Kara and Lindsey both hike in separate directions from their campsite, with Kara hiking straight to the east and Lindsey hiking straight north. At
2:00 p.m., Kara hiked twice as far to the east as Lindsey hiked to the north. At 2:30 p.m., Kara had covered another mile, while Lindsey had
covered another half of a mile. If x represents Lindsey's distance, in miles, from the campsite at 2:00p.m., what function could be used to
represent the area of the triangular region formed by the girls' locations and the campsite at 2:30 p.m.?

Answer:

False

Step-by-step explanation:

15-0=0

0-15=-15

Answer: base = 20 inches , height = 8 inches

Step-by-step explanation:

The formula fro calculating the area of  a triangle , given the base and the height is given as ;

A = [tex]\frac{1}{2}[/tex]bh

The ratio of its base to the height is given as 5: 2 , this means that

2b = 5h , that is

b = [tex]\frac{5h}{2}[/tex]

Substitute this into the formula for finding area , that is

80 = [tex]\frac{1}{2}[/tex] X [tex]\frac{5h}{2}[/tex] X h

80 = [tex]\frac{5h^{2}}{4}[/tex]

Therefore :

[tex]5h^{2}[/tex] = 80 x 4

[tex]5h^{2}[/tex] = 320

[tex]h^{2}[/tex] = 320 / 5

[tex]5h^{2}[/tex] = 64

h = 8 inches

Substitute h = 8 into b = [tex]\frac{5h}{2}[/tex] , then

b = 20 inches

Therefore , the base of the triangle is 20 inches and the height is 8 inches

Answer:

Step-by-step explanation:

The slope-intercept form of an equation of a line:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept

We have the equation i point-slope form.

Convert to the slope-intercept form:

[tex]y-4=-2(x-5)[/tex]    use the distributive property

[tex]y-4=-2x+(-2)(-5)[/tex]

[tex]y-4=-2x+10[/tex]             add 4 t oboth sides

[tex]y-4+4=-2x+10+4\\\\y=-2x+14[/tex]

Answer:

The equation of the line is [tex]y=-8[/tex]

Step-by-step explanation:

we know that

The equation of the line [tex]y=9[/tex] is a horizontal line (parallel to the x-axis)

The equation of a horizontal line is equal to the y-coordinate of the point that passes through it

In this problem, the line passes through the point (3,-8)

The y-coordinate is -8

therefore

The equation of the line is [tex]y=-8[/tex]

Answer:

Charlie could gather 30 pieces of fruit.

Fetching Information:

As Charlie has gathered apples pears and plums, and the number of apples and plums are 10 partners, and also there are same number of apples and pears.

What to Determine?

How many pieces of fruit could Charlie determine?

Solution:

Let 'a' be the number of apples, 'b' be the number of plums, and 'c' be the number of pears.

As the number of plums and apples is same i.e both are 10 in numbers.

So, a = b = 10

Note that number of pears and apples is also same. So, the the total number of pears will be 10.

So, c = 10

Total number of pieces of fruit = number of apples + number of plums + number of pears

Hence,

            Total number of pieces of fruit = a + b + c

                                                                 = 10 + 10 + 10

                                                                  = 30

Thus, Charlie could gather 30 pieces of fruit.

Keywords: number, total

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Answer:

68

Step-by-step explanation:

P- parentheses

E- exponential

M- multiplication

D- division

A- addition

S- subtraction

2 x 36 = 72

72 - 24 ÷ 6

24 ÷ 6 = 4

72 - 4 = 68

Answer:

68

Step-by-step explanation:

*Remember the order of operations PEMDAS*(Parentheses, Exponents, Multiplication and Division, Addition and Subtraction)

hope it helps:)

Answer:

linear equation in Standard form that can be used to determine how many of each prize Caleb can buy is [tex]1.25x+ 2.50y = 25[/tex]

Step-by-step explanation:

Given:

Total cost spent on prizes for games = $25

Cost of one lip balm = $1.25

Cost of one mini notebook  = $2.50

A) linear equation in STANDARD FORM that can be used to determine how many of each prize she can buy.

Let the number of lip balms be x and the number of mini note books be y. Then

[tex]1.25x+ 2.50y = 25[/tex]

B. Graph the equation using x- and y- intercepts.

Now by trial and error method

[tex]1.25(0)+ 2.50(10) = 25[/tex]

[tex]1.25(2)+ 2.50(9) = 25[/tex]

[tex]1.25(4)+ 2.50(8) = 25[/tex]

[tex]1.25(6)+ 2.50(7) = 25[/tex]

[tex]1.25(8)+ 2.50(6) = 25[/tex]

[tex]1.25(10)+ 2.50(5) = 25[/tex]

[tex]1.25(12)+ 2.50(4) = 25[/tex]

[tex]1.25(14)+ 2.50(3) = 25[/tex]

[tex]1.25(16)+ 2.50(2) = 25[/tex]

[tex]1.25(18)+ 2.50(1) = 25[/tex]

[tex]1.25(20)+ 2.50(0) = 25[/tex]

Thus Caleb can buy 0,2,4,6,8,9,10,12,14,1,6,18,20 lip balms and

0,1,2,3,4,5,6,7,8,9,10 mini note books respectively

Now plotting these value in the graph, we get the below graph

Answer:

I THINK IT IS OB

HOPE IT HELPS!

Answer:

B

Step-by-step explanation:

Answer:

5 guests

Step-by-step explanation:

10 slices per cake

half of that is 5 slices

1 slice = 1 guest

The equation y2=3x+1 is a function.

Determine whether y2=3x+1 is a function

A function is a relation in which each input has exactly one output. To determine if the equation y2=3x+1 is a function, we need to check if each input value of x corresponds to exactly one output value of y.

In this case, the equation represents a quadratic curve, which passes the vertical line test, meaning that it is indeed a function.

For example, when x=1, we can substitute it into the equation as follows: y2 = 3(1) + 1 = 4.

Therefore, for every value of x, there is a unique value of y, indicating that the equation y2=3x+1 is a function.

Answer:

w = d + r²

Step-by-step explanation:

Given

d = w - r² ( isolate w by adding r² to both sides )

d + r² = w

The equation of the line in the point-slope form is y - 15 = [tex]-\frac{3}{2}[/tex] (x - 10)

Step-by-step explanation:

The point-slope form of a linear equation is [tex]y-y_{1}=m(x-x_{1})[/tex] , where

∵ Point A = (10 , 15)

∵ The x-coordinate of the second point is 125% of x-coordinate

  of point A

∴ x-coordinate of second point = [tex]\frac{125}{100}[/tex] × 10

∴ x-coordinate of second point = 12.5

∵ The y-coordinate of the second point is 75% of y-coordinate

  of point A

∴ y-coordinate of second point = [tex]\frac{75}{100}[/tex] × 15

∴ y-coordinate of second point = 11.25

∴ The coordinates of the second point are (12.5 , 11.25)

Let us find the slope of the line by using the rule of it above

∵ [tex](x_{1},y_{1})[/tex] = (10 , 15)

∵ [tex](x_{2},y_{2})[/tex] = (12.5 , 11.25)

∴ [tex]m=\frac{11.25-15}{12.5-10}=\frac{-3.75}{2.5}=-\frac{3}{2}[/tex]

Now we can write the equation

∵ The point-slope form is [tex]y-y_{1}=m(x-x_{1})[/tex]

∵ [tex]m=-\frac{3}{2}[/tex]

∵ [tex](x_{1},y_{1})[/tex] = (10 , 15)

- Substitute these values in the form of the equation

∴ y - 15 = [tex]-\frac{3}{2}[/tex] (x - 10)

The equation of the line in the point-slope form is y - 15 = [tex]-\frac{3}{2}[/tex] (x - 10)

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Answer:

1.  x > 4

2.  m < 2

3.  x > 2

4.  x < -6

Step-by-step explanation:

These 4 inequalities will be solved the same way we solve equations. We take variables to one side and numbers to another and use algebra to solve. Each of them are solved shown below:

1.

[tex]4+6x<x+6x\\4+6x<7x\\4<7x-6x\\4<x[/tex]

so x is greater than 4, we can write (variable first):

x > 4

2.

[tex]m+16>8m+2\\16-2>8m-m\\14>7m\\\frac{14}{7}>m\\2>m[/tex]

so m is less than 2, we can write:

m < 2

3.

[tex]5x-1>13-2x\\5x+2x>13+1\\7x>14\\x>\frac{14}{7}\\x>2[/tex]

so x is greater than 2, we can write:

x > 2

4.

[tex]-3x-2>-x+10\\-2-10>-x+3x\\-12>2x\\\frac{-12}{2}>x\\-6>x[/tex]

so x is less than -6, we can write:

x < -6

Answer:

The first picture is a function while the second one is not.

Step-by-step explanation:

Reason - first picture passed the vertical line test, the other didn't.

Answer:

[tex]\frac{8}{5} x^{2}  - \frac{16}{5} xy + 4x[/tex]

[tex]xy^{2} + \frac{2}{3}y - 8y^{2}z[/tex]

Step-by-step explanation:

We have to simplify the followings:  

1) [tex]- \frac{4}{5}x (- 2x + 4y - 5)[/tex]

= [tex]- \frac{4}{5}x \times (- 2x) +  - \frac{4}{5}x \times (4y) + - \frac{4}{5}x \times (- 5)[/tex]  

{By distributive property of multiplication}

= [tex]\frac{8}{5} x^{2}  - \frac{16}{5} xy + 4x[/tex] (Answer)

2) [tex]2y^{2}( \frac{1}{2} x + \frac{2}{6}y - 4z)[/tex]

= [tex]2y^{2} \times (\frac{1}{2} x) + 2y^{2} \times ( \frac{2}{6}y) - 2y^{2} \times (4z)[/tex]

{By distributive property of multiplication}

= [tex]xy^{2} + \frac{2}{3}y - 8y^{2}z[/tex] (Answer)

Final answer:

The area of a rectangular field that is 400 meters long and 350 meters wide is calculated by multiplying the length and width in meters to get square meters and then converting to square kilometers. The field's area is 0.14 square kilometers.

Explanation:

To calculate the area of a rectangular field, you multiply the length by the width. The area is usually given in square units.

In this case, the field is 400 meters long and 350 meters wide. To find the area in square meters, we do the following calculation:

Area = Length × Width

Area = 400 m × 350 m

Area = 140,000 m2

To convert square meters to square kilometers, you need to remember that 1 square kilometer equals 1,000,000 square meters. Therefore, you divide the area in square meters by 1,000,000 to get the area in square kilometers:

Area in square kilometers = Area in square meters / 1,000,000

Area in square kilometers = 140,000 m2 / 1,000,000

Area in square kilometers = 0.14 km2

The area of the field is 0.14 square kilometers.

To find the area of the rectangular field in square kilometers, the measurements of 400 meters and 350 meters must first be converted to kilometers, resulting in an area of 0.14 square kilometers.

To calculate the area of a rectangular field in square kilometers, we can use the formula for the area of a rectangle which is length × width. First, we need to convert the measurements into the same unit, so we will convert meters to kilometers. We know that 1 kilometer is equivalent to 1000 meters. Therefore, a field that is 400 meters long is 0.4 kilometers long (400 ÷ 1000 = 0.4 km), and a field that is 350 meters wide is 0.35 kilometers wide (350 ÷ 1000 = 0.35 km).

Now, with both measurements in kilometers, we can find the area:

Answer:

Never

Step-by-step explanation:

we know that

A system of linear equations with the same slope and the same y-intercept has infinite solutions (identical lines)

A system of linear equations with the same slope and different y-intercept has no solutions (parallel lines)

A system of linear equations with different slopes and different y-intercept has only one solution  

Answer:19/34

Step-by-step explanation:

Answer: [tex]d)x=4[/tex]

Step-by-step explanation:

[tex]a)x=-1\\b)x=0\\c)x=3\\d)x=4[/tex]

By definition, a relation is a function if and only if each input value has one and only one output value.

It is important to remember that the input values are the values of "x" and the output values are the values of "y".

Observe the graph attached.

You can identify in the graph that the function f(x) and the function g(x) intersect each other at the following point:

[tex](4,3)[/tex]

Where the x-coordinate (input value) is:

[tex]x=4[/tex]

And the y-coordinate (output value) is:

[tex]y=3[/tex]

Therefore, you can conclude that the input value that produces the same output value for the  two functions on the graph, is:

[tex]x=4[/tex]

Sequence by the given rule will be 0, 6, 12, 18, 24, 30, 36.

   Given rule for the sequence to be formed,

        Here, x = 0, 1, 2, 3, 4, 5

To write the sequence, substitute the values of x in the rule given,

1st term → 6 × 0 = 0

2nd term → 6 × 1 = 6

3rd term → 6 × 2 = 12

4th term → 6 × 3 = 18

5th term → 6 × 4 = 24

6th term → 6 × 5 = 30

   Therefore, sequence will be → 0, 6, 12, 18, 24, 30, 36.

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Answer:

[tex]y=-2x-2[/tex]

Step-by-step explanation:

we have

[tex]y=-2x+5[/tex]

This is the equation of a line in slope intercept form

where

[tex]m=-2[/tex] ---> the slope

[tex]b=5[/tex] ----> the y-intercept

we know that

If the given line was shifted down 7 units, then the new y-intercept is equal to

[tex]b=5-7=-2[/tex]

The slope of the new line will be the same that the original line, because are parallel lines

so

The new equation is

[tex]y=-2x-2[/tex]

Answer:

Step-by-step explanation:

-2(-8x - 4y + 3/4) =

16x + 8y - 3/2 ....(-3/2 is the same as - 1 1/2)

errors.....

A. the first term should be positive

B. the second term should be positive

C. the last term should be - 1 1/2

Daniel expanded the expression . The errors made by Daniel are

A. The first term should be positive.

B. The second term should be positive.

C. The last term should be -1 1/2, not -1 1/4.

Given :

Daniel expanded the expression as shown

[tex]-2(-8x-4y+3/4)\\-10x-8y-1 1/4[/tex]

Lets multiply -2 inside the parenthesis and see what happens

[tex]-2(-8x-4y+3/4) \\-2 (-8x)-2(-4y)-2(\frac{3}{4} )[/tex]

we know that negative times negative is positive

Also to simplify the fraction ,we can cancel out 2  and 4

[tex]-2 (-8x)-2(-4y)-2(\frac{3}{4} )\\+16x+8y-\frac{3}{2} \\+16x+8y-1\frac{1}{2} \\[/tex]

So the first and second terms are positive

Also the constant term is -1 1/2

So the errors he make are

A. The first term should be positive.

B. The second term should be positive.

C.The last term should be -1 1/2, not -1 1/4.

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Answer:

required bank balance=$148

Step-by-step explanation:

simple interest=[tex](  \right )P\times R\times  T\left )\div 100[/tex]

where P=principle=$100

           R=rate of interest=4%

           T=time=12 year

simple interest=[tex](  \right )100\times 4\times  12\left )\div 100[/tex]

simple interest=[tex]\frac{4800}{100}[/tex]

simple interest=48

required bank balance=principle+simple interest

required bank balance=$100+$48=$148

required bank balance=$148

Answer:

The coordinates are (5.3)

Step-by-step explanation:

Answer:

d = 1.2 + 2.3t

Step-by-step explanation:

A backpacker parked his car and hiked a distance of 1.2 km on the first day. On the second day, he continued hiking away from his car with an average speed of 2.3 km/hr.

Now, on the second day he started from distance 1.2 km from his car and continues to hike with an average speed of 2.3 km/hr.

Therefore, the distance of the backpacker from his car on the second day is given by  

d = 1.2 + 2.3t

where d is the distance in km and t is the time in hours he hiked. (Answer)

For this case we must find the solution set of the given inequalities:

[tex]-15x + 4 <109[/tex]

We subtract 4 from both sides of the inequality:

[tex]-15x <109-4\\-15x <105[/tex]

We divide between 15 on both sides of the inequality:

[tex]-x <\frac {105} {15}\\-x <7[/tex]

We multiply by -1 on both sides taking into account that the sense of inequality changes:

[tex]x> -7[/tex]

The solution is given by all values of x greater than -7.

[tex]-6x + 70> -2[/tex]

Subtracting 70 from both sides of the inequality:

[tex]-6x> -2-70\\-6x> -72[/tex]

We divide by 6 on both sides of the inequality:

[tex]-x> - \frac {72} {6}\\-x> -12[/tex]

We multiply by -1 on both sides taking into account that the sense of inequality changes:

[tex]x <12[/tex]

Thus, the solution set is given by:

[tex]x> -7\ U\ x <12[/tex]

Therefore the solution is all real numbers.

Answer:

All real numbers.

Answer:

D

Step-by-step explanation:

To determine which ordered pair is a solution.

Substitute the x and y values into the inequalities.

Note that both must be true for the pair to be a solution of the system.

(4, 8)

8 > 2(4) → 8 > 8 ← False

8 > 7 ← True

(0, 0)

0 > 2(0) → 0 > 0 ← False

0 > 7 ← False

(3, 7)

7 > 2(3) → 7 > 6 ← True

7 > 7 ← False

(1, 9)

9 > 2(1) → 9 > 2 ← True

9 > 7 ← True

Thus (1, 9) is a solution to the system of equations. → D

The ordered pair (1,9) is the solution to the system of inequalities.

To determine which ordered pair is a solution to the system of inequalities, we need to check if each pair satisfies both inequalities. Let's check:

A. (4,8): For y > 2x, 8 > 2(4) = 8 > 8, which is false. For y > 7, 8 > 7, which is true. Therefore, (4,8) is NOT a solution to the system.

B. (0,0): For y > 2x, 0 > 2(0) = 0 > 0, which is false. For y > 7, 0 > 7, which is false. Therefore, (0,0) is NOT a solution to the system.

C. (3,7): For y > 2x, 7 > 2(3) = 7 > 6, which is true. For y > 7, 7 > 7, which is false. Therefore, (3,7) is NOT a solution to the system.

D. (1,9): For y > 2x, 9 > 2(1) = 9 > 2, which is true. For y > 7, 9 > 7, which is true. Therefore, (1,9) is a solution to the system.

Thus, the ordered pair (1,9) is the solution to the system of inequalities.

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Answer:

1. 3/5                        c

2. 7                           c

3. 2/5                       b

4. $3.24                   c  

5. -3.2                      b

Step-by-step explanation:

1.

2/5 + 1/5  =    3/5

2.

a negative + a negative = a positive

2+5 = 7

3.

terminating means the decimal ends. When u divide a & c they keep on going but 2/5 ends

4.

divide 16.8 by 5.19 = 3.23 round up so 3.24

5.

multiply the two together to get the answer

Answer:

No.

Explanation:

The term linear function refers to two distinct but related notions. This is just one point.