasses of lemonade can she pour

Step-by-step explanation:

Unit rate defined as rates are expressed as a quantity of 1, such as 3 feet per second or 8 miles per hour, they are called unit rates.

As per the statement: Rita has 3/4 gallon of lemonade she pours 1/24 gallon of lemonade into each glass.

Number of lemonade Rita has  = 3/4 gallon

[tex]\text{Unit rate per glass} = \frac{1}{24} \text{gallons}[/tex]

By definition of unit rate;

[tex]\text{Number of glasses} = \frac{\text{Number of lemonade}}{\text{Unit rate per glass}}[/tex]

Substitute the given values we get;

[tex]\text{Number of glasses} = \frac{\frac{3}{4}}{\frac{1}{24}}[/tex]

[tex]\text{Number of glasses} = \frac{3}{4} \times 24 = 3 \times 6 = 18[/tex]

Therefore, number of glasses of lemonade can she pour is, 18

Answer:

C) BA=4 cm  

D)the perimeter of triangle ABC= 12 cm

Step-by-step explanation:

Answer:

234

Step-by-step explanatio:acabo  de  

a

Answer: D He has 255.17 more in debts than in credits

Step-by-step explanation:

Finished A P E X